ELECTRONIC STRUCTURE OF IONIZED NON …iopenshell.usc.edu/people/thesis-golubeva.pdfProf. Anna...

ELECTRONIC STRUCTURE OF IONIZED NON-COVALENT DIMERS:

METHODS DEVELOPMENT AND APPLICATIONS

by

Anna A. Golubeva

A Dissertation Presented to theFACULTY OF THE GRADUATE SCHOOL

UNIVERSITY OF SOUTHERN CALIFORNIAIn Partial Fulfillment of the

Requirements for the DegreeDOCTOR OF PHILOSOPHY

(CHEMISTRY)

May 2010

Copyright 2010 Anna A. Golubeva

Acknowledgements

I would like to mention the following people to whom I owe a great debt of gratitude.

Prof. Anna Krylov, my advisor, has contributed greatly to my development as a

researcher - curious, motivated and thinking - in the past four years. As a person truly

inspired by science, she is a perpetuum mobile of the group, never letting the research to

stop. Her motivation and enthusiasm are quite contagious. What is even more important,

however, is that Anna Krylov is a great person to work with - fair, understanding, open-

minded, patient and with a sense of humor. Not every scientist is gifted with such a

personality, but she has it all – and I’m very happy to be a part of her group.

While in graduate school, I was lucky to have some outstanding teachers. I truly

enjoyed the fun and engaging lectures on Statistical Mechanics by Prof. Chi Mak. His

class was the place where I first found out that one can model the stock market with

statistics. Prof. Wlodek Proskurowski’s class on Numerical Analysis at the Department

of Mathematics significantly broadened my knowledge of linear algebra and program-

ming. Now I know exactly how the Hamiltonian is diagonalized, and that Householder

matrix has little to do with running a household. I would also like to acknowledge

Dr. Michael Quinlan. With him as the undergraduate lab director, TAing never seemed

boring.

ii

My scientific work was greatly influenced by Prof. Alexander Nemukhin - my

advisor at the Moscow State University (MSU). His lectures on Quantum Mechanics

is where I first got interested in the subject of Computational Chemistry.

Many thanks go to Evgeny Epifanovsky, Vadim Mozhayskiy, Dr. Vitalii Vanovschi,

Dr. Kadir Diri, Dr. Lukasz Koziol and Dr. Kseniya Bravaya, as well as all other former

and present Electronic Structure group members.

Finally, I do believe that behind all my achievements, there is always my Family.

My husband, Anton Zadorozhnyy, made sure I never felt left alone with the difficul-

ties. He provided me with support and advice whenever I was close to collapsing. My

father, Alexey Golubev, a theoretical chemist himself, advised me to join the special-

ized computational chemistry group at MSU when I was only 17 years old. Back then

I believed that all computational chemists do is about calculating how much grams of

A is needed in order to get that much grams of B. My mother, Valentina Golubeva, an

analytical chemist, was the first to show me the pH paper and to teach me how to grow

a crystal. These experiments resulted in major excitement of me as a 10-year old girl

and, perhaps, that was why I decided to become a chemist. My sisters, Vera and Alena,

are always there for me to cheer me up. My grandparents - Galina Golubeva, Viktor

Golubev, Lubov Vinogradova and Nikolay Vinogradov - always believed in me and sup-

ported me. They also always welcomed all curious child questions from me like “Can

we see atoms using a microscope?”, providing the grounds for me becoming a scientist.

iii

Table of Contents

Acknowledgements ii

List of Figures vii

List of Tables xii

Abstract xvi

1 Ionized non-covalent dimers: Fascinating and challenging 11.1 Non-covalent interactions . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Ionized non-covalent dimers as model charge-transfer systems . . . . . 21.3 Methodological challenges . . . . . . . . . . . . . . . . . . . . . . . . 41.4 Equation-of-motion coupled-cluster family of methods . . . . . . . . . 61.5 Bonding in ionized non-covalent dimers: The qualitative Dimer Molec-

ular Orbitals and Linear Combinations of Atomic Orbitals framework . 81.6 Reference list . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2 Configuration interaction approximation of equation-of-motion method forionization potentials: A benchmark study 162.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.2 The IP-CISD method . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.3 Computational details . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.4 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.4.1 Equilibrium geometries and electronically excited states of theuracil cation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.4.2 Equilibrium geometries of the three isomers of the benzene dimercation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.4.3 Water dimer cation . . . . . . . . . . . . . . . . . . . . . . . . 272.4.4 Timings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292.6 Reference list . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

iv

3 The electronic structure, ionized states and properties of the uracil dimers 363.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.2 Computational details . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.3.1 Prerequisites: Electronic states and spectrum of the uracil cation 383.3.2 Electronic structure of the uracil dimers . . . . . . . . . . . . . 403.3.3 Vertical ionization energies of the monomer and the dimers . . . 423.3.4 The electronic spectra of dimer cations . . . . . . . . . . . . . 48


4 Ionization-induced structural changes in uracil dimers and their spectro-scopic signatures 574.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574.2 Computational detais . . . . . . . . . . . . . . . . . . . . . . . . . . . 574.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.3.1 Molecular orbital framework . . . . . . . . . . . . . . . . . . . 604.3.2 Ionization-induced structural changes: Equilibrium geometries

of the uracil dimer cations . . . . . . . . . . . . . . . . . . . . 634.3.3 Binding energies of the neutral and ionized uracil dimers: Poten-

tial and free energy calculations . . . . . . . . . . . . . . . . . 704.3.4 The electronic spectra of the uracil dimer cations . . . . . . . . 74


5 Ionized states of dimethylated uracil dimers 865.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 865.2 Computational details . . . . . . . . . . . . . . . . . . . . . . . . . . . 865.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 88

5.3.1 Potential energy surface of the neutral dimers: Structures andenergetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

5.3.2 The effect of methylation on the ionized states of the monomerand the dimers . . . . . . . . . . . . . . . . . . . . . . . . . . 92

5.3.3 Ionization-induced changes in the monomer and the dimers: Struc-tures and properties . . . . . . . . . . . . . . . . . . . . . . . . 96


6 Ionized non-covalent dimers: Outlook and future research directions 1136.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1136.2 Conical intersections in ionized non-covalent dimers: Benzene dimer

cation revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

v

6.3 The effect of substituents in ionized non-covalent dimers: Electronicstructure and properties . . . . . . . . . . . . . . . . . . . . . . . . . . 122

6.4 Reference list . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

Bibliography 129. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

A EOM-IP optimized geometries of Bz+2 139X-displaced isomer (XD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139Y-displaced isomer (YD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140T-shaped isomer (TS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141Strongly x-displaced isomer (XSD) . . . . . . . . . . . . . . . . . . . . . . . 142Strongly y-displaced isomer (YSD) . . . . . . . . . . . . . . . . . . . . . . . 143Fused isomer (FD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

vi

List of Figures

1.1 The DMO-LCFMO description of the two lowest ionized states in theuracil dimer. In-phase and out-of-phase overlap between the FMOsresults in the bonding (lower) and antibonding (upper) dimer’s MOs.Changes in the MO energies, and, consequently, IEs, are demonstratedby the Hartree-Fock orbital energies (hartrees). Ionization from the anti-bonding orbital changes the bonding from non-covalent to covalent, andenables a new type of electronic transitions, which are unique to theionized dimers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.1 Definitions of the geometric parameters for uracil (upper panel) andwater dimer (lower panel) at the proton-transferred geometry. . . . . . 20

2.2 Definitions of the geometric parameters for three isomers of the benzenedimer:x-displaced (top),y-displaced (middle), and t-shaped (bottom). 21

2.3 Selected bondlengths in the five lowest electronic states of the uracilcation. The corresponding values of the neutral are shown by dashedlines. The MOs from which electron is removed are shown for eachstate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.4 The CNC(2) angle in the five lowest electronic states of uracil cation.Dashed line shows the corresponding value at the geometry of neutral. . 33

2.5 The CC bond lengths of the three benzene dimer cation isomers in theground electronic state optimized with IP-CISD/6-31(+)G(d) and IP-CCSD/6-31(+)G(d). Only the values of the symmetry unique param-eters for corresponding symmetry non-equivalent fragments are shown

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.6 Selected bondlengths and angles in the two lowest electronic states ofthe water dimer cation optimized with IP-CISD and IP-CCSD with dif-ferent bases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

vii

3.1 π-stacking and hydrogen-bonding in DNA (top) and the geometries ofthe stacked (a) and hydrogen-bonded (b) uracil dimers. . . . . . . . . . 37

3.2 Electronic spectrum and relvant MOs of the uracil cation at the geometryof the neutral. The MO hosting the hole in the ground state of the cationis also shown (top left). Dashed lines show the transitions with zerooscillator strength. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.3 MOs and IEs (eV) of the ten lowest ionized states of the stacked uracildimer. Ionization from the highest MO yields ground electronic stateof the dimer cation, and ionizations from the lower orbitals result inelectronically excited states. . . . . . . . . . . . . . . . . . . . . . . . 41

3.4 MOs and IEs (eV) of the ten lowest ionized states of the hydrogen-bonded uracil dimer. Ionization from the highest MO yields groundelectronic state of the dimer cation, and ionizations from the lower orbitalsresult in electronically excited states. . . . . . . . . . . . . . . . . . . 42

3.5 Basis set dependence of the five lowest IEs of uracil. The shaded areasrepresent the range of the expertimental values. . . . . . . . . . . . . . 44

3.6 Vertical electronic spectrum of the stacked uracil dimer cation at thegeometry of the neutral. Dashed lines show the transitions with zerooscillator strength. MOs hosting the unpaired electron in final electronicstate, as well as their symmetries, are shown for each transition. The MOcorresponding to the initial (ground) state of the cation is shown in themiddle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.7 Vertical electronic spectra of the stacked uracil dimer cation at twodifferent geometries: the geometry of the neutral (bold lines) and therelaxed cation geometry (dashed lines). MOs hosting the unpaired elec-tron in final electronic state are shown for each transition. . . . . . . . 52

3.8 Vertical electronic spectrum of the hydrogen-bonded uracil dimer cationat the geometry of the neutral. Dashed lines show the transitions withzero oscillator strength. MOs hosting the unpaired electron in finalelectronic state, as well as their symmetries, are shown for each tran-sition. The MO corresponding to the initial (ground) state of the cationis shown in the middle. . . . . . . . . . . . . . . . . . . . . . . . . . . 54

4.1 The ten lowest ionized states of the t-shaped uracil dimer at the neutralgeometry calculated with the IP-CCSD/6-311(+)G(d,p). . . . . . . . . 62

viii

4.2 The geometries of the cations versus the respective neutrals for the threeuracil dimer isomers . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

4.3 The definitions of the intra- and inter-fragment geometric parameters foruracil dimer isomers. . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

4.4 Two highest occupied MOs of the three isomers of the uracil dimer atthe neutral and cation geometry. . . . . . . . . . . . . . . . . . . . . . 68

4.5 The binding energies (kcal/mol) of the three isomers of neutral uracildimer calculated at two levels of theory: IP-CCSD/6-311(+)G(d,p) (bold)andωB97X-D/6-311(+)G(d,p) (italic). . . . . . . . . . . . . . . . . . 71

4.6 The binding energies (kcal/mol) of the three isomers of uracil dimercation calculated at two levels of theory: IP-CCSD/6-311(+)G(d,p) (bold)andωB97X-D/6-311(+)G(d,p) (italic). For the proton-transfered h-bondeduracil dimer cation, the binding energies corresponding to the two dis-sociation limits are presented. . . . . . . . . . . . . . . . . . . . . . . 72

4.7 The electronic spectra (top panel) of the stacked uracil dimer cation atthe neutral (solid black) and the cation (dashed blue) geometries calcu-lated with IP-CCSD/6-31(+)G(d) and the electronic states correspond-ing to the three most intense transitions (bottom panel). . . . . . . . . . 76

4.8 The electronic spectra (top panel) of the h-bonded uracil dimer cationat the neutral (solid black), symmetric transition state (dashed blue) andthe proton-transferred cation (dash-dotted pink) geometries calculatedwith IP-CCSD/6-31(+)G(d) and the electronic states corresponding tothe three most intense transitions (bottom panel). . . . . . . . . . . . . 78

4.9 The electronic spectra (top panel) of the t-shaped uracil dimer cation atthe neutral (solid black) and the cation (dashed blue) geometries calcu-lated with IP-CCSD/6-31(+)G(d) and the electronic states correspond-ing to the three most intense transitions (bottom panel). . . . . . . . . . 81

5.1 Five isomers of the stacked neutral 1,3-dimethyluracil dimer and theirbinding energies (kcal/mol). The energy spacings (kcal/mol) betweenthe lowest-energy structure and other isomers are given in the paren-thesis. All values were obtained withωB97X-D/6-311(+,+)G(2d,2p)except for theDe value of isomer 1 shown in bold, which is the IP-CCSD/6-31(+)G(d) estimate. . . . . . . . . . . . . . . . . . . . . . . 89

ix

5.2 The five lowest ionized states and the molecular orbitals of dimethylu-racil (top) and uracil (bottom) calculated by IP-CCSD/6-311(+)G(d,p).

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

5.3 The ten lowest ionized states and the corresponding MOs of the lowest-energy isomer of the neutral stacked 1,3-dimethyluracil computed withIP-CCSD/6-31(+)G(d). . . . . . . . . . . . . . . . . . . . . . . . . . . 95

5.4 Five low-lying isomers of the 1,3-dimethyluracil dimer cation and thedissociation energies (kcal/mol). The energy spacings (kcal/mol) betweenthe lowest-energy structure and other isomers are given in the paren-thesis. All values were obtained withωB97X-D/6-311(+,+)G(2d,2p)except for theDe value of isomer 1 (shown in bold), which is the IP-CCSD/6-31(+)G(d) estimate. . . . . . . . . . . . . . . . . . . . . . . 97

5.5 The ionization-induced changes in geometry, binding energies (kcal/mol)and the MOs of isomer 1 of the stacked 1,3-dimethyluracil dimer. TheωB97X-D/6-311(+,+)G(2d,2p) optimized structures, dissociation ener-gies and the HF/6-31(+)G(d) MOs are presented. . . . . . . . . . . . . 99




5.9 The changes in geometry, binding energies (kcal/mol) and the MOs ofisomer 5 of the stacked 1,3-dimethyluracil dimer at ionization. TheωB97X-D/6-311(+,+)G(2d,2p) optimized structures, dissociation ener-gies and the HF/6-31(+)G(d) MOs are presented. . . . . . . . . . . . . 103

5.10 The electronic spectra of 1,3-dimethyluracil (left) and uracil (right) atthe vertical (solid black) and the relaxed (dashed blue) geometries cal-culated by IP-CCSD/6-31(+)G(d). . . . . . . . . . . . . . . . . . . . . 104

x

5.11 The three most intense transitions in the electronic spectrum of the low-est isomer of stacked 1,3-dimethyluracil cation at vertical (solid black)and cation (dashed blue) geometries. The DMOs corresponding to theground state (framed) and excited states (regular) are shown. The posi-tions of the peaks were calculated at IP-CCSD/6-31(+)G(d) level, whilethe intensities are from the non-methylated dimer calculations. . . . . . 107

6.1 The six optimized geometries of the benzene dimer cation and the corre-sponding energy gaps calculated at the IP-CCSD(dT)/6-31(+)G(d) (italic)and IP-CCSD/6-311(+,+)G(d,p) (bold) levels of theory. . . . . . . . . . 115

6.2 The definitions of structural parameters for the benzene dimer cation.The distance between the centers of mass of the fragmentsdCOM , sepa-rationh and sliding coordinates∆ are shown. . . . . . . . . . . . . . . 116

6.3 The evolution of the four lowest electronic states of the benzene dimercation along thex- (top panel) andy- (bottom panel) displecement coor-dinates calculated with IP-CCSD/6-31(+)G(d). Two moderately (XD,YD) and two strongly-displaced (XSD, YSD) fully-optimized ground-state structures were employed. The blue arrows depict the CR tran-sitions at four geometries and the dashed lines interconnect the relatedelectronic states. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

xi

List of Tables

2.1 The IP-CCSD bondlengths (A) in the five electronic states of the uracilcation and absolute errors (in parenthesis) of IP-CISD relative to IP-CCSD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.2 The IP-CCSD angles (degrees) in the five electronic states of the uracilcation and absolute errors (in parenthesis) of IP-CISD relative to IP-CCSD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.3 IP-CCSD and IP-CISD permanent dipole moments (a.u.) of the fivelowest electronic states of the uracil cation computed at the respectiveoptimized geometries relative to the center of mass. . . . . . . . . . . . 24

2.4 The IP-CCSD and IP-CISD excitation energies (eV) and transition dipolemoments (a.u.) of the uracil cation at the equilibrium geometries of theneutral and the cation. . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.5 The bondlengths (A), angles (degrees), interfragment distances and slid-ing displacements (A) in the ground state of thex-displaced,y-displacedand t-shaped benzene dimer cations calculated with IP-CISD/6-31(+)G(d).For thex- andy-displaced structures, geometric parameters for only oneof the benzene fragments are provided (the fragments are equivalent bysymmetry). Absolute errors of IP-CISD relative to IP-CCSD are pre-sented in parenthesis. Average absolute errors are calculated using thedata for symmetry unique parameters. . . . . . . . . . . . . . . . . . . 26

2.6 The IP-CCSD bondlengths (A) and angles (degrees) in the two elec-tronic states of the water dimer cation and absolute errors (in parenthe-sis) of IP-CISD relative to IP-CCSD calculated with different bases. . . 28

3.1 Five lowest verical IEs (eV) of the uracil monomer calculated withEOM-IP-CCSD. The number of basis functions (b.f.) is given for eachbasis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

xii

3.2 Excitation energies, transition dipole moments and oscillator strengthsof the electronic transitions in the uracil cation calculated with EOM-IP-CCSD with different bases. . . . . . . . . . . . . . . . . . . . . . . 45

3.3 Ten lowest vertical IEs (eV) of the stacked uracil dimer calculated withEOM-IP-CCSD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

3.4 Ten lowest verical IEs (eV) of the hydrogen-bonded uracil dimer calcu-lated with EOM-IP-CCSD. . . . . . . . . . . . . . . . . . . . . . . . . 47

3.5 Ten lowest verical IEs (eV) of the stacked dimer calculated with EOM-IP-CCSD/6-311(+)G(d,p) versus the energy-additivity scheme resultsestimated using 6-31(+)G(d). . . . . . . . . . . . . . . . . . . . . . . 48

3.6 Ten lowest vertical IEs (eV) of the hydrogen-bonded uracil dimer calcu-lated with EOM-IP-CCSD/6-311(+)G(d,p) versus the energy-additivityscheme results estimated from 6-31(+)G(d). . . . . . . . . . . . . . . . 49

3.7 Oscillator strengths and transition dipole moments for the electronictransitions in the ionized stacked uracil dimer calculated with EOM-IP-CCSD/6-31(+)G(d) at the geometry of the neutral. . . . . . . . . . . 51

3.8 Oscillator strengths and transition dipole moments for the electronictransitions in the ionized stacked uracil dimer calculated with EOM-IP-CCSD/6-31(+)G(d) at the equilibrium geometry of the ionized dimer.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.1 The values of optimized structural parameters (A, Degree) of the frag-ments in the stacked, h-bonded, h-transfered h-bonded and t-shapeduracil dimer cations. The differences (A, Degree) w.r.t. the equilibriumgeometry of the respective neutral complex are also given showing theionization-induced changes in geometry. See Fig. 4.3 for the definitionsof the parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

4.2 The values of inter-fragment structural parameters (A, Degree) of thestacked, h-bonded, h-transfered h-bonded and t-shaped uracil dimer cations.The differences (A, Degree) w.r.t. the equilibrium geometry of the respec-tive neutral complexes are given in parenthesis. See Fig. 4.3 for thedefinitions of the parameters. . . . . . . . . . . . . . . . . . . . . . . 67

xiii

4.3 Total (Etot, hartree) and dissociation (De, kcal/mol) energies of the fourisomers of the uracil dimer in the neutral and ionized states computedby CCSD/IP-CCSD with 6-311(+)G(d,p). Relevant total energies of theuracil monomer are also given. The relaxation energies (∆E, kcal/mol)defined as the difference in total energies of the cation at the neutral andrelaxed cation geometries are also shown. For HU+

2 (PT) dissociationenergies corresponding to the U0 + U+ / (U - H)0 + UH+ channels aregiven. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

4.4 The dissociation energies (kcal/mol) and standard thermodynamic quan-tities of the neutral and the cation uracil dimers calculated at theωB97X-D/6-311(+)G(d,p) level. For the proton-transfered cation the values cor-responding to the two different dissociation limits are given. . . . . . . 73

4.5 The excitation energies (∆E, eV), transition dipole moments (< µ2 >,a.u.) and oscillator strengths (f ) of the stacked dimer cation at the geom-etry of the neutral and cation, IP-CCSD/6-31(+)G(d). . . . . . . . . . . 77

4.6 The excitation energies (∆E, eV), transition dipole moments (< µ2 >,a.u.) and oscillator strengths (f ) of the symmetric h-bonded dimercation at the geometry of the neutral and cation, IP-CCSD/6-31(+)G(d). 79

4.7 The excitation energies (∆E, eV), transition dipole moments (< µ2 >,a.u.) and oscillator strengths (f ) of the h-bonded dimer cation at theoptimized proton-transferred geometry, IP-CCSD/6-31(+)G(d). . . . . 80

4.8 The excitation energies (∆E, eV), transition dipole moments (< µ2 >,a.u.) and oscillator strengths (f ) of the t-shaped dimer cation at thegeometry of the neutral and cation, IP-CCSD/6-31(+)G(d). . . . . . . . 82

5.1 The total (hartree) and dissociation energies (kcal/mol) of the neutraland ionized 1,3-dimethyluracil monomer and dimers calculated at theωB97X-D/6-311(+,+)G(2d,2p) level of theory. . . . . . . . . . . . . . 90

5.2 The total (hartree) and dissociation energies (kcal/mol) of the neutraland ionized 1,3-dimethyluracil and its dimer (lowest energy isomer) cal-culated at the IP-CCSD/6-31(+)G(d) level of theory. For the monomerand the dimer cations, the relaxation energy (∆ECCSD

relax , kcal/mol) isprovided.a The uracil and uracil dimer IP-CCSD/6-31(+)G(d) resultsb

are included for comparison. . . . . . . . . . . . . . . . . . . . . . . . 91

xiv

5.3 The five lowest ionized states and the corresponding IEs (eV) of the 1,3-dimethyluracil at the vertical geometry calculated by IP-CCSD with the6-31(+)G(d) and 6-311(+)G(d,p) bases. The IE shifts (eV) with respectto the uracil values are given in parenthesis. . . . . . . . . . . . . . . . 94

5.4 The electronic spectrum of the 1,3-dimethyluracil cation at the verticaland relaxed geometries calculated at the IP-CCSD/6-31(+)G(d) level. . 105

5.5 The ionization energies (eV) and the DMO charactera corresponding tothe ten lowest ionized states of the stacked 1,3-dimethyluracil dimer atthe vertical geometry (isomer 1) calculated at the IP-CCSD/6-31(+)G(d)level. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

6.1 The ground state total energies (in hartree) of the six isomers of Bz+2 cal-

culated at three levels of theory: IP-CCSD/6-31(+)G(d), IP-CCSD(dT)/6-31(+)G(d) and IP-CCSD/6-311(+,+)G(d,p)+FNO(99.25%) . . . . . . . 116

6.2 The characteristic geometric parameters of the six ground-state struc-tures of the benzene dimer cation. The distances between the centersof mass of the fragmentsdCOM (in A), separationh (in A) and slidingcoordinate∆ (in A) values are presented. . . . . . . . . . . . . . . . . 117

6.3 The six lowest symmetry-allowed transitions in the electronic spectrumof the benzene dimer cation at the XD and XSD optimized geometries.Calculated with IP-CCSD/6-31(+)G(d). . . . . . . . . . . . . . . . . . 120

6.4 The six lowest symmetry-allowed transitions in the electronic spectrumof the benzene dimer cation at the YD and YSD optimized geometries.Calculated with IP-CCSD/6-31(+)G(d). . . . . . . . . . . . . . . . . . 121

6.5 Theoretical estimates of the lowest VIE (in eV) of the nucleobase monomersandπ-stacked dimers. . . . . . . . . . . . . . . . . . . . . . . . . . . 125

xv

Abstract

Several prototypical ionized non-covalent dimers - the uracil, 1,3-dimethylated uracil

and benzene dimer cations - are studied by high-level ab initio approaches including the

equation-of-motion coupled cluster method for ionization potentials (EOM-IP-CC). The

qualitative Dimer Molecular Orbitals as Linear Combinations of Fragment Molecular

Orbitals (DMO-LCFMO) framework is used to interpret the results of calculations.

As the simplest model systems, the neutral and ionized non-covalent dimers, such as

π-stacked and H-bonded nucleobase dimers, can shed some light on the complex mech-

anism of the charge transfer in DNA. The correct treatment of non-covalent interactions

is challenging to the ab initio methodology, therefore the special attention is given to the

development and benchmarking of the new methods.

First, we introduce and benchmark the cost-saving configuration-interaction variant

of the EOM-IP-CCSD method: EOM-IP-CISD. The computational scalling of EOM-

IP-CISD in N5, as opposed to the N6 scalling of EOM-IP-CCSD. The EOM-IP-CISD

structures for the open-shell systems are of a similar quality as the HF geometries of

well-behaved closed-shell molecules, while the excitation energies are of a semiquanti-

tative value. The performance of promising Density Functional Theory developments,

i.e. the novel long-range and dispersion-corrected functionals, is also assessed through-

out this work.

xvi

Next, the potential energy surfaces, electronic structure and properties of uracil

dimer and 1,3-dimethylated uracil dimer cations are investigated. The electronic struc-

ture of dimers is explained by DMO-LCFMO. Non-covalent interactions lower the ver-

tical ionization energies by up to 0.35 eV, the largest red-shift is observed for the stacked

and t-shaped structures. Ionization induces significant changes in bonding patterns,

structures and binding energies. In the cations the interaction between the fragments

becomes more covalent and the binding energies are 1.5-2.0 times larger than in the

neutrals. The relaxation of the cation structures is governed by two different mecha-

nisms: the hole delocalization and the electrostatic stabilization. The electronic spectra

of dimer cations exhibit significant changes upon relaxation, which can be exploited

to experimentally monitor the ionization-induced dynamics. The position and inten-

sity of the charge-resonance transitions can be used as spectroscopic probes in such

experiments. Finally, we investigate the effect of substituents on the electronic struc-

ture of non-covalent dimers. For weak perturbations, i.e. the CH3 group, the effect of

substituents can be incorporated into the qualitative DMO-LCFMO picture as constant

shifts of the dimers and the monomers levels.

Future research topics, such as the conical intersections in the benzene dimer cations

and the electronic structure of the chemically-modified nucleobase dimers, are discussed

in the last chapter.

xvii

Chapter 1

Ionized non-covalent dimers:

Fascinating and challenging

1.1 Non-covalent interactions

From the chemist’s perspective, there are two types of molecular interactions - cova-

lent and non-covalent. Covalent interactions giving rise to chemical bonds arise when

two atoms share the electrons. In the electronic structure terms, covalent interaction

originate in the atomic orbital overlap, which increases the electron delocalization and,

thus, lowers electronic energy. Non-covalent interactions are everything beyond the

covalent definition. They include the electrostatic, induction and dispersion intermolec-

ular forces, the latter being also known as van der Waals interactions. Hydrogen bond

straddles the two domains, as it includes partial electron sharing, but also a degree of

electrostatic interaction. The non-covalent interactions are weak relative to the covalent

or pure ionic ones. Typical stabilization energies for a chemical bond are of the order

of hundred kilocalories per mole, whereas the hydrogen-bonded and dispersion inter-

acting systems are bound by tenth to several kilocalories per mole, respectively. Nev-

ertheless, the importance of non-covalent interactions for chemistry cannot be overes-

timated. Condensed-phase chemistry, biochemistry, surface chemistry, catalysis, poly-

mer science - these are just several fields of modern chemistry that are defined by the

non-covalent interactions to a considerable degree [1–3]. For instance, the 3D structure

of one of the most important molecules in biochemistry - the DNA double helix - is

1

a result of a network of hydrogen-bonding andπ-stacking interactions that are of the

non-covalent nature. Other examples include protein secondary and tertiary structure,

enzyme-substrate binding, and more.

1.2 Ionized non-covalent dimers as model charge-

transfer systems

In recent years, significant efforts were directed towards investigating charge transfer

(CT) in DNA, which is related to the DNA damage processes. The DNA’s photo- and

oxidizing damage is of great importance to the biology and medicine, as it is likely to

be realted to some of the serious deseases [4].

Under the oxidizing or photoionizing conditions, the hole is injected in the DNA

molecule, in particular, in its easiest-to-ionize guanine site. The hole then migrates

through the DNA strand over large distances of more than 100A, which was experi-

mentally observed for both pure DNA/DNA [5, 6] and mixed DNA/RNA duplexes [7].

In addition to the biological significance of this process, this nano-scale conductivity of

DNA and RNA is attractive for the molecular electronics applications [8–10]. Despite

its importance, the CT phenomenon is not yet fully understood and the progress requires

joint experimental and theoretical efforts.

Several mechanisms of CT in DNA have been proposed [11–16], but none of them

offers a complete description of the process. Different factors were shown to be impor-

tant: the DNA sequence and composition (in particular, the percentage of GC and AT

Watson-Crick base pairs), thermally-induced chain fluctuations, the presence of Na+

counterions [17]. Moreover, the non-covalent interactions between the bases, especially

2

theπ-stacking, appear to be crucial for this process [18–20]. The study of ionized nucle-

obase dimers - the simpliest model systems for the CT in DNA - can shed some light at

this complex phenomenon.

While ionization energies (IEs) of nucleic acid bases in the gas phase have been

characterized both experimentally [21–27] and computationally [28–31], much less is

known about the effects of interactions present in realistic environments, likeπ-stacking

and h-bonding, on the ionized states of nucleobases.

We characterized the electronic structure of the ionized uracil dimers [32, 33] and

dimethylated uracil dimers [34]. Other ionized nucleobase dimers, like the adenine and

thymine homo- and hetero-dimers [35] and cytosine dimers [36] were also investigated

recently. Calculations [32–36] and VUV measurements [35,36] demonstrated that non-

covalent interactions lower vertical ionization energies (VIEs) by as much as 0.7 eV

(in cytosine dimers). Interestingly, the magnitude and origin of the effect are different

for different isomers. The largest drop in IEs was observed in the symmetric stacked

and non-symmetric h-bonded dimers. In the former case, the IE is lowered due to the

hole delocalization over the two fragments, while in the latter case the stabilization is

achieved by the electrostatic interaction of hole with the “neutral” fragment. Therefore,

non-covalent interactions seem to reduce the gaps in IEs of purines and pyrimidines,

which may play an important role in hole migration through DNA.

Earlier studies of the effects ofπ-stacking on IEs of nucleobases include Hartree-

Fock and DFT estimates using Koopmans theorem [37–41], MP2 (Møller-Plesset per-

turbation theory) and CASPT2 (perturbatively-correcte d complete active space self-

consistent field) calculations [28,30,42].

3

1.3 Methodological challenges

The correct treatment of non-covalent interactions is difficult for ab initio methodology

[1, 3, 43], especially for the systems dominated by dispersion interactions. Dispersion

forces originate in correlated motion of the electrons, so highly-correlated approaches,

such as coupled cluster methods, are required for reliable results. However, theN6-N8

scalling of these methods quickly rules out their application to large systems (i.e., more

than 40-50 atoms). A less expensive alternative to the traditional correlated wave func-

tion based methods, Density Functional Theory (DFT), fails to account for dispersion

interaction when used with standard functionals [44, 45]. The reason is the local and

semi-local character of the approximate exchange-correlation functional (εXC). For a

cluster AB, where charge densities on A and B fragments do not overlap:

εXC(AB) = εXC(A) + εXC(B), (1.1)

whereεXC(A) andεXC(B) depend solely on the densities (or the density and its gra-

dient) on fragments A and B, respectively. Such model cannot account for the long-

range attractive dispersion and fails to adequately describe non-covalent systems at large

separations, when the dispersion forces dominate. Moreover, the situation is far from

prefect at short-range where the attractive dispersion interaction is underestimated by

DFT due to the incorrect asymptotic behavior of standard functionals [44]. The latest

developements of the semi-empirical dispersion-corrected functionals [46,47], where an

empiricalR−6 term is included to account for the long-range dispersion interaction, are

promising; however, they do not provide a universal solution. Other problems include

the shallow potential energy surfaces (PES) of non-covalent complexes and technical

issues such as Basis Set Superposition Error (BSSE) [1]. Thus, even a closed-shell

4

system is a challenge for modern computational chemistry when it is dominated by non-

covalent interactions.

With the open-shell systems such as ionized non-covalent dimers additional issues

emerge. The single-reference post-HF approaches, e.g. MP2 and CCSD, are plagued by

the spin-contamination, symmetry-breaking and imbalanced description of the closely-

lying multiple electronic states. The former follows from the fact that the HF variational

solution (i.e., the unrestricted HF solution) is generally not an eigenfunction of the〈S2〉

operator. Consequently, the UHF wave function is a mixture of states of different multi-

plicity. The correct spin symmetry can be enforced in HF by restricting the spatial parts

of the orbitals to be equal for the electrons with different spin (the restricted open-shell

HF). However, this solution problem is not optimal from variational principle point of

view, as it is higher in energy.

The imbalance originates in the multi-configurational character of the open-shell

wave functions, which can be accounted for by correlated multi-reference (MR)

approaches, like CASPT2 or MR-CISD. However, some of the imbalance is still present

in the MR wave function, because the configurations of similar importance are not

treated on the same footing. Other disadvantages that limit the applications of MR meth-

ods are the high cost and inconvenience resulting from the need to choose the relevant

configurations manually.

The DFT description of the ionized non-covalent systems suffers from self-

interaction erorrs (SIE) in addition to the issues mentioned previously [48]. Because

of the approximate character of the exchange-correlation functional, the exchange and

repulsion terms do not cancel out for one electron in DFT. This results in unphysical

situation when the electron interacts with itself. The SIE is responsible for the incorrect

behavior at the dissociation limit for the symmetric dimer cations, for instance, the ion-

ized rare gas and nucleobase dimers [48]. The total energy of the dissociating system

5

becomes much lower than the sum of the total energies of the products. The resulting

potential energy profiles instead of levelling off at infinite separations exhibit a char-

acteristic downward curve. This behaviour is suppressed if the Hartree-Fock exchange

is used, which is exploited in the long-range corrected (LC) functionals. One of the

promising functionals isωB97X-D [49], which includes both LR Hartree-Fock and dis-

persion correction. TheωB97X-D shows significant improvement over traditional DFT

functionals when applied to non-covalent systems.

1.4 Equation-of-motion coupled-cluster family of meth-

ods

The equation-of-motion coupled-cluster (EOM-CC) methods [50–60] offer an original

solution to open-shell problems. Instead of dealing with the symmetry-broken and spin-

contaminated wave function of the open-shell state of interest, the EOM-CC accesses

the target states via a well-behaved reference state employing various excitation oper-

ators. The reference state is chosen such that it is free from spin-contamination and

symmetry-breaking at the Hartree-Fock level. Thus, the EOM methods do not suffer

from these common flaws of traditional wave function approaches. When used properly,

they yield balanced wave functions that include all the important configurations from the

target manifold. Other advantages of the EOM approach include embedded dynamical

correlation effects and elegant formalism. The EOM-CC methods are universal and

can be successfullly applied to diverse open-shell situations, including the open-shell

cations, anions, di- and tri-radicals, bond-breaking, exactly and nearly-degenerate elec-

tronic states.

6

The wave function of the target state in EOM-CC is represented as follows:

ΨEOM−CC = ReT Φ0, (1.2)

where Φ0 is Hartree-Fock determinant of the closed-shell reference state,T is the

coupled-cluster operator andR is the appropriate excitation operator generating the tar-

get configurations from the reference CCSD wave function. Depending on an EOM-CC

model, different excitation operators are used. For instance, in the EOM model for

ionization potentials (EOM-IP) [58], which is an appropriate choice for ionized non-

covalent systems, the operatorR is ionizing and generates all1h (one hole) and2h1p

(two hole one particle) determinants from the reference configuration. This model is

capable of accessing the doublet states of the radical cations from the neutral reference.

The second-quantization expressions forR andT operators for one of the extensions of

the EOM-IP model with single and double substitutions (EOM-IP-CCSD) are:

R = R1 + R2 (1.3)

R1 =∑

i

rii (1.4)

R2 =1

2

∑ija

raija

+ji (1.5)

T = T1 + T2 (1.6)

T1 =∑ia

tai a+i (1.7)

T2 =1

4

∑ijab

tabij a

+b+ij (1.8)

wheretai , tabij andri, ra

ij are the unknown amplitudes of the coupled-cluster and EOM

excitation operators. The EOM-CC solutions are obtained in a two-step procedure. First,

the coupled-cluster equations for the reference state are solved and the amplitude vector

7

for the operatorT is obtained in a procedure that scales asN6. Second, the EOM states

(or equivalently the left and right amplitude vectors of operatorR for EOM states) are

found by the diagonalization of the similarity-transformed HamiltonianH = e−THeT

at theN5 cost.

HR = ER (1.9)

LH = ER (1.10)

LIRJ = δij (1.11)

Other EOM-CC models include the electron atachment (EA) [57], spin flip (SF)

[55, 56] and electron excitations (EE) [54] variants. These ideas can be implemented

within the CI approach [61] and one of the methods, EOM-IP-CISD, is described in

Section 2.2.

1.5 Bonding in ionized non-covalent dimers: The qual-

itative Dimer Molecular Orbitals and Linear Com-

binations of Atomic Orbitals framework

The DMO-LCFMO (Dimer Molecular Orbital Linear Combination of Fragment Molec-

ular Orbitals) framework [62] enables the qualitative prediction of the bonding and

properties of non-covalent dimers. Within this framework, the electronic structure of

the dimer is described in terms of the fragment (i.e. monomer) molecular orbitals

(FMOs). Symmetric and non-symmetric dimers are treated analogously to the famil-

iar MO-LCAO approach to of homo- and hetero-nuclear diatomics [63].

8

ν(F1) = πCC(F1) ν(F2) = πCC(F2)

ψ+(ν)

-0.361

-0.384-0.372 -0.372

ψ-(ν)

Figure 1.1: The DMO-LCFMO description of the two lowest ionized states in the uracildimer. In-phase and out-of-phase overlap between the FMOs results in the bonding(lower) and antibonding (upper) dimer’s MOs. Changes in the MO energies, and, con-sequently, IEs, are demonstrated by the Hartree-Fock orbital energies (hartrees). Ioniza-tion from the antibonding orbital changes the bonding from non-covalent to covalent,and enables a new type of electronic transitions, which are unique to the ionized dimers.

As illustrated in Figure 1.1, the dimer molecular orbitals (DMOs) are symmetric and

antisymmetric linear combinations of the FMOs:

ψ+(ν) =1√

2(1 + sνν)(ν(F1) + ν(F2)) (1.12)

ψ−(ν) =1√

2(1− sνν)(ν(F1)− ν(F2)) (1.13)

whereν(F1) andν(F2) are the FMOs centered on two equivalent fragments F1 and

F2, ψ+(ν) andψ−(ν) denote the bonding and antibonding orbitals with respect to the

interfragment interaction andsνν = 〈ν(F1) | ν(F2)〉 is the overlap integral. Folowing

9

the MO-LCAO reasoning, the energy splitting between the bonding and antibonding

orbitals is proportional to the overlapsνν [63]. Therefore, the dimer system ionizes

at lower ionization energies relative to the monomer and the decrease in dimer IE is

proportional to the FMO overlap. From Figure 1.1 we can also predict the behaviour

of the ionization-induced changes in the dimer system. As the electron is ejected from

the dimer, the formal bond order changes from0 to 12

and the interfragment interaction

increases.

Twice as many ionized states appear in dimer relative to the monomer. In the elec-

tronic spectrum of the dimer cation, all transitions can be classified into two categories:

the charge resonance (CR) and the local excitations (LE). The CR transitions are defined

as transitions between the ionized states corresponding to the in- and out-of-phase com-

bined FMOs of the same character, i.e.ψ−(ν) → ψ+(ν). The LE are the transitions

between the DMOs combined out of FMOs of different character, i.e.ψ−(ν) → ψ+(ζ)

orψ−(ν) → ψ−(ζ). The CR transitions are unique to the dimer, whereas LE are similar

to the transitions present in the electronic spectrum of monomer cation. It can be shown

that the intensity of the CR transitions is sensitive to the FMO overlap and interfragment

separation:

I(ψ−(ν) → ψ+(ν)) ∝ RF1···F2√1− sνν

(1.14)

wheresνν = 〈ν(F1) | ν(F2))〉. When the cation relaxes from the vertical geometry,

the FMO overlap increases (sν(F1)ν(F2) → 1), and the CR band intensity rises in the

electronic spectrum. Therefore, the CR transitions can be used to probe the structural

changes occuring in the dimer cation.

In non-symmetric dimers, the transitions corresponding to charge-transfer between

the fragments become important.

10

1.6 Reference list

[1] K. M uller-Dethlefs and P. Hobza, Noncovalent interactions: A challenge for exper-iment and theory, Chem. Rev.100, 143 (2000).

[2] J. Cerny and P. Hobza, Non-covalent interactions in biomacromolecules, Phys.Chem. Chem. Phys.9, 5291 (2007).

[3] C.D. Scherrill, Reviews in Computational Chemistry, chapter Chapter 1: Compu-tations of noncovalentπ interactions, pages 1–38. Jon Wiley & Sons, 2009.

[4] M.S. Cooke, M. D. Evans, M. Dizdaroglu, and J. Lunec, Oxidative DNA damage:Mechanisms, mutation and disease, The FASEB Journal17, 1195 (2003).

[5] M.E. Nu nez, D.B. Hall, and J.K. Barton, Long-range oxidative damage to DNA:Effects of distance and sequence, Chem. and Biol.6, 85 (1999).

[6] T. Takada, K. Kawai, M. Fujitsuka, and T. Majima, Direct observation of holetransfer through double-helical DNA over 100a, Proc. Nat. Acad. Sci.101, 14002(2004).

[7] D. T. Odom and J. K. Barton, Long-range oxidative damage in DNA/RNAduplexes, Biochemistry40, 8727 (2001).

[8] A. Okamoto, K. Tanaka, and I. Saito, Rational design of a DNA wire possessingan extremely high hole transport ability, J. Am. Chem. Soc.125, 5066 (2003).

[9] G.R. Hutchison, M.A. Ratner, and T.J. Marks, Intermolecular charge transferbetween heterocyclic oligomers. Effects of heteroatom and molecular packing onhopping transport in organic semiconductors, J. Am. Chem. Soc.127, 16866(2005).

[10] K. Kawai, H. Kodera, Y. Osakada, and T. Majima, Sequence-independent andrapid long-range charge transfer through DNA, Nature Chemistry1, 156 (2009).

[11] R.A. Marcus and N. Sutin, Electron transfers in chemistry and biology, Biochim.Biophys. Acta811, 265 (1985).

[12] B. Giese, Long-distance charge transport in DNA: The hopping mechanism, Acc.Chem. Res.33, 631 (2000).

[13] B. Giese, J. Amaudrut, A.-K. Kohler, M. Spormann, and S. Wessely, Direct obser-vation of hole transfer through DNA by hopping between adenine bases and bytunnelling, Nature412, 318 (2001).

11

[14] R. N. Barnett, C. L. Cleveland, A. Joy, U. Landman, and G.B. Schuster, Chargemigration in DNA: Ion-gated transport, Science294, 567 (2001).

[15] P.T. Henderson, D. Jones, G. Hampikian, Y. Kan, and G.B. Schuster, Long-distance charge transport in duplex DNA: The phonon-assisted polaron-like hop-ping mechanism, Proc. Nat. Acad. Sci.96, 8353 (1999).

[16] D. Roca-Sanjuan, M. Merchan, and L. Serrano-Andres, Modelling hole transferin DNA: Low-lying excited states of oxidized cytosine homodimer and cytosine-adenine heterodimer., Chem. Phys.349, 188 (2008).

[17] B. Giese, Long-distance electron tranfer through DNA, Annu. Rev. Biochem.71,51 (2002).

[18] M. Bixon and J. Jortner, Hole trapping, detrapping, and hopping in DNA, J. Phys.Chem. A105, 10322 (2001).

[19] F.L. Gervasio, A. Laio, M. Parrinello, and M. Boero, Charge localization in DNAfibers, Phys. Rev. Lett.94, 158103 (2005).

[20] E.R. Bittner, Lattice theory of ultrafast excitonic and charge-transfer dynamics inDNA, J. Chem. Phys.125, 094909 (2006).

[21] D. Dougherty, K. Wittel, J. Meeks, and S. P. McGlynn, Photoelectron spectroscopyof carbonyls. Ureas, uracils, and thymine, J. Am. Chem. Soc.98, 3815 (1976).

[22] S. Urano, X. Yang, and P.R. LeBrenton, UV photoelectron and quantum mechani-cal characterization of DNA and RNA bases: Valence electronic structures of ade-nine, 1,9-dimethylguanine, 1-methylcytosine, thymine and uracil, J. Mol. Struct.214, 315 (1989).

[23] G. Lauer, W. Schafer, and A. Schweig, Functional subunits in the nucleic acidbases uracil and thymine, Tetrahedron Lett.16, 3939 (1975).

[24] C. Yu, T.J. O’Donnel, and P.R. LeBreton, Ultraviolet photo-electron studies ofvolatile nucleoside models - vertical ionization-potential measurements of methy-lated uridine, thymidine, cytidine, and adenosine, J. Phys. Chem.85, 3851 (1981).

[25] S.K. Kim, W. Lee, and D.R. Herschbach, Cluster beam chemistry: Hydration ofnucleic acid bases; Ionization potentials of hydrated adenine and thymine, J. Phys.Chem.100, 7933 (1996).

[26] H. Satzger, D. Townsend, and A. Stolow, Reassignment of the low lying cationicstates in gas phase adenine and 9-methyl adenine, Chem. Phys. Lett.430, 144(2006).

12

[27] L. Belau, K.R. Wilson, S.R. Leone, and M. Ahmed, Vacuum-ultravioled photoion-ization studies of the microhydration of DNA bases (guanine, cytosine, adenine,and thymine), J. Phys. Chem. A111, 7562 (2007).

[28] E. Cauet, D. Dehareng, and J. Lievin, Ab initio study of the ionization of the DNAbases: Ionization potentials and excited states of the cations, J. Phys. Chem. A110, 9200 (2006).

[29] D. Roca-Sanjuan, M. Rubio, M. Merchan, and L. Serrano-Andres, Ab initio deter-mination of the ionization potentials of DNA and RNA nucleobases, J. Chem.Phys.125, 084302 (2006).

[30] E. Cauet and J. Lievin, Radical cations of the nucleic bases and radiation damageto DNA: Ab initio study, Adv. Quantum Chem.52, 121 (2007).

[31] H.R. Hudock, B.G. Levine, A.L. Thompson, H. Satzger, D. Townsend, N. Gador,S. Ulrich, A. Stolow, and T.J. Martınez, Ab initio molecular dynamics and time-resolved photoelectron spectroscopy of electronically excited uracil and thymine,J. Phys. Chem. A111, 8500 (2007).

[32] A.A. Golubeva and A.I. Krylov, The effect ofπ-stacking and H-bonding on ion-ization energies of a nucleobase: Uracil dimer cation, Phys. Chem. Chem. Phys.11, 1303 (2009).

[33] A.A. Zadorozhnaya and A.I. Krylov, Ionization-induced structural changes inuracil dimers and their spectroscopic signatures, J. Chem. Theory Comput. (2010),In press.

[34] A.A. Zadorozhnaya and A.I. Krylov, Zooming into pi-stacked manifolds of nucle-obases: Ionized states of dimethylated uracil dimers, J. Phys. Chem. A (2010), Inpress.

[35] K.B. Bravaya, O. Kostko, M. Ahmed, and A.I. Krylov, The effect ofπ-stacking,h-bonding, and electrostatic interactions on the ionization energies of nucleic acidbases: Adenine-adenine, thymine-thymine and adenine-thymine dimers, Phys.Chem. Chem. Phys. (2010), in press, DOI:10.1039/b919930f.

[36] O. Kostko, K.B. Bravaya, A.I. Krylov, and M. Ahmed, Ionization of cytosinemonomer and dimer studied by VUV photoionization and electronic structure cal-culations, Phys. Chem. Chem. Phys. (2010), In press, DOI: 10.1039/B921498D.

[37] A.-O. Colson, B. Besler, and M.D. Sevilla, Ab initio molecular orbital calculationson DNA base pair radical ions: Effect of base pairing on proton-transfer energies,electron affinities, and ionization potentials, J. Phys. Chem.96, 9787 (1992).

13

[38] A.-O. Colson, B. Besler, and M.D. Sevilla, Ab initio molecular orbital calculationson DNA radical ions. 4. Effect of hydration on electron affinities and ionizationpotentials of base pairs, J. Phys. Chem.97, 13852 (1993).

[39] H. Sugiyama and I. Saito, Theoretical studies of GC-specific photocleavage ofDNA via electron transfer: Significant lowering of ionization potential and 5’-localization of HOMO of stacked GG bases in B-form DNA, J. Am. Chem. Soc.118, 7063 (1996).

[40] F. Prat, K.N. Houk, and C.S. Foote, Effect of guanine stacking on the oxidation of8-oxoguanine in B-DNA, J. Am. Chem. Soc.120, 845 (1998).

[41] S. Schumm, M. Prevost, D. Garcia-Fresnadillo, O. Lentzen, C. Moucheron, andA. Krisch-De Mesmaeker, Influence of the sequence dependent ionization poten-tials of guanines on the luminescence quenching of Ru-labeled oligonucleotides:A theoretical and experimental study, J. Phys. Chem. B106, 2763 (2002).

[42] D. Roca-Sanjuan, M. Merchan, and L. Serrano-Andres, Modelling hole-transferin DNA: Low-lying excited states of oxidized cytosine homodimer and cytosine-adenine heterodimer, Chem. Phys.349, 188 (2008).

[43] G.S. Tschumper,Reviews in Computational Chemistry, chapter Chapter 2: Reli-able electronic structure computations for weak noncovalent interactions in clus-ters, pages 39–90. Jon Wiley & Sons, 2009.

[44] S. Kristyan and P. Pulay, Can (semi)local density functional theory account for theLondon dispersion forces?, Chem. Phys. Lett.229, 175 (1994).

[45] P. Hobza, J.Sponer, and T. Reschel, Density functional theory and molecularclusters, J. Comput. Chem.16, 1315 (1995).

[46] S. Grimme, Accurate description of van der Waals complexes by density func-tional theory including empirical corrections, J. Comput. Chem.25, 1463 (2004).

[47] S. Grimme, Semiempirical GGA-type density functional constructed with a long-range dispersion correction, J. Comput. Chem.27, 1787 (2006).

[48] Y. Zhang and W. Yang, A challenge for density functionals: Self-interaction errorincreases for systems with a noninteger number of electrons, J. Chem. Phys.109,2604 (1998).

[49] J.-D. Chai and M. Head-Gordon, Long-range corrected hybrid density functionalswith damped atom-atom dispersion interactions, Phys. Chem. Chem. Phys.10,6615 (2008).

14

[50] D.J. Rowe, Equations-of-motion method and the extended shell model, Rev. Mod.Phys.40, 153 (1968).

[51] K. Emrich, An extension of the coupled-cluster formalism to excited states (I),Nucl. Phys.A351, 379 (1981).

[52] H. Sekino and R.J. Bartlett, A linear response, coupled-cluster theory for excitationenergy, Int. J. Quant. Chem. Symp.26, 255 (1984).

[53] J. Geertsen, M. Rittby, and R.J. Bartlett, The equation-of-motion coupled-clustermethod: Excitation energies of Be and CO, Chem. Phys. Lett.164, 57 (1989).

[54] J.F. Stanton and R.J. Bartlett, The equation of motion coupled-cluster method.A systematic biorthogonal approach to molecular excitation energies, transitionprobabilities, and excited state properties, J. Chem. Phys.98, 7029 (1993).

[55] A.I. Krylov, Size-consistent wave functions for bond-breaking: The equation-of-motion spin-flip model, Chem. Phys. Lett.338, 375 (2001).

[56] S.V. Levchenko and A.I. Krylov, Equation-of-motion spin-flip coupled-clustermodel with single and double substitutions: Theory and application to cyclobuta-diene, J. Chem. Phys.120, 175 (2004).

[57] M. Nooijen and R.J. Bartlett, Equation of motion coupled cluster method for elec-tron attachment, J. Chem. Phys.102, 3629 (1995).

[58] S. Pal, M. Rittby, R.J. Bartlett, D. Sinha, and D. Mukherjee, Multireferencecoupled-cluster methods using an incomplete model space — application toionization-potentials and excitation-energies of formaldehyde, Chem. Phys. Lett.137, 273 (1987).

[59] K. Kowalski and P. Piecuch, The active space equation-of-motion coupled-clustermethods for excited electronic states: the EOMCCSDt approach, J. Chem. Phys.113, 8490 (2000).

[60] A.I. Krylov, Equation-of-motion coupled-cluster methods for open-shell and elec-tronically excited species: The hitchhiker’s guide to Fock space, Annu. Rev. Phys.Chem.59, 433 (2008).

[61] A.I. Krylov, Spin-flip configuration interaction: An electronic structure model thatis both variational and size-consistent, Chem. Phys. Lett.350, 522 (2001).

[62] P.A. Pieniazek, A.I. Krylov, and S.E. Bradforth, Electronic structure of the benzenedimer cation, J. Chem. Phys.127, 044317 (2007).

[63] P.W. Atkins and R.S. Friedman,Molecular Quantum Mechanics. New York:Oxford University Press, 2005.

15

Chapter 2

Configuration interaction

approximation of equation-of-motion

method for ionization potentials: A

benchmark study

2.1 Overview

A configuration interaction variant of EOM-IP-CCSD method is introduced. The per-

formance and capabilities of the new approach are demonstrated by application to the

uracil cation, water dimer and benzene dimer cations by benchmarking against more cor-

related EOM-IP-CCSD. The formal introduction of IP-CISD is given in Section 2.2, its

performance and errors for structural parameters and excitation energies are discussed

in Section 2.4.1, 2.4.2 and 2.4.3.

2.2 The IP-CISD method

The IP-CISD wave function for state can be written as:

ΨIP−CISD = RΦ0, (2.1)

16

In this equationΦ0 is the Hartree-Fock determinant of the reference closed-shell system

and the operatorR = R1 + R2 is the familiar EOM-IP excitation operator:

R1 =∑

i

rii (2.2)

R2 =1

2

∑ija

raija

+ji (2.3)

(2.4)

In other words,R1 andR2 generate the linear combinations of all possible ionized (i.e.,

1h) and ionized-excited (2h1p) determinants with appropriate spin-projection (either

Ms=12

orMs = −12) from the reference HF wave function.

The equations for the amplitudes ofR of the electronic state K are derived by apply-

ing the variational principle to the CI energy functional:

EK =< ΨIP−CISD(K)|H|ΨIP−CISD(K) >

< ΨIP−CISD(K)|ΨIP−CISD(K) >(2.5)

and are:

(H − E0)R = RΩ, (2.6)

whereH is the matrix of the Hamiltonian in the basis of the1h and2h1p determinants,

matrix R contains the amplitudes,Ω is a matrix composed of the energy differences

with respect to the reference state,ωk = EK − E0, andE0 =< Φ0|H|Φ0 >. Thus, the

amplitudes and target states’ energies are found by diagonalization of the Hamiltonian

in the1h, 2h1p space.

HSS − E0 HSD

HDS HDD − E0

R1(K)

R2(K)

= ωK

R1(K)

R2(K)

(2.7)

(2.8)

17

whereHSS,HDS, andHDD denote1h− 1h, 2h1p− 1h, and2h1p− 2h1p blocks of the

Hamiltonian matrix, respectively.

The key advantages of a more correlated EOM-IP-CCSD method are common to

its less-expensive configuration-interaction approximation. For the closed-shell refer-

ences, the set of ionized and ionized-excited determinants is spin-complete and multiple

ionized states are treated on the same footing in IP-CISD.

2.3 Computational details

Equilibrium geometries of the five lowest ionized states of uracil were optimized using

analytic gradients underCs constraint at the IP-CCSD and IP-CISD levels with the 6-

31+G(d) basis set [1]. The cation excitation energies and transition properties were

computed at the neutral uracil geometry (optimized by RI-MP2/cc-pVTZ, see Ref. 24),

and at the optimized geometry of the lowest electronic state of the cation using the 6-

31+G(d) and 6-311+G(d,p) bases [1,2], with the core electrons frozen.

Permanent dipole moments were computed at the respective optimized geometries

using fully relaxed IP-CCSD and IP-CISD one-particle density matrices. Since the

dipole moments of charged systems are not origin-invariant, all the dipoles were com-

puted relative to the center of mass of the cations.

In water dimer calculations, the geometries of the neutrals from Ref. 70 were

employed. The cation geometries were optimized by IP-CISD and IP-CCSD with

the 6-311(+,+)G(d,p), 6-311(2+,+)G(d,p), 6-311(2+,+)G(2df) and aug-cc-pVTZ basis

sets [1–3] with symmetry constraint.

Benzene dimer calculations were carried out with IP-CISD and IP-CCSD with 6-

31(+)G(d) basis and under symmetry constraint, as in Ref. 6. The wave functions for

18

the t-shaped were analyzed using the Natural Bond Orbitals (NBO) [4] procedure and

the charge of the individual fragments was calculated.

All optimizations were conducted using defaultQ-CHEM optimization thresholds:

the gradient and energy tolerance were set to3 · 10−4 and1.2 · 10−3 respectively; maxi-

mum energy change was set to1 · 10−6. The IP-CCSD geometries of the benzene dimer

isomers were computed using tighter thresholds [5].

All electrons were correlated in the uracil, water dimer and benzene dimer geometry

optimizations and properties calculations.

Figs. 2.1 and 2.2 provide the definitions of the geometric parameters for uracil, water

dimer and three benzene dimer isomers.

2.4 Numerical results

2.4.1 Equilibrium geometries and electronically excited states of the

uracil cation

Uracil has eight different bonds between heavy atoms, as depicted in Fig. 2.1. Fig. 2.3

shows the values of the CC(1), CO(1), CO(2), and CN(2) bondlengths for the five low-

est electronic states of the cation, as well as the corresponding values in the neutrals.

The MOs hosting the unpaired electron are also shown. In agreement with molecular

orbital considerations, ionization results in significant changes in some bond lengths,

which vary from state to state. For example, the CC(1) bond becomes much longer in

the first ionized state derived by ionization from theπCC orbital, whereas the CO bonds

undergo significant changes in the states derived by ionization from the respective oxy-

gen lone pairs. As one can see from Fig. 2.3, IP-CISD systematically underestimates the

19

CC(1)

CN(1)NC(1)

CN(2)

NC(2) CC(2)

CO(1)

CO(2)

CCN(1)

CNC(1)

NCN(1)

CNC(2)

NCC(1)

CCC(1)

H1

O1H2

O2

H3

H4

O1O2

Figure 2.1: Definitions of the geometric parameters for uracil (upper panel) and waterdimer (lower panel) at the proton-transferred geometry.

bond lengths, probably because of the uncorrelated Hartree-Fock reference. However, it

reproduces the trends, such as structural differences between the states, very well.

The absolute errors of IP-CISD versus IP-CCSD are summarized in Table 2.1.

For the bondlengths, the IP-CISD errors are always negative. The table also presents

average absolute errors and standard deviations for each state, which are around 0.014-

0.016A and 0.007-0.010A, respectively. Absolute average error and standard deviation

20

C1 C2

C3

C4C5

C6

C1C2

C3

C4 C5

C6

Fragment 2

C2h x-displaced isomer

Fragment 1 Fragment 1

Fragment 2

C2h y-displaced isomer

C1C2

C3C4 C5

C6

C1 C2

C3C4C5

C6

Fragment 1

Fragment 2

C2v t-shaped isomer

C1C2

C3C4 C5

C6

C1

C2

C3C4

C5

C6

Figure 2.2: Definitions of the geometric parameters for three isomers of the benzenedimer:x-displaced (top),y-displaced (middle), and t-shaped (bottom).

for these eight bonds in five electronic states are 0.015A and 0.008A, respectively.

The results for six bond angles are summarized in Table 2.2. The results are similar to

the bondlengths behavior — IP-CISD reproduces the trend in structural changes very

well. Average absolute error and standard deviation for all angles in the five states are

0.343 and 0.266 degrees, respectively. Fig. 2.4 visualizes changes in CNC(2) angle

upon ionization. The computed permanent dipole moments in the center of mass frame

are given in Table 2.3. The IP-CCSD and IP-CISD values are very similar indicating

that IP-CISD reproduces well both the equilibrium structures and electron distributions.

IP-CISD values are systematically 0.1-0.2 a.u. too large. Thus, IP-CISD wave func-

tions inherit limitations of the uncorrelated Hartree-Fock reference and are too ionic,

21

Table 2.1: The IP-CCSD bondlengths (A) in the five electronic states of the uracil cationand absolute errors (in parenthesis) of IP-CISD relative to IP-CCSD.

Bonds 12A′′ 12A′ 22A′′ 22A′ 32A′′

CC(1) 1.403 (0.017) 1.365 (0.009) 1.352 (0.014) 1.345 (0.014) 1.375 (0.013)

CN(1) 1.321 (0.005) 1.357 (0.013) 1.390 (0.012) 1.392 (0.010) 1.471 (0.028)

NC(1) 1.460 (0.027) 1.386 (0.009) 1.358 (0.011) 1.351 (0.010) 1.371 (0.017)

CN(2) 1.386 (0.011) 1.427 (0.021) 1.416 (0.032) 1.351 (0.013) 1.398 (0.009)

NC(2) 1.403 (0.016) 1.341 (0.003) 1.426 (0.029) 1.387 (0.007) 1.425 (0.009)

CC(2) 1.469 (0.012) 1.423 (0.010) 1.444 (0.001) 1.459 (0.003) 1.473 (0.005)

CO(1) 1.215 (0.020) 1.286 (0.024) 1.231 (0.018) 1.236 (0.028) 1.204 (0.027)

CO(2) 1.199 (0.021) 1.199 (0.024) 1.226 (0.017) 1.272 (0.025) 1.230 (0.023)

average abs. error 0.016 0.014 0.017 0.014 0.016

standard deviation 0.007 0.008 0.010 0.009 0.009

as compared to more correlated IP-CCSD ones. Table 2.4 presents vertical excitation

energies and transition dipole moments of the uracil cation at two different geometries,

i.e., the geometry of the neutral and the equilibrium geometry of the lowest ionized

state. IP-CISD errors are 0.1-0.3 eV and they are consistently larger for the low-lying

states. Overall, the order of states is reproduced correctly, however, IP-CISD excitation

energies are of semi-quantitative accuracy only. Intensities of transitions are in qualita-

tive agreement. Most importantly, both methods agree which states are dark and which

are bright, indicating that the underlying wave functions are qualitatively similar. Other

important trends, e.g., the lowering of the transition dipoles for the two highest states

upon geometric relaxation (from the neutral to the cation), are also reproduced.

The basis set dependence of the errors is small, as evidenced by the results in two

different bases.

22

Tabl

e2.

2:T

heIP

-CC

SD

angl

es(d

egre

es)

inth

efiv

eel

ectr

onic

stat

esof

the

urac

ilca

tion

and

abso

lute

erro

rs(in

pare

nthe

sis)

ofIP

-CIS

Dre

lativ

eto

IP-C

CS

D.

Bon

ds12A

′′12A

′22A

′′22A

′32A

′′

CC

N(1

)11

9.21

7(0

.156

)12

2.52

9(0

.078

)12

2.64

8(0

.280

)12

1.82

6(0

.223

)12

0.74

5(0

.728

)

CN

C(1

)12

5.63

6(0

.152

)12

4.33

4(0

.232

)12

3.33

3(0

.621

)12

1.30

9(0

.101

)12

2.44

6(0

.027

)

NC

N(1

)11

3.07

7(0

.496

)11

2.38

1(0

.584

)11

3.97

7(1

.260

)11

8.07

9(0

.225

)11

4.01

8(0

.215

)

CN

C(2

)12

6.73

3(0

.533

)12

4.29

1(0

.383

)12

6.22

4(0

.556

)12

4.31

5(0

.099

)12

9.40

9(0

.318

)

NC

C(2

)11

5.21

4(0

.463

)12

0.78

1(0

.046

)11

4.48

1(0

.644

)11

6.35

2(0

.105

)11

3.36

5(0

.222

)

CC

C(1

)12

0.12

3(0

.429

)11

5.68

4(0

.093

)11

9.33

7(0

.447

)11

8.12

0(0

.145

)12

0.01

6(0

.430

)

aver

age

abs.

erro

r0.

372

0.23

60.

635

0.15

00.

323

stan

dard

devi

atio

n0.

172

0.21

20.

334

0.06

00.

239

23

Table 2.3: IP-CCSD and IP-CISD permanent dipole moments (a.u.) of the five lowestelectronic states of the uracil cation computed at the respective optimized geometriesrelative to the center of mass.

12A′′ 12A′ 22A′′ 22A′ 32A′′

IP-CCSD 2.509 1.474 1.144 1.384 2.641

IP-CISD 2.632 1.602 1.279 1.511 2.759

2.4.2 Equilibrium geometries of the three isomers of the benzene

dimer cation

Geometrical parameters (see Fig. 2.2) for the three isomers of the benzene dimer cation

are summarized in Table 2.5 and visualized in Fig. 2.5. On this example, we investigate

how well IP-CISD reproduces the structures of the ionized non-covalent dimers. Ioniza-

tion of such systems changes the bonding from non-covalent to covalent, which results

in significant structural changes, in particular the interfragment distance. For example,

the interfragment distance shrinks from 3.9 to 3.3A in the sandwich isomers. IP-CISD

overestimates the interplanar separation in the displaced sandwich isomers by approxi-

mately 0.2A, while the sliding displacement is reproduced quite accurately. Similarly,

the separation between the rings in the t-shaped structure is overestimated.

In the t-shaped structure the two fragments are nonequivalent, and the charge is

unevenly distributed between the rings. The degree of charge distribution determines

the intensity of charge resonance bands, which can be used to probe the structure and

dynamics of the system. The NBO analysis of the IP-CISD densities for the states

involved in this transition yields an 0.888 and 0.101 partial charge on fragment 1 (stem),

which is in excellent agreement with the IP-CCSD values [6] of 0.880 and 0.099, respec-

tively. Charge-resonance transition energies are 0.71 and 0.81 eV for EOM-IP-CCSD

and IP-CISD, respectively.

24

Table 2.4: The IP-CCSD and IP-CISD excitation energies (eV) and transition dipolemoments (a.u.) of the uracil cation at the equilibrium geometries of the neutral and thecation.

neutral cation

6-31(+)G(d,p) IP-CCSD IP-CISD IP-CCSD IP-CISD

E µ2 E µ2 E µ2 E µ2

12A′ 0.668 0.000 0.367 0.000 1.175 0.000 0.820 0.000

22A′′ 1.063 0.000 0.867 0.000 1.809 0.000 1.577 0.000

22A′ 1.647 0.790 1.427 0.819 2.385 0.611 2.156 0.613

32A′′ 3.566 1.342 3.627 0.955 4.209 0.940 4.223 0.611

average abs. error 0.195 0.208

neutral cation

6-311(+)G(d,p) IP-CCSD IP-CISD IP-CCSD IP-CISD

E µ2 E µ2 E µ2 E µ2

12A′ 0.642 0.000 0.335 0.000 1.144 0.000 0.785 0.000

22A′′ 1.037 0.000 0.848 0.000 1.779 0.000 1.557 0.000

22A′ 1.614 0.786 1.388 0.820 2.349 0.603 2.112 0.611

32A′′ 3.543 1.358 3.613 0.968 4.187 0.952 4.209 0.620

average abs. error 0.198 0.211

The changes in intramolecular parameters are reproduced by IP-CISD very well

— average absolute error in bond lengths for all three isomers is 0.01A. Note that

Jahn-Teller displacements in the t-shaped isomer are also accurately described. The

contraction of the interfragment distance is reproduced correctly, however, the distance

is overestimated. We interpret this by the absence of dispersion in uncorrelated Hartree-

Fock reference employed by IP-CISD. The absolute error is slightly larger owing to the

larger distance.

25

Tabl

e2.

5:T

hebo

ndle

ngth

s(

A),

angl

es(d

egre

es),

inte

rfra

gmen

tdi

stan

ces

and

slid

ing

disp

lace

men

ts(

A)

inth

egr

ound

stat

eof

thex

-dis

plac

ed,y

-dis

plac

edan

dt-

shap

edbe

nzen

edi

mer

catio

nsca

lcul

ated

with

IP-C

ISD

/6-3

1(+

)G(d

).F

orth

ex

-an

dy-

disp

lace

dst

ruct

ures

,ge

omet

ricpa

ram

eter

sfo

ron

lyon

eof

the

benz

ene

frag

men

tsar

epr

ovid

ed(t

hefr

agm

ents

are

equi

vale

ntby

sym

met

ry).

Abs

olut

eer

rors

ofIP

-CIS

Dre

lativ

eto

IP-C

CS

Dar

epr

esen

ted

inpa

rent

hesi

s.A

vera

geab

solu

teer

rors

are

calc

ulat

edus

ing

the

data

for

sym

met

ryun

ique

para

met

ers.

Par

amet

er(n

umbe

r)x

-dis

plac

edy-d

ispl

aced

t-sh

aped

(fra

gmen

t1)

t-sh

aped

(fra

gmen

t2)

CH

bond

rang

e1.

075

(0.0

13)

-1.

076

(0.0

14)

1.07

4(0

.014

)-

1.07

6(0

.013

)1.

073

(0.0

09)

-1.

077

(0.0

12)

1.07

5(0

.014

)

C1C

21.

373

(0.0

10)

1.38

5(0

.011

)1.

419

(0.0

10)

1.39

3(0

.012

)

C2C

31.

408

(0.0

11)

1.41

4(0

.011

)1.

376

(0.0

01)

1.38

7(0

.012

)

C3C

41.

400

(0.0

11)

1.38

4(0

.011

)1.

414

(0.0

11)

1.39

3(0

.012

)

C4C

51.

379

(0.0

10)

1.38

4(0

.011

)1.

414

(0.0

11)

1.39

3(0

.012

)

C5C

61.

400

(0.0

11)

1.41

4(0

.011

)1.

376

(0.0

01)

1.38

7(0

.012

)

C6C

11.

408

(0.0

11)

1.38

5(0

.011

)1.

419

(0.0

10)

1.39

3(0

.012

)

Ave

rage

abs.

erro

r0.

011

0.01

10.

007

0.01

2

C1C

2C

311

9.56

9(0

.032

)12

0.47

3(0

.009

)11

9.42

8(0

.018

)11

9.93

3(0

.009

)

C2C

3C

412

0.80

7(0

.026

)12

0.30

7(0

.010

)11

9.28

2(0

.096

)11

9.93

3(0

.009

)

C3C

4C

511

9.60

7(0

.012

)11

9.30

1(0

.041

)12

1.51

4(0

.120

)12

0.13

3(0

.015

)

C4C

5C

611

9.60

7(0

.012

)12

0.30

7(0

.010

)11

9.28

2(0

.096

)11

9.93

3(0

.009

)

C5C

6C

112

0.80

7(0

.026

)12

0.47

2(0

.010

)11

9.42

8(0

.018

)11

9.93

3(0

.009

)

C6C

1C

211

9.56

9(0

.032

)11

9.09

2(0

.051

)12

1.06

5(0

.108

)12

0.13

3(0

.015

)

Ave

rage

abs.

erro

r0.

023

0.02

00.

078

0.01

1

inte

rfr.

dist

ance

3.31

/3.0

83.

31/3

.07

4.81

/4.5

8

sl.

disp

lace

men

t1.

04/1

.07

1.03

/1.1

0-

26

2.4.3 Water dimer cation

Table 2.6 summarizes geometrical parameters (see Fig. 2.1) for the two lowest electronic

states of the water dimer cation. Selected bondlengths and angles are visualized in

Fig. 2.6. The errors for the intramolecular parameters are similar to those in uracil and

benzene dimers. The trends in intramolecular distances are similar to the benzene

dimer cations, however, in this case ionization introduces even stronger perturbation

to electronic structure and leads to the proton-transfer and formation of OH· · ·H3O+

complex, as evident from the value of O1H2 distance in Table 2.6. The OO bondlength

shortens by about 0.3A in the lowest ionized state relative to the neutral. The values of

the OO distance between the two lowest ionized states differ by about 0.06A. IP-CISD

reproduces these trends and structural differences between the different ionized states

correctly.

The absolute errors for the intermolecular parameters are slightly larger, e.g., 0.05-

0.06A for the OO distance, however, one should keep in mind that the value of this bond

is about 2.5A. As in the benzene dimer example, IP-CISD overestimates the intramolec-

ular distances.

An important result is that the errors of IP-CISD relative to IP-CCSD are not very

sensitive to the basis set, as one might expect in view of different amount of correlation

included in the latter. The absolute average errors in bondlengths for two electronic

states are 0.043, 0.044, 0.037 and 0.040A in the 6-311(+,+)G(d,p), 6-311(2+,+)G(d,p),

6-311(2+,+)G(2df) and aug-cc-pVTZ bases, respectively.

2.4.4 Timings

To demonstrate gains in computational cost, we present timings for IP-CCSD and IP-

CISD calculations of the uracil dimer on a Xeon 3.2 GHz Linux machine using parallel

27

Tabl

e2.

6:T

heIP

-CC

SD

bond

leng

ths

(A

)an

dan

gles

(deg

rees

)in

the

two

elec

tron

icst

ates

ofth

ew

ater

dim

erca

tion

and

abso

lute

erro

rs(in

pare

nthe

sis)

ofIP

-CIS

Dre

lativ

eto

IP-C

CS

Dca

lcul

ated

with

diffe

rent

base

s.

6-31

1(+

,+)G

(d,p

)6-

311(

2+,+

)G(d

,p)

6-31

1(2+

,+)G

(2df

)au

g-cc

-pV

TZ

Par

amet

er12A

′′12A

′12A

′′12A

′12A

′′12A

′12A

′′12A

′

H1O

10.

978(

0.01

2)0.

973(

0.01

0)0.

978(

0.01

2)0.

973(

0.01

0)0.

977(

0.01

2)0.

973(

0.01

0)0.

975(

0.01

0)0.

970(

0.00

8)

O1H

21.

425(

0.12

7)1.

525(

0.08

1)1.

423(

0.12

8)1.

522(

0.08

3)1.

526(

0.08

2)1.

592(

0.08

3)1.

429(

0.11

5)1.

519(

0.07

9)

H3O

20.

970(

0.01

4)0.

971(

0.01

5)0.

970(

0.01

4)0.

971(

0.01

5)0.

972(

0.01

6)0.

973(

0.01

5)0.

968(

0.01

3)0.

970(

0.01

4)

O2H

40.

970(

0.01

4)0.

971(

0.01

5)0.

970(

0.01

4)0.

971(

0.01

5)0.

972(

0.01

6)0.

973(

0.01

5)0.

968(

0.01

3)0.

970(

0.01

4)

O1O

22.

475(

0.08

2)2.

532(

0.06

0)2.

474(

0.08

2)2.

529(

0.06

2)2.

549(

0.05

4)2.

592(

0.06

2)2.

478(

0.07

4)2.

524(

0.06

1)

H1O

1H

212

3.71

3(6.

795)

176.

809(

0.52

2)12

3.48

5(6.

881)

176.

520(

0.67

1)12

6.14

1(2

.966

)17

6.85

8(0

.671

)12

0.55

3(6.

235)

177.

434(

0.16

9)

H3O

2H

410

9.87

4(2.

495)

111.

259(

2.27

9)10

9.81

6(2.

517)

111.

187(

2.28

7)11

0.25

6(1

.302

)11

1.25

0(2

.287

)10

9.90

2(2.

287)

111.

147(

1.97

6)

Ave

rage

abs.

erro

rs

Bon

ds0.

050

0.03

60.

050

0.03

70.

036

0.03

70.

045

0.03

5

Ang

les

4.64

51.

400

4.69

91.

479

2.13

41.

479

4.19

81.

073

28

version (threaded over two processors) of the CCSD and EOM code (the Hartree-Fock

and integral transformation modules were not parallelized). The symmetry of the dimer

is C2, and two lowest states in each irrep were requested. In 6-31+G(d) basis (320

basis functions), the wall time for total (including SCF and integral transformation) IP-

CCSD and IP-CISD calculations was 5.82 and 1.50 hours, respectively. The IP-CISD

calculation in 6-311+G(2d,p) basis (480 basis functions) took only 10.5 hours.

2.5 Conclusions

The benchmark study of the novel configuration-interaction variant of EOM-IP-CCSD

method is reported. The method is naturally spin-adapted, variational, and size-

intensive. The computational scaling isN5, in contrast to theN6 scaling of EOM-

IP-CCSD, which results in significant computational savings. The performance of the

method was tested on the uracil cation (five electronic states), water dimer cation (two

electronic states), and three isomers of the benzene dimer cation (ground electronic

state). The results demonstrate that the equilibrium geometries of the ionized states are

reproduced reasonably well. Using symmetry unique parameters from these ten struc-

tures optimized in a modest basis set, we computed average absolute error and standard

deviation for bond lengths and angles relative to the IP-CCSD values. For bondlengths,

average absolute error and standard deviation are 0.014 and 0.007A, respectively, and

for angles — 0.255 and 0.264 degrees. It is informative to compare these numbers with

mean absolute errors and standard deviations of the HF and CCSD methods for well-

behaved closed-shell molecules relative to the experiment [7]. For bondlengths, the

CCSD/cc-pVTZ and CCSD/cc-pVDZ values are 0.0064/0.0066 and 0.0119/0.0076A,

respectively [7]. The HF errors and standard deviations in cc-pVTZ and cc-pVDZ are

0.0263/0.0223 and 0.0194/0.0225A, respectively [7]. Thus, IP-CISD structures are of

29

similar quality as HF geometries of closed-shell molecules. Inheriting limitations of the

underlying Hartree-Fock reference, IP-CISD systematically underestimates bondlengths

and overestimates interfragment distances. Most importantly, IP-CISD correctly repro-

duces structural changes induced by ionization and structural differences between dif-

ferent ionized states.

Molecular properties such as permanent and transition dipole moments and charge

distributions are reproduced very well demonstrating that IP-CISD wave functions are

qualitatively correct. Ionization energies cannot be computed by IP-CISD because of the

use of uncorrelated Hartree-Fock description of the neutral, however, energy differences

between the ionized states are of semi-quantitative accuracy (errors of about 0.3 eV

relative to IP-CCSD).

Our results suggest that IP-CISD is most useful as an economical alternative for

geometry optimization in the ionized systems. Using IP-CISD structures, more accurate

energy differences can be computed with more expensive IP-CCSD. Moreover, IP-CISD

wave functions may be employed as zeroth-order wave functions in subsequent pertur-

bative treatment.

2.6 Reference list

[1] W.J. Hehre, R. Ditchfield, and J.A. Pople, Self-consistent molecular orbital meth-ods. XII. Further extensions of gaussian-type basis sets for use in molecular orbitalstudies of organic molecules, J. Chem. Phys.56, 2257 (1972).

[2] R. Krishnan, J.S. Binkley, R. Seeger, and J.A. Pople, Self-consistent molecularorbital methods. XX. A basis set for correlated wave functions, J. Chem. Phys.72,650 (1980).

[3] T.H. Dunning, Gaussian basis sets for use in correlated molecular calculations. I.The atoms boron through neon and hydrogen, J. Chem. Phys.90, 1007 (1989).

30

[4] E.D. Glendening, J.K. Badenhoop, A.E. Reed, J.E. Carpenter, J.A. Bohmann, C.M.Morales, and F. Weinhold, NBO 5.0., Theoretical Chemistry Institute, Universityof Wisconsin, Madison, WI, 2001.

[5] P.A. Pieniazek, S.E. Bradforth, and A.I. Krylov, Charge localization and Jahn-Tellerdistortions in the benzene dimer cation, J. Chem. Phys.129, 074104 (2008).

[6] P.A. Pieniazek, S.A. Arnstein, S.E. Bradforth, A.I. Krylov, and C.D. Sherrill,Benchmark full configuration interaction and EOM-IP-CCSD results for prototyp-ical charge transfer systems: Noncovalent ionized dimers, J. Chem. Phys.127,164110 (2007).

[7] T. Helgaker, P. Jørgensen, and J. Olsen,Molecular electronic structure theory.Wiley & Sons, 2000.

31

Fig

ure

2.3:

Sel

ecte

dbo

ndle

ngth

sin

the

five

low

este

lect

roni

cst

ates

ofth

eur

acil

catio

n.T

heco

rres

pond

ing

valu

esof

the

neut

ral

are

show

nby

dash

edlin

es.

The

MO

sfr

omw

hich

elec

tron

isre

mov

edar

esh

own

for

each

stat

e.

1.33

1.34

1.35

1.36

1.37

1.38

1.39

1.40

1.41

CC(1) bond length, Angstrom

Ele

ctro

nic

Stat

e

IP-C

ISD

IP-C

CS

D

12A

˝

12A

´

22A

´

22A

˝

32A

˝

1.18

1.20

1.22

1.24

1.26

1.28

1.30

CO(1) bond length, Angstrom

Ele

ctro

nic

Sta

te

IP-C

ISD

IP-C

CSD

12A

˝

12A

´

22A

´

22A

˝

32A

˝

1.17

1.18

1.19

1.20

1.21

1.22

1.23

1.24

1.25

1.26

1.27

1.28

IP-C

ISD

IP-C

CS

D

CO(2) bond length, Angstrom

Ele

ctro

nic

Stat

e

12A

˝

12A

´

22A

´

22A

˝

32A

˝

1.33

1.34

1.35

1.36

1.37

1.38

1.39

1.40

1.41

1.42

1.43

CN(2) bond length, Angstrom

Ele

ctro

nic

Stat

e

IP-C

ISD

IP-C

CS

D

12A

˝

12A

´

22A

´

22A

˝

32A

˝

32

123.0

123.5

124.0

124.5

125.0

125.5

126.0

126.5

127.0

127.5

128.0

128.5

129.0

129.5

130.0

CN

C(2

) ang

le, D

egre

e

Electronic State

IP-CISD IP-CCSD

12A˝

12A´

22A´

22A˝32A˝

Figure 2.4: The CNC(2) angle in the five lowest electronic states of uracil cation.Dashed line shows the corresponding value at the geometry of neutral.

33

Fig

ure

2.5:

The

CC

bond

leng

ths

ofth

eth

ree

benz

ene

dim

erca

tion

isom

ers

inth

egr

ound

elec

tron

icst

ate

optim

ized

with

IP-C

ISD

/6-3

1(+

)G(d

)an

dIP

-CC

SD

/6-3

1(+

)G(d

).O

nly

the

valu

esof

the

sym

met

ryun

ique

para

met

ers

for

corr

espo

ndin

gsy

m-

met

ryno

n-eq

uiva

lent

frag

men

tsar

esh

own

1.37

0

1.37

5

1.38

0

1.38

5

1.39

0

1.39

5

1.40

0

1.40

5

1.41

0

1.41

5

1.42

0CC bond length, Angstrom

Par

amet

er

x-d

ispl

aced

isom

er, I

P-C

ISD

/6-3

1(+)

G*

x-d

ispl

aced

isom

er, I

P-C

CS

D/6

-31(

+)G

*

C1C

2C

2C3

C3C

4C

4C5

1.38

0

1.38

5

1.39

0

1.39

5

1.40

0

1.40

5

1.41

0

1.41

5

1.42

0

1.42

5

CC bond length, Angstrom

Para

met

er

y-d

ispl

aced

isom

er, I

P-C

ISD

/6-3

1(+)

G*

y-d

ispl

aced

isom

er, I

P-C

CS

D/6

-31(

+)G

*

C1C

2C

2C3

C3C

4

1.37

0

1.38

0

1.39

0

1.40

0

1.41

0

1.42

0

1.43

0


Par

amet

er

t-sh

aped

isom

er, f

ragm

ent 1

, IP

-CIS

D/6

-31(

+)G

* t-

shap

ed is

omer

, fra

gmen

t 1, I

P-C

CS

D/6

-31(

+)G

*

C1C

2C

2C3

C3C

41

21.

380

1.38

2

1.38

4

1.38

6

1.38

8

1.39

0

1.39

2

1.39

4

1.39

6

1.39

8

1.40

0

1.40

2

1.40

4


Par

amet

er

t-sh

aped

, fra

gmen

t 2, I

P-C

ISD

/6-3

1(+)

G*

t-sh

aped

, fra

gmen

t 2, I

P-C

CS

D/6

-31(

+)G

*

C1C

2C

2C3

34

60 80 100 120 140 160 180 2001.4

1.6

1.8

2.0

2.2

2.4

2.6

Bond

leng

th, A

ngst

rom

Number of basis functions

O1H2 / 12A'' / IP-CISD

O1O2 / 12A" / IP-CISD

O1H2 / 12A' / IP-CISD

O1O2 / 12A' / IP-CISD

O1H2 / 12A" / IP-CCSD

O1O2 / 12A" / IP-CCSD

O1H2 / 12A' / IP-CCSD

O1O2 / 12A' / IP-CCSD

60 80 100 120 140 160 180 200

110

120

130

140

150

160

170

180

Ang

le, D

egre

e


H1O1H2 / 12A" /IP-CISD

H3O2H4 / 12A" /IP-CISD

H1O1H2 / 12A' /IP-CISD

H3O2H4 / 12A' /IP-CISD

H1O1H2 / 12A" / IP-CCSD

H3O2H4 / 12A" / IP-CCSD

H1O1H2 / 12A' / IP-CCSD

H3O2H4 / 12A' / IP-CCSD

Figure 2.6: Selected bondlengths and angles in the two lowest electronic states of thewater dimer cation optimized with IP-CISD and IP-CCSD with different bases.

35

Chapter 3

The electronic structure, ionized states

and properties of the uracil dimers

3.1 Overview

The electronic structure and spectral properties of ionized uracil andπ-stacked and h-

bonded uracil dimers are characterized by EOM-IP-CCSD. In Sections 3.3.1 and 3.3.2

we discuss the electronic structure of uracil and uracil dimers, respectively. Section 3.3.3

presents the calculated vertical ionization energies for five lowest electronic states of the

monomer and ten lowest electronic states of the dimers. Special attention is given to

the monomer basis set effect (Section 3.3.3) as well as the proposed cost-saving energy-

additivity scheme (Section 3.3.3). Lastly, we present the electronic spectra of the two

uracil dimer cations calculated at the neutral and relaxed geometries (Section 3.3.4).


In all calculations of vertical IEs, we employ the uracil dimer structures presented in

Fig. 3.1 from the S22 set of Hobza and coworkers [1]. The monomer calculations are

carried out using the RI-MP2/cc-pVTZ optimized neutral’s geometry. For the calcula-

tions of IEs and electronic spectrum of the stacked uracil dimer at the cation geometry,

its structure was relaxed with DFT/6-311(+)G(d,p) with 50-50 functional (i.e., equal

mixture of the following exchange and correlation parts: 50% Hartree-Fock + 8 %

36

C2hC2

(a) (b)

Figure 3.1:π-stacking and hydrogen-bonding in DNA (top) and the geometries of thestacked (a) and hydrogen-bonded (b) uracil dimers.

Slater + 42 % Becke for exchange, and 19% VWN + 81% LYP for correlation). Differ-

ent isomers were located on the cation potential energy surface, e.g., the t-shaped and

stacked-like structures. Here we focus on just one of the stacked uracil dimer isomers.

37

The optimized structures and relative energies of the other isomers will be discussed

elsewhere [2].

IEs of the dimers and the monomer were calculated at the EOM-IP-CCSD level

using several Pople bases [3, 4], i.e., 6-31(+)G(d), 6-311(+)G(d,p), and others. In the

monomer calculations, we also employed the 6-31G(d) and 6-31+G(d) bases with a

modifiedd-function exponent (0.2 instead of 0.8) as in Ref. 10. The core orbitals were

frozen in the IE calculations.

Electronic spectra of the cations were computed at the EOM-IP-CCSD/6-31(+)G(d)

level. The monomer spectrum was also calculated with a bigger cc-pVTZ basis set [5].

The molecular structures and relevant total energies are given in the supplementary

materials of Ref. 25. All calculations were conducted using theQ-CHEM electronic

structure package [6].

3.3 Results and Discussion

3.3.1 Prerequisites: Electronic states and spectrum of the uracil

cation

We begin with a brief overview of the electronic structure of uracil. It is a planar closed-

shell molecule ofCs symmetry. The five lowest electronic states of the uracil cation

correspond to ionizations from the five MOs shown in Fig. 3.2. Among these orbitals,

there are twoπ orbitals ofa′′ symmetry corresponding to the C—C and C—O double

bonds of uracil; two orbitals ofa′ symmetry corresponding to the oxygen lone pairs,

and onea′′ orbital of a mixed character. The highest occupied molecular orbital isπCC .

Vertical IEs of the five lowest ionized states of uracil are presented in Table 3.1, and

the corresponding electronic spectrum of the uracil cation is shown in Fig. 3.2. The

38

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00.00

0.02

0.04

0.06

0.08

0.10

0.12

Osc

illat

or S

treng

th

Energy, eV

πCC / a''

lp(O2) / a'

lp(O) + lp(N) / a''

lp(O1) / a'

lp(N) + πCC+ πCO / a''

Figure 3.2: Electronic spectrum and relvant MOs of the uracil cation at the geometry ofthe neutral. The MO hosting the hole in the ground state of the cation is also shown (topleft). Dashed lines show the transitions with zero oscillator strength.

ground state of the cation corresponds toπCC (or 1a′′) orbital being singly occupied (the

corresponding orbital is shown in the picture). Four excited cation states are derived

from ionization from the1a′, 2a′′, 2a′ or 3a′′ orbitals. All four electron transitions are

symmetry allowed, but their intensity is different: the parallel (allowed inx, y-direction)

A′′ → A′′ transitions are intense and the perpendicular (allowed inz-direction)A′′ → A′

transitions are weak due to unfavorable orbital overlap. Overall, the calculated vertical

IEs (e.g., with cc-pVTZ) for the monomer are in agreement with the experimentally

determined values [7–9], with the exception of the32A′′ transition, for which the calcu-

lated IE value at 13 eV is outside the experimental range of 12.5-12.7 eV. This difference

is within the EOM-IP-CCSD error bars (0.2-0.3 eV). The absolute differences between

EOM-IP-CCSD/cc-pVTZ and CASPT2 IEs from Ref.10 are within 0.13-0.49 eV range

39

Table 3.1: Five lowest verical IEs (eV) of the uracil monomer calculated with EOM-IP-CCSD. The number of basis functions (b.f.) is given for each basis.

Basis b.f. 12A′′ 12A′ 22A′′ 22A′ 32A′′

6-31G(d) 128 9.13 9.75 10.17 10.75 12.71

6-31G(d)a 128 9.11 9.72 10.11 10.69 12.73

6-31(+)G(d) 160 9.38 10.05 10.44 11.03 12.95

6-31(+)G(d)a 160 9.28 9.92 10.30 10.92 12.88

6-31(2+)G(d) 192 9.39 10.05 10.45 11.03 12.95

6-311(+)G(d,p) 200 9.48 10.11 10.51 11.09 13.02

6-31(2+)G(d,p) 204 9.41 10.07 10.47 11.04 12.97

6-31(+)G(2d) 208 9.45 10.13 10.52 11.10 12.99

6-31(+)G(2d,p) 220 9.46 10.13 10.53 11.11 13.00

6-311(2+,+)G(d) 224 9.43 10.09 10.47 11.07 12.97

6-311(+)G(2d) 228 9.49 10.20 10.57 11.16 13.02

6-311(2+)G(d,p) 232 9.48 10.12 10.52 11.09 13.02

6-311(2+,+)G(d,p) 236 9.48 10.12 10.52 11.09 13.02

6-31(+)G(2df) 284 9.60 10.30 10.69 11.26 13.13

cc-pVTZ 296 9.55 10.21 10.62 11.17 13.08

Exp.b 9.45-9.6 10.02-10.13 10.51-10.56 10.90-11.16 12.50-12.70

CASPT2c 9.42 9.83 10.41 10.86 12.59a Modified d-orbital exponent.

b Experimental results are from Refs. 7–9c Empirically corrected (IPEA=0.25) CASPT2/ANO-L 431/21 from Ref. 10

and are slightly larger than the discrepancies between the EOM-IP-CCSD and the exper-

imental values. Note that the CASPT2 results shown in Table 3.1 are obtained using the

empirical IPEA correction [10], which improves the agreement with the experiment

(e.g., not IPEA corrected CASPT2 value [10] for the lowest IE is 9.22 eV, which is 0.23

eV below the experimental range).

3.3.2 Electronic structure of the uracil dimers

Fig. 3.3 displays the calculated Hartree-Fock MOs corresponding to the ten lowest ion-

ized states of the stacked uracil dimer and the corresponding ionization energies (IEs)

40

calculated with EOM-IP-CCSD/6-311(+)G(d,p). The ten highest occupied orbitals of

the stacked dimer are symmetric and antisymmetric combinations of the five highest

occupied FMOs. The biggest splitting (0.53 eV) is between the states derived from

bonding and antibonding combinations of theπ-like FMOs, whereas the combinations

of FMOs of the lone pair character are almost degenerate. As Fig. 3.4 shows, the elec-

9.14 9.6610.14 10.20

10.5210.47

11.07 11.0212.96

12.67

Orb

ital e

nerg

y

State energy

Figure 3.3: MOs and IEs (eV) of the ten lowest ionized states of the stacked uracil dimer.Ionization from the highest MO yields ground electronic state of the dimer cation, andionizations from the lower orbitals result in electronically excited states.

tronic structure of hydrogen-bonded dimer exhibits similar trends, i.e., the FMOs of

the same character are combined to produce bonding and anti-bonding DMOs. The

important difference is that the overlap between the FMOs is the biggest for the in-

plane orbitals, resulting in the biggest splitting for the DMOs formed from FMOs cor-

responding to the lone pairs on the two neighboring oxygens. Overall, the splittings are

smaller than in theπ-stacked dimer, i.e., the largest splitting is 0.35 eV, and the splittings

between the two lowest states is only 0.10 eV.

41

9.35 9.47

10.20

10.69

10.25

10.72

11.5511.19

12.83 12.95

Orb

ital e

nerg

y State energy

Figure 3.4: MOs and IEs (eV) of the ten lowest ionized states of the hydrogen-bondeduracil dimer. Ionization from the highest MO yields ground electronic state of the dimercation, and ionizations from the lower orbitals result in electronically excited states.

Note that the orbital splitting does not change state ordering in the dimers relative to

the monomer.

3.3.3 Vertical ionization energies of the monomer and the dimers

Monomer ionization energies, transition dipoles, and the basis set effects

We investigate the basis set effects using monomer IEs to choose an optimal basis

set for the dimer calculations. Basis set convergence is illustrated in Fig. 3.5. The

range of the experimental IEs is shown by the shaded areas. As one can see, beyond

the 6-311(+)G(d,p) basis the variations in IEs are less than 0.12 eV. The analysis of

42

the data in Table 3.1 leads to the following conclusions. Firstly, the triple-ζ qual-

ity basis is desirable, as double-ζ and triple-ζ IEs differ by up to 0.07 eV — com-

pare, for example, 6-31(2+)G(d,p) vs. 6-311(2+)G(d,p), and 6-31(+)G(2d) vs. 6-

311(+)G(2d) results. Secondly, the polarization on hydrogens and additional polar-

ization on heavy atoms have a noticeable effect on IEs: for example switching from

6-31(2+)G(d) to 6-31(2+)G(d,p) results in a just 0.02 eV change; yet the difference

between 6-311(2+,+)G(d) and 6-311(2+,+)G(d,p) values is 0.05 eV. Difference between

the 6-31(+)G(2df) and 6-31(+)G(2d) values is 0.17 eV. Lastly, adding diffuse func-

tions on hydrogens and extra diffuse functions on heavy atoms has a negligible effect

on IEs — compare, for example, 6-31(+)G(d) vs. 6-31(2+)G(d); 6-311(+)G(d,p) vs.

6-311(2+)G(d,p); and 6-311(2+)G(d,p) vs. 6-311(2+,+)G(d,p). Thus, we choose 6-

311(+)G(d,p) as an optimal basis for the dimers. The results with the modified d-orbital

exponent [10] do not show systematic improvement over the values obtained with the

standard polarization function. Overall, calculated vertical IEs for the monomer are in

agreement with the experimentally determined values, with the exception of the32A′′

transition, for which the calculated IE value at 13 eV is outside the experimental range

of 12.5-12.7 eV. The difference is within the EOM-IP-CCSD error bars (0.2-0.3 eV).

Another observation is that both the state ordering and the energy gaps between the

states do not depend on the basis set, i.e., the curves in Fig. 3.5 are almost parallel.

This suggests that cost-reducing energy-additivity schemes can be employed for the IE

calculations.

Finally, Table 3.2 contains monomer excitation energies and oscillator strengths

calculated with different bases ranging from 6-31(+)G(d) to cc-pVTZ. Interestingly, the

energies, transition dipole values and oscillator strengths change only slightly with the

basis set increase, and the 6-31(+)G(d) basis set appears to be sufficient for the transition

property calculations.

43

6-31G*

6-31(+)G*

6-311(+)G**

6-31(+)G(2d)

6-31(+)G(2df)

cc-pVTZ6-311G(2+,+)**

120 140 160 180 200 220 240 260 280 3009.0

9.5

10.0

10.5

11.0

11.5

12.0

12.5

13.0

X 2A''

1 2A'

2 2A''

3 2A'

4 2A''

Ioni

zatio

n en

ergy

, eV


Figure 3.5: Basis set dependence of the five lowest IEs of uracil. The shaded areasrepresent the range of the expertimental values.

Dimer IEs and the energy additivity scheme

The monomer results from Sec. 3.3.3 suggest to employ the 6-311(+)G(d,p) basis for

the dimer IE calculations together with energy-additivity schemes. Here we investi-

gate whether these results apply for the dimers, whose description may require a basis

larger than 6-311(+)G(d,p), i.e., augmented by additional diffuse functions, to accurately

describe theπ-stacking or hydrogen-bonding interaction.

Tables 3.3 and 3.4 contain calculated IEs for the ten lowest ionized states of the

stacked and hydrogen-bonded complexes, respectively. The IE data in Table 3.3 exhibit

similar basis set effects as in the monomer. Additional sets of diffuse functions on heavy

atoms or hydrogens have negligible effect on IEs, whereas extra polarization leads to

noticeable changes in IEs. Overall, the results from Tables 3.3 and 3.4 confirm that the

44

Table 3.2: Excitation energies, transition dipole moments and oscillator strengths of theelectronic transitions in the uracil cation calculated with EOM-IP-CCSD with differentbases.

Property Basis 12A′ 22A′′ 22A′ 32A′′

∆E, eV 6-31(+)G(d) 0.668 1.647 1.063 3.566

6-311(+)G(d,p) 0.642 1.614 1.037 3.543

cc-pVTZ 0.664 1.627 1.069 3.533

< µ2 >, a.u. 6-31(+)G(d) 0.0003 0.0000 0.7888 1.3419

6-311(+)G(d,p) 0.0003 0.0000 0.7859 1.3586

cc-pVTZ 0.0002 0.0000 0.7378 1.3306

f 6-31(+)G(d) 0.0000 0.0000 0.0205 0.1172

6-311(+)G(d,p) 0.0000 0.0000 0.0200 0.1180

cc-pVTZ 0.0000 0.0000 0.0193 0.1152

6-311(+)G(d,p) basis is indeed an optimal choice for the stacked dimer in terms of accu-

racy versus computational cost. Surprisingly, a single set of diffuse functions is suf-

ficient for adequate representation of the ionizedπ-stacked dimer, although additional

diffuse functions might become more important at shorter interfragment distances.

The stacked dimer IEs from Table 3.3 demonstrate that, similarly to the monomer,

the energy spacing between the ionized states remains almost constant in different bases,

thus suggesting that energy-additivity schemes can be employed.

IEs for the hydrogen-bonded dimer are collected in Table 3.4 and exhibit the same

trends as in the stacked dimer.

Finally, we describe a simple energy-additivity scheme for the dimer IE calculations.

As the IE curves remain parallel both in the monomer and dimer, we approximate the

target dimer IEs calculated with a large basis,IED,largeEOM−IP−CCSD, using the dimer IEs

calculated with a smaller basis,IED,smallEOM−IP−CCSD, and the monomer IEs calculated with

the large and small bases (IEM,largeEOM−IP−CCSD andIEM,small

EOM−IP−CCSD, respectively):

45

Tabl

e3.

3:Te

nlo

wes

tver

tical

IEs

(eV

)of

the

stac

ked

urac

ildi

mer

calc

ulat

edw

ithE

OM

-IP

-CC

SD

.

Sta

te6-

31G

(d)

6-31

(+)G

(d)

6-31

(2+

)G(d

)6-

31(2

+)G

(d,p

)6-

311(

+)G

(d,p

)6-

311(

++

)G(d

,p)

6-31

1(2+

)G(d

,p)

X2B

8.81

9.03

9.04

9.06

9.14

9.14

9.14

12A

9.31

9.56

9.56

9.59

9.66

9.66

9.66

22B

9.77

10.0

610

.06

10.0

710

.14

10.1

410

.14

22A

9.81

10.1

210

.12

10.1

310

.20

10.1

910

.19

32B

10.1

110

.38

10.3

910

.41

10.4

710

.47

10.4

7

32A

10.1

510

.44

10.4

410

.46

10.5

210

.52

10.5

2

42B

10.6

710

.94

10.9

410

.96

11.0

211

.02

11.0

2

42A

10.7

210

.99

10.9

911

.00

11.0

711

.06

11.0

6

52B

12.3

812

.61

12.6

112

.63

12.6

712

.69

12.6

8

52A

12.6

512

.88

12.8

812

.91

12.9

612

.96

12.9

6

b.f.

256

320

384

408

416

424

480

46

Table 3.4: Ten lowest verical IEs (eV) of the hydrogen-bonded uracil dimer calculatedwith EOM-IP-CCSD.

State 6-31G(d) 6-31(+)G(d) 6-311(+)G(d,p)

X2Au 9.01 9.26 9.35

12Bg 9.11 9.37 9.47

12Bu 9.84 10.13 10.20

12Ag 9.89 10.17 10.25

22Bg 10.37 10.62 10.69

22Au 10.35 10.65 10.72

22Bu 10.85 11.12 11.19

22Ag 11.20 11.49 11.55

32Au 12.53 12.76 12.83

32Bg 12.63 12.87 12.95

IED,largeEOM−IP−CCSD ≈ IED,small

EOM−IP−CCSD + (IEM,largeEOM−IP−CCSD − IEM,small

EOM−IP−CCSD)

(3.1)

As follows from the data from Tables 3.5 and 3.6, this scheme yields the results that

are very close to the exact calculation. All IEs estimated from the dimer 6-31(+)G(d)

values are within 0.01-0.02 eV from the full EOM-IP-CCSD/6-311(+)G(d,p) dimer

results for both complexes. This difference is negligible compared to the 0.2-0.3 eV

error bars of EOM-IP-CCSD. To rationalize the excellent performance of the energy-

additivity scheme, let us rewrite Eq. (3.1) separating the dimer and monomer terms as

follows:

IED,largeEOM−IP−CCSD − IED,small

EOM−IP−CCSD ≈ IEM,largeEOM−IP−CCSD − IEM,small

EOM−IP−CCSD

(3.2)

47

Table 3.5: Ten lowest verical IEs (eV) of the stacked dimer calculated with EOM-IP-CCSD/6-311(+)G(d,p) versus the energy-additivity scheme results estimated using 6-31(+)G(d).

State IED6−31(+)G(d) ∆IEM

6−311(+)−6−31(+)G(d) IED,estimated6−311(+)G(d,p) IED

6−311(+)G(d,p) Abs. Error

X2B 9.03 0.10 9.13 9.14 0.01

12A 9.56 0.10 9.66 9.66 0.00

22B 10.06 0.07 10.13 10.13 0.00

22A 10.12 0.07 10.19 10.19 0.00

32B 10.38 0.07 10.45 10.46 0.01

32A 10.44 0.07 10.51 10.52 0.01

42B 10.94 0.06 11.00 11.00 0.00

42A 10.99 0.06 11.05 11.05 0.00

52B 12.61 0.08 12.69 12.67 0.02

52A 12.88 0.08 12.96 12.96 0.00

Eq. (3.2) thus implies that the basis set correction is the same for the monomer, stacked

or hydrogen-bonded dimer and the splitting between the overlapping FMOs is well

reproduced even in a relatively small basis set, i.e., 6-31(+)G(d).

3.3.4 The electronic spectra of dimer cations

This Section compares the electronic spectra of the monomer and the dimer cations

calculated by EOM-IP-CCSD. The transitions are between the states of the cation cor-

responding to different orbitals being singly-occupied. Our best estimates, i.e., EOM-

IP-CCSD/6-311(+)G(d,p), show that stacking and hydrogen-bonding interactions lower

the first ionization energy of the dimer by 0.34 and 0.13 eV, respectively, relative to

uracil. The magnitude of the IE decrease in the stacked dimer is remarkably close to

that in benzene. Thus, the uracil dimers are ionized more easily than the monomer.

Another interesting observation is a relationship between the drop in IE and the degree

of initial hole localization. Since a larger IE drop is a consequence of better orbital over-

lap, the dimer configurations that ionize easier would feature more extensive initial hole

48

Table 3.6: Ten lowest vertical IEs (eV) of the hydrogen-bonded uracil dimer calculatedwith EOM-IP-CCSD/6-311(+)G(d,p) versus the energy-additivity scheme results esti-mated from 6-31(+)G(d).

State IED6−31(+)G(d) ∆IEM

6−311(+)−6−31(+)G(d) IED,estimated6−311(+)G(d,p) IED

6−311(+)G(d,p) Abs. Error

X2Au 9.26 0.10 9.36 9.35 0.01

12Bg 9.37 0.10 9.47 9.47 0.00

12Bu 10.13 0.06 10.19 10.20 0.01

12Ag 10.17 0.06 10.23 10.25 0.02

22Bg 10.62 0.07 10.69 10.69 0.00

22Au 10.65 0.07 10.72 10.72 0.00

22Bu 11.12 0.06 11.18 11.19 0.01

22Ag 11.49 0.06 11.55 11.55 0.00

32Au 12.76 0.07 12.83 12.83 0.00

32Bg 12.87 0.07 12.94 12.95 0.01

delocalization. This might have mechanistic consequences for the ionization-induced

processes in DNA, where different relative nucleobase configurations are present due to

structural fluctuations.

Electronic transitions in the dimers belong to the two different types, namely,

CR (charge resonance) and LE (local excitations). The former are derived from

the transitions between the bonding and anti-bonding DMOs, e.g., see Fig. 1.1 and

Eqns. (1.12),(1.13), and are unique for the ionized dimers. The latter are the transi-

tions between DMOs formed from different FMOs, and resemble the monomer transi-

tions. Another difference between the CR and LE transitions is that the transition dipole

moment of the former increases linearly with the fragment separation, whereas the LE

bands decay [11]. The strong sensitivity of the CR bands to the dimer geometry sug-

gests to employ these transitions as a spectroscopic probe of structure and dynamics in

ionizedπ-stacked and h-bonded systems.

49

Stacked uracil dimer cation

The calculated electronic spectrum of stacked dimer cation at the neutral’s geometry is

shown in Fig. 3.6; the corresponding excitation energies, transition dipoles and oscillator

strengths are provided in Table 3.7 The ground electronic state of the cation is12B (the

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00.00

0.02

0.04

0.06

0.08

0.10

Osc

illat

or S

treng

th

Energy, eV

b

a

b a b

a

b a

b

a

Figure 3.6: Vertical electronic spectrum of the stacked uracil dimer cation at the geom-etry of the neutral. Dashed lines show the transitions with zero oscillator strength. MOshosting the unpaired electron in final electronic state, as well as their symmetries, areshown for each transition. The MO corresponding to the initial (ground) state of thecation is shown in the middle.

respective singly-occupied orbital is shown). All nine arising transitions are allowed by

symmetry: the transitions of theB → A type are perpendicular, whereas theB → B

transitions are parallel with respect to the inter-fragment axis. The four most intense

bands correspond to the final electronic states12A, 32A, 52B and52A, the first one

giving rise to the CR band. Note that the intensity of the LE transitions between the

lone-pair like andπ-like orbitals remains very small.

50

Table 3.7: Oscillator strengths and transition dipole moments for the electronic transi-tions in the ionized stacked uracil dimer calculated with EOM-IP-CCSD/6-31(+)G(d) atthe geometry of the neutral.

Transition ∆E, eV < µ2 >, a.u. f

X2B → 12A 0.523 7.2917 0.0935

X2B → 22B 1.027 0.0028 0.0000

X2B → 22A 1.081 0.1503 0.0039

X2B → 32B 1.349 0.1141 0.0037

X2B → 32A 1.406 0.5170 0.0178

X2B → 42B 1.906 0.0023 0.0001

X2B → 42A 1.952 0.0052 0.0002

X2B → 52A 3.844 0.3530 0.0332

X2B → 52B 3.573 0.9990 0.0874

To estimate the effect of geometry relaxation of the cation on the spectrum, we also

computed the excitation spectrum at the relaxed dimer cation geometry. The correspond-

ing excitation energies, transition dipoles, and oscillator strengths are given in Table 3.8.

As in the benzene dimer cation, the optimized geometry of the uracil dimer cation fea-

tures shorter interfragment distance that facilitates more efficient orbital overlap.

Fig. 3.7 compares the spectra calculated at the neutral geometry and at the opti-

mized geometry of the cation. The intensity pattern is similar to the spectrum at the

neutral geometry: the most intense bands correspond to the final electronic states12A,

32A, 52B and52A. A significant increase (approximately threefold) in intensity of the

CR band is observed; LE band intensity increases for some electronic states (32A ) and

slightly decreases for the others (52B and52A). Overall, the excitation energies uni-

formly increase, with the shift being around 1.1 eV.

51

Table 3.8: Oscillator strengths and transition dipole moments for the electronic transi-tions in the ionized stacked uracil dimer calculated with EOM-IP-CCSD/6-31(+)G(d) atthe equilibrium geometry of the ionized dimer.

Transition ∆E, eV < µ2 >, a.u. f

X2B → 12A 1.60 6.6438 0.2601

X2B → 22B 2.08 0.0006 0.0000

X2B → 22A 2.10 0.0075 0.0003

X2B → 32B 2.48 0.0721 0.0044

X2B → 32A 2.63 0.4591 0.0295

X2B → 42B 3.09 0.0011 0.0000

X2B → 42A 3.09 0.0008 0.0000

X2B → 52A 4.88 0.1995 0.0238

X2B → 52B 4.60 0.7477 0.0842

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.00.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

0.28

Osc

illat

or S

treng

th

Energy, eV

Figure 3.7: Vertical electronic spectra of the stacked uracil dimer cation at two differentgeometries: the geometry of the neutral (bold lines) and the relaxed cation geometry(dashed lines). MOs hosting the unpaired electron in final electronic state are shown foreach transition.

52

Hydrogen-bonded uracil dimer cation

The spectrum of the hydrogen-bonded dimer at the geometry of neutral is presented in

Fig. 3.8. Comparison of this spectrum with the stacked dimer example instantly reveals

an important difference, i.e., smaller number of peaks with non-zero intensity owing to

higher symmetry of hydrogen-bonded complex. The ground electronic state of cation

is X2Au and theAu → Au andAu → Bu transitions are now forbidden by symmetry.

Two transitions derived from the allowed parallel transitions,Au → Ag, are also of zero

intensity in the spectrum. Three transitions of theAu → Bg type are the most intense,

among them theX2Au → 12Bg CR band. The CR band in h-bonded dimer appears

at 0.11 eV, which is 0.4 eV below that of theπ-stacked dimer, however, its oscillator

strength is only slightly smaller (0.076 vs. 0.094). The intensity of the CR transition is

lower than the most intense LE transition, i.e.,X2Au → 32Bg.

3.4 Conclusions

We charactarized the electronic structure of theπ-stacked and hydrogen-bonded uracil

dimer cations by EOM-IP-CCSD. We computed IEs corresponding to the ground and

electronically excited states of the cations and calculated transition dipoles and oscilla-

tor sthengths for the electronic transions between the cation states. The results of the

calculations are rationalized within DMO-LCFMO framework.

Similarly to the benzene dimer, theπ-stacking lowers the first IE by about 0.4 eV

vertically. The magnitude of the IE decrease correlates with the degree of initial hole

localization, as both depend on orbital overlap. Thus, the dimer configurations that

ionzie easier would feature a more delocalized hole.

Ionization changes the bonding from non-covalent to covalent, which induces sig-

nificant geometrical changes, e.g., fragments move closer to each other to maxmize the

53

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00.00

0.02

0.04

0.06

0.08

0.10

0.12

Osc

illat

or S

treng

th

Energy, eV

bu ag

bg

au bu ag au

au

bg

bg

Figure 3.8: Vertical electronic spectrum of the hydrogen-bonded uracil dimer cationat the geometry of the neutral. Dashed lines show the transitions with zero oscillatorstrength. MOs hosting the unpaired electron in final electronic state, as well as theirsymmetries, are shown for each transition. The MO corresponding to the initial (ground)state of the cation is shown in the middle.

orbital overlap. The electronic spectra of the ionized dimers feature strong CR bands

whose position and intensity is very sensitive to the structure: geometrical relaxation

in the π-stacked dimer blue-shifts the CR band by more than 1 eV and results in the

three-fold intensity increase. These properties of the CR transitions may be exploited

in pump-probe experiments targeting the ionization-induced dynamics in systems with

π-stacking interactions, e.g., DNA or RNA strands. The perturbation in the LE bands in

the dimer is also described. The hydrogen-bonded dimer features slightly less intense

CR bands at lower energies.

Benchmark calculations in a variety of basis sets show that 6-311(+)G(d,p) basis

yields sufficiently converged IEs, and that energy-additivity scheme based on dimer

54

calculations in a small 6-31(+)G(d) basis allows efficient and accurate evaluation of the

dimer IEs.

3.5 Reference list

[1] P. Jurecka, J.Sponer, J.Cerny, and P. Hobza, Benchmark database of accurate(MP2 and CCSD(T) compl ete basis set limit) interaction energies of small modelcomplexes, DNA base pairs, and amino acid pairs, Phys. Chem. Chem. Phys.8,1985 (2006).





[6] Y. Shao, L.F. Molnar, Y. Jung, J. Kussmann, C. Ochsenfeld, S. Brown, A.T.B.Gilbert, L.V. Slipchenko, S.V. Levchenko, D.P. O’Neil, R.A. Distasio Jr, R.C.Lochan, T. Wang, G.J.O. Beran, N.A. Besley, J.M. Herbert, C.Y. Lin, T. VanVoorhis, S.H. Chien, A. Sodt, R.P. Steele, V.A. Rassolov, P. Maslen, P.P. Koram-bath, R.D. Adamson, B. Austin, J. Baker, E.F.C. Bird, H. Daschel, R.J. Doerksen,A. Drew, B.D. Dunietz, A.D. Dutoi, T.R. Furlani, S.R. Gwaltney, A. Heyden, S.Hirata, C.-P. Hsu, G.S. Kedziora, R.Z. Khalliulin, P. Klunziger, A.M. Lee, W.Z.Liang, I. Lotan, N. Nair, B. Peters, E.I. Proynov, P.A. Pieniazek, Y.M. Rhee, J.Ritchie, E. Rosta, C.D. Sherrill, A.C. Simmonett, J.E. Subotnik, H.L. WoodcockIII, W. Zhang, A.T. Bell, A.K. Chakraborty, D.M. Chipman, F.J. Keil, A. Warshel,W.J. Herhe, H.F. Schaefer III, J. Kong, A.I. Krylov, P.M.W. Gill, M. Head-Gordon,Advances in methods and algorithms in a modern quantum chemistry programpackage, Phys. Chem. Chem. Phys.8, 3172 (2006).

55

[7] D. Dougherty, K. Wittel, J. Meeks, and S. P. McGlynn, Photoelectron spectroscopyof carbonyls. Ureas, uracils, and thymine, J. Am. Chem. Soc.98, 3815 (1976).

[8] S. Urano, X. Yang, and P.R. LeBrenton, UV photoelectron and quantum mechani-cal characterization of DNA and RNA bases: Valence electronic structures of ade-nine, 1,9-dimethylguanine, 1-methylcytosine, thymine and uracil, J. Mol. Struct.214, 315 (1989).

[9] G. Lauer, W. Schafer, and A. Schweig, Functional subunits in the nucleic acidbases uracil and thymine, Tetrahedron Lett.16, 3939 (1975).



56

Chapter 4

Ionization-induced structural changes

in uracil dimers and their spectroscopic

signatures

4.1 Overview

Ionization-induced structural changes and properties of the three representative isomers

of the ionized uracil dimer, i.e. the stacked, t-shaped and h-bonded, are characterized by

high-level electronic structure calculations. First we discuss the electronic structure of

the t-shaped isomer (Section 4.3.1). Then, the equilibrium geometries (Section 4.3.2),

energetics (Section 4.3.3), and electronic spectroscopy (section 4.3.4) are considered.

Finally, the benchmark results for density functional theory (DFT) with long-range cor-

rected functionals are presented in the Postscript.

4.2 Computational detais

We used EOM-IP-CCSD in calculations of IEs, electronic spectra, and dissociation ener-

gies of the dimers, whereas for geometry optimizations and frequencies we employed

IP-CISD andωB97X-D. IP-CISD with the 6-31(+)G(d) basis [1] was used to optimize

the SU+2 and HU+

2 (TS) structures. The TU+2 and HU+2 (PT) structures were optimized

with ωB97X-D and the 6-311(+)G(d,p) basis set [2].

57

For both the IP-CISD and DFT-D optimizations, tight convergence criteria were

enforced: the gradient and energy tolerance were set to3 · 10−5 and1.2 · 10−4 respec-

tively; maximum energy change was set to1·10−7. To ensure the accuracy of the DFT-D

optimizations we employed the extra-fine EML(99,590) grid.

We use the best available geometries for calculations of energy differences. The

choice of the geometries is described below. In calculations of vertical properties (i.e.,

at the equilibrium geometries of the neutral dimers) we used the geometries from the

S22 set of Hobza and coworkers [3]. The geometry of the t-shaped isomer was opti-

mized with the DFT-D as described above. To assess possible effect of the BSSE on

the structures, our study of adenine and thymine dimers [4] compared the B3LYP-D/6-

31+G(d,p) optimized structure of the stacked AT dimer versus the one from the S22

set [3]. We found that the interfragment distance differs from the BSSE-corrected RI-

MP2/TZVPP value [3] by only 0.076A. The increase of the basis set from 6-31+G(d,p)

to 6-311++G(2df,2pd) results in 0.004A increase in inter-fragment separation. Thus,

we do not expect significant BSSE effects on our optimized structures.

In monomer calculations, we used the structures of the uracil cation and the neutral

optimized by IP-CISD/6-31(+)G(d) and RI-MP2/cc-pVTZ, respectively, with the stan-

dard convergence thresholds (the gradient and energy tolerance3 · 10−4 and1.2 · 10−3

and maximum energy change1 · 10−6). In all optimizations of the symmetric structures

(i.e., all isomers, except for the TU02, TU+2 , and HU+

2 (PT)) the symmetry was enforced.

For the stacked dimer cation we carried out an additional DFT-D optimization without

theC2 symmetry constraint that showed that the minimum indeed corresponds to the

symmetric structure. In addition, vibrational analysis was also performed.

58

For the accurate energy estimates, single-point calculations were carried out at

the geometries obtained as described above. The IP-CCSD method with the 6-

311(+)G(d,p) basis was employed. For benchmark purposes, we also presentωB97X-

D/6-311(+)G(d,p)/EML(99,590) estimates calculated at the respective DFT-D minima.

The performance of different methods is discussed in the Postscript.

While the BSSE corrections can be substantial for weakly-bound systems when

compact basis sets are employed [3, 5, 6], using augmented triple-zeta bases reduces

the BSSE considerably. Moreover, empirical dispersion correction in DFT-D methods

mitigates the BSSE. For example, the counterpoise correction for binding energy in

the stacked adenine-thymine dimer at the B3LYP-D/6-311+G(2df) is only 1.4 kcal/mol

[4,7].

For the neutral stacked uracil dimer, theωB97X-D and CCSD values ofDe are 10.5

and 11.1 kcal/mol (with the 6-311(+)G(d,p) basis set), in a good agreement with the

CCSD(T)/CBS value of 9.7 kcal/mol [8]. Thus, the BSSE effects are relatively small

at theωB97X-D/6-311(+)G(d,p) level even for the most problematic neutral stacked

dimers. In the ionized systems, which are much stronger bound, the effect of BSSE on

the binding energy should be even smaller. To quantify this, we computed the counter-

poise correction for the stacked uracil dimer cation. The computed BSSE is 1.3 kcal/mol

as estimated at theωB97X-D level with 6-311(+)G(d,p) basis set.

To obtain the standard thermodynamic quantities and the ZPE corrections, we per-

formed the vibrational analysis at theωB97X-D/6-311(+)G(d,p)/EML(99,590) level for

all complexes at the respective reoptimized geometries.

The electronic spectra of the dimer cations were obtained with IP-CCSD/6-

31(+)G(d) at the cation and neutral geometries described above.

59

All open-shell DFT-D calculations employed the spin-unrestricted references. In

these calculations, the spin-contamination of the doublet Kohn-Sham determinant was

low with the typical〈S2〉 values of 0.76 - 0.78.

All electrons were correlated in all the optimizations; in the single-point energy

and spectra calculations the core electrons were frozen unless otherwise stated. The

optimized geometries, corresponding reference energies and frequencies are provided

in the Supplementary Materials of Ref. 101.

Throughout this work, we use the following notations for the isomers: HU2, SU2 and

TU2 refer to the h-bonded, stacked and t-shaped isomers, respectively. For the hydrogen-

bonded cations, we distinguish between the symmetric structure, which is a transition

state (TS), and a proton-transferred one (PT) corresponding to the true minimum.

4.3 Results and discussion

4.3.1 Molecular orbital framework

The character of electronic states and the bonding patterns in ionized non-covalent

dimers depend strongly on the relative orientation of the fragments [4, 9–12]. Orbital

overlap and electrostatic interactions are the most important factors determining the

degree of hole delocalization, changes in bond strength due to ionization, and subse-

quent nuclear dynamics. When the two fragments are equivalent by symmetry, as in

sandwich benzene dimers [9] or stackedC2 nuclear base dimers [4,11], the dimer states

are derived from in-phase (bonding) and out-of-phase (antibonding) combination of the

fragments MOs, and the initial hole is equally delocalized between the two fragments.

The changes in IE due to dimerization depend on the orbital overlap, e.g., larger changes

are observed for the states derived from ionizations ofπ orbitals [4, 9, 11]. Ioniza-

tions from anti-bonding orbitals increase formal inter-fragment bond order, and produce

60

tighter-bound structures, whereas ionizations from the bonding orbitals result in disso-

ciative states.

Orbital picture, changes in vertical IEs and initial hole delocalization are similar in

symmetric hydrogen bonded dimers, however, the ionization-induced dynamics is more

complex and involves proton transfer [4, 13]. The changes in vertical IEs are smaller

for most of the states due to a less favorable overlap. In dimers with non-equivalent

fragments, the MOs (and, consequently, the initial hole) become more localized, how-

ever, changes in IEs and wave functions can also be explained by overlap considerations

within DMO-LCFMO framework [10, 12]. Finally, in non-symmetric h-bonded dimers

electrostatic interactions become more important than orbital overlap. For example, we

observed large changes (0.4-0.7 eV) in IEs and binding energies in some non-symmetric

hydrogen-bonded dimers of thymine and cytosine [4,13]. In these dimers, the hole local-

ized on one of the fragments is stabilized by the dipole moment of the neutral fragment.

The electronic structure of the stacked and symmetric h-bonded uracil dimers at the

respective neutral geometries was discussed in detail in Ref. 11. Below we focus on

the t-shaped isomer. The principal difference between the t-shaped and the stacked or h-

bonded structures is that in the former the two fragments are not equivalent by symmetry,

which affects its electronic structure. The ten lowest ionized states of the t-shaped uracil

dimer and the corresponding MOs are presented in Figure 4.1. As in the stacked and

h-bonded systems, the dimer MOs are formed from the MOs of the fragments, and the

ionized states of the dimer correlate well with the states of the monomer (i.e., no mixing

of the MOs of different character is observed). For example, the two highest-lying MOs

are the linear combinations of theπCC MOs of the fragments. However, the MOs of

the t-shaped dimer are more localized. For example, thelp(O) MO of the dimer is a

localizedlp(O) orbital of one of the fragments. For the four delocalized dimer orbitals

(formed by theπCC and lp(O) + lp(N) fragment orbitals) the distribution of electron

61

Ioni

zatio

n En

ergy

, eV

9.13 9.24

9.839.94

10.1410.28

10.7110.87

12.6712.72

Figure 4.1: The ten lowest ionized states of the t-shaped uracil dimer at the neutralgeometry calculated with the IP-CCSD/6-311(+)G(d,p).

density is also uneven. Owing to a less favorable overlap between the fragment MOs,

the splittings between the pairs of ionized states in the t-shaped dimer is smaller. The

largest splitting of 0.14 eV was observed for the dimer states derived from from the

π-like lp(O) + lp(N) fragment orbitals.

Despite less efficient overlap and smaller splittings between the pairs of states

derived from the same FMOs, the absolute changes in IEs in this isomer are similar

to those in the stacked dimer. For example, the lowest IE of this isomer is 9.13 eV.

This value is red-shifted by 0.35, 0.22 and 0.01 eV relative to the 1st IE of the monomer,

symmetric h-bonded andπ-stacked dimers, respectively. This is similar to large changes

in IEs observed in the non-symmetric h-bonded dimers of thymine and cytosine, where

lowering of IE was due to electrostatic stabilization of the localized hole by the dipole

moment of the “neutral” fragment. The dipole moment of uracil is 4.19 D, which is

comparable to the dipole moment of thymine (4.11 D).

62

4.3.2 Ionization-induced structural changes: Equilibrium geome-

tries of the uracil dimer cations

Ionization induces significant structural changes in the dimers, as can be seen from Fig-

ure 4.2. In the analysis below, we distinguish between the changes in the structures of

the fragments (and compare those to ionization-induced changes in the monomer) and

the inter-fragment relaxation. The definitions of parameters are given in Figure 4.3,

and their values are summarized in Tables 4.1 and 4.2. Only the symmetry-unique

parameters are given. First, let us consider the effect of ionization on intra-fragment

parameters (see Table 4.1) and compare the monomer and the symmetric dimer cations

data. The magnitude of relaxation in the monomer is larger than in the stacked and

h-bonded dimers. For instance, the C5C6 bond increases by 0.043A in the monomer

versus 0.018A and 0.002A in the stacked and h-bonded dimers, respectively. The sign

of the change in the monomer and the symmetric dimers is the same for all the parame-

ters, which is consistent with the DMO-LCFMO picture. The magnitude of the changes

is smaller in the dimers because the hole is delocalized over the two fragments. In the

non-symmetric dimers, the fragments are not equivalent and the orbital picture is more

complicated. The hole is distributed unevenly between the two fragments, such that the

positive charge is localized on one of them. Comparing the data presented in Table 4.1

for the h-bonded proton-transfered and the t-shaped dimer cations with the monomer, we

observe that the structural changes of Fragment 1 of HU+2 (PT), Fragment 2 of TU+2 and

the monomer cation are very similar. For instance, the C5C6 bond increases by 0.057,

0.050 and 0.043A in Fragment 1 of HU+2 (PT), Fragment 2 of TU+2 and the monomer

cation, respectively. Thus, one of the fragments in non-symmetric dimers relaxes simi-

larly to the monomer cation, while the other adjusts accordingly. This is similar to the

t-shaped benzene dimer [10].

63

Tabl

e4.

1:T

heva

lues

ofop

timiz

edst

ruct

ural

para

met

ers

(A

,D

egre

e)of

the

frag

men

tsin

the

stac

ked,

h-bo

nded

,h-

tran

sfer

edh-

bond

edan

dt-

shap

edur

acil

dim

erca

tions

.T

hedi

ffere

nces

(A

,D

egre

e)w

.r.t.

the

equi

libriu

mge

omet

ryof

the

resp

ectiv

ene

utra

lco

mpl

exar

eal

sogi

ven

show

ing

the

ioni

zatio

n-in

duce

dch

ange

sin

geom

etry

.S

eeF

ig.

4.3

for

the

defin

ition

sof

the

para

met

ers.

Par

amet

erS

U+ 2H

U+ 2

(TS

)H

U+ 2

(PT

),F

1H

U+ 2(P

T),

F2

TU+ 2

,F1

TU

+ 2,F

2U

+

C4C

51.

461

+0.

010

1.46

1+

0.01

11.

461

+0.

011

1.45

8+

0.00

81.

431

-0.0

261.

475

+0.

024

1.45

7+

0.01

1

C5C

61.

367

+0.

018

1.35

2+

0.00

21.

407

+0.

057

1.33

7-0

.013

1.35

3+

0.01

11.

392

+0.

050

1.38

6+

0.04

3

C6N

11.

330

-0.0

381.

352

-0.0

171.

310

-0.0

591.

391

+0.

022

1.35

7-0

.012

1.32

4-0

.045

1.31

6-0

.049

N1C

21.

405

+0.

023

1.37

9+

0.01

21.

411

+0.

044

1.33

2-0

.035

1.38

9-0

.002

1.42

9+

0.04

41.

433

+0.

053

C2N

31.

368

-0.0

141.

349

-0.0

221.

363

-0.0

081.

331

-0.0

401.

401

+0.

023

1.37

7-0

.003

1.35

7-0

.017

N3C

41.

384

-0.0

171.

399

-0.0

081.

400

-0.0

071.

438

+0.

031

1.36

5-0

.032

1.38

4-0

.007

1.38

7-0

.010

C4O

21.

198

-0.0

241.

190

-0.0

281.

204

-0.0

141.

194

-0.0

241.

257

+0.

041

1.20

6-0

.014

1.19

5-0

.020

C2O

11.

182

-0.0

341.

208

-0.0

231.

216

-0.0

151.

287

+0.

056

1.19

5-0

.012

1.19

0-0

.017

1.17

8-0

.034

C4C

5C

611

9.3

-0.5

119.

5-0

.111

9.4

-0.2

120.

4+

0.7

118.

4-1

.111

9.5

+0.

3119

.7-0

.1

C5C

6N

112

1.0

-0.9

121.

1-1

.512

3.1

+0.

612

1.8

-0.7

121.

9+

0.2

120.

1-1

.811

9.4

-2.6

C6N

1C

212

4.3

+0.

812

3.4

+0.

912

0.1

-2.4

121.

0-1

.512

3.7

+0.

212

4.9

+1.

4125

.5+

2.0

N1C

2N

311

3.8

+0.

811

5.4

+1.

111

8.2

+3.

911

8.8

+4.

511

2.9

-0.6

113.

5+

0.41

13.6

+0.

8

C2N

3C

412

6.9

-1.2

126.

3-1

.812

5.5

-2.6

125.

5-2

.612

6.2

-1.1

127.

0-0

.412

6.2

-2.4

N3C

4C

511

4.7

+1.

311

4.3

+1.

411

3.7

+0.

811

2.5

-0.4

116.

9+

2.5

114.

7+

0.21

15.7

+2.

4

Σ(a

ngle

)71

9.9

+0.

3–

––

720.

0+

0.0

719.

7+

0.1

720.

0+

0.0

64

Figure 4.2: The geometries of the cations versus the respective neutrals for the threeuracil dimer isomers .

SU20

C2C2

SU2+

TU2+ TU2

0

C1 C1

Cs

HU2+

C2h

HU20

C2h

65

Figure 4.3: The definitions of the intra- and inter-fragment geometric parameters foruracil dimer isomers.

N12

3

4

5

6

1

C2

N3

C4C5

C6

O1

O2

H2

H1

O2N1

C5C6

F2F1O2H1

O1H1

F2H2O2

O2C5 O2C6

F1

The ionization-induced changes in the inter-fragment parameters (given in Table 4.2)

and the MOs (shown in Fig. 4.4) are consistent with the DMO-LCFMO predictions —

the fragments adjust their relative orientation to maximize the overlap between their

HOMOs (πCC). The change in the MOs is illustrated in Figure 4.4 depicting HOMOs

at the neutral and the cation geometries. In the stacked dimer, the twoπCC FMOs give

rise to the efficient overlap lending a partial covalent character to the ionized dimer.

In the t-shaped dimer, the changes in HOMO are different. Upon relaxation, the hole

becomes more localized on the lower fragment, and the only contribution to the overlap

66

Tabl

e4.

2:T

heva

lues

ofin

ter-

frag

men

tstr

uctu

ralp

aram

eter

s(

A,D

egre

e)of

the

stac

ked,

h-bo

nded

,h-t

rans

fere

dh-

bond

edan

dt-

shap

edur

acil

dim

erca

tions

.T

hedi

ffere

nces

(A

,Deg

ree)

w.r.

t.th

eeq

uilib

rium

geom

etry

ofth

ere

spec

tive

neut

ralc

ompl

exes

are

give

nin

pare

nthe

sis.

See

Fig

.4.3

for

the

defin

ition

sof

the

para

met

ers.

SU

+ 2H

U+ 2

(TS

)H

U+ 2

(PT

)T

U+ 2

C5C

63.

299

(-0.

451)

O1H

11.

828

(+0.

053)

O1H

11.

749

(-0.

026)

H2O

22.

000

(+0.

072)

O2N

13.

116

(-0.

175)

O2H

11.

828

(+0.

053)

O2H

11.

018

(-0.

757)

O2C

52.

178

(-1.

099)

O2C

62.

701

(-0.

950)

α18

.4(+

5.6)

––

–

d3.

51(+

0.34

)–

––

67

Figure 4.4: Two highest occupied MOs of the three isomers of the uracil dimer at theneutral and cation geometry.

SU20 SU2

+

HU20

HU2+ (TS)

HU2+(HT)

TU20 TU2

+

68

is due to the the oxygen lone pair of the top fragment pointing towards theπCC MO of

the lower one.

The magnitude of the relaxation is quantified by Table 4.3, which presents the dif-

ferences in the total energies between the relaxed and vertical structures of the dimer

cations calculated by EOM-IP-CCSD/6-311(+)G(d,p). For the t-shaped, stacked and

h-bonded isomers,∆ECCSD is -12.71, -6.48 kcal/mol, and -0.64 kcal/mol respectively.

Such a large relaxation effect in the t-shaped cation is somewhat surprising, as from

Figure 4.4 the FMOs overlap more efficiently in the stacked dimer. The reason is the

electrostatic interaction of the lone pair on oxygen of Fragment 1 and the hole on the

Fragment 2, which stabilizes the t-shaped structure [4]. The inter-fragment parame-

Table 4.3: Total (Etot, hartree) and dissociation (De, kcal/mol) energies of the fourisomers of the uracil dimer in the neutral and ionized states computed by CCSD/IP-CCSD with 6-311(+)G(d,p). Relevant total energies of the uracil monomer are alsogiven. The relaxation energies (∆E, kcal/mol) defined as the difference in total energiesof the cation at the neutral and relaxed cation geometries are also shown. For HU+

2 (PT)dissociation energies corresponding to the U0 + U+ / (U - H)0 + UH+ channels are given.

Complex ECCSDtot DCCSD

e ∆ECCSD

U0 -413.882 346 – –

U+ -413.542 383 – -5.41

UH+ -414.209 422 – –

(U-H)0 -413.212 558 – –

SU02 -827.782 419 11.1 –

SU+2 -827.456 874 20.2 -6.48

HU02 -827.793 226 17.9 –

HU+2 (TS)a -827.450 565 16.2 -0.64

HU+2 (PT)b -827.475 648 32.0/33.7 –

TU02 -827.779 232 9.1 –

TU+2 -827.463 991 24.6 -12.71

a Transition state.b Proton-transferred structure, UH+(U–H)˙.

69

ters presented in Table 4.2 are consistent with the MO changes. In the stacked dimer

cation, the fragments slide with respect to each other, so the overlap of FMOs centered

on C5, C6, N1 and O2 atoms increases (see Figure 4.4). The C5C6 and O2N1 distances

decrease by 0.451 and 0.175A, respectively. Surprisingly, the distance between the

centers-of-masses of the fragments increases by 0.34A in the cation with respect to the

neutral. This illustrates that the average geometric parameters in polyatomic systems

can be misleading.

In the t-shaped cation, the fragments move to minimize the distance between the lone

pair on O2 of the top fragment and theπCC MO of the bottom one. The characteristic

parameters in this case are the O2C5 and O2C6 distances, which decrease by 1.099 and

0.950A, respectively.

In the symmetric h-bonded dimer, the structural changes and, consequently, relax-

ation energy are small. As one can see from Figure 4.4, there is also no significant

changes in MOs upon relaxation due to unfavorable orbital overlap. Moreover, this

symmetric structure is a transition state, as shown by the vibrational analysis discussed

later. Much larger stabilization is achieved by a proton transfer, which lowers the total

energy by 15.7 kcal/mol making the proton-transfered h-bonded isomer the lowest-

energy structure on the cation’s PES.

4.3.3 Binding energies of the neutral and ionized uracil dimers:

Potential and free energy calculations

Potential energy profile

Figures 4.5 and 4.6 present the relative ordering and binding energies of the neutral and

ionized uracil dimers calculated by IP-CCSD andωB97X-D with the 6-311(+)G(d,p)

basis. In the neutral, the symmetric h-bonded uracil dimer is the minimum energy

70

HU20

SU20

TU20

C1

C2h

C2

-De, kcal/mol

De = 17.9 / 19.4

De = 11.1 / 10.5

De = 9.1 / 8.3

Figure 4.5: The binding energies (kcal/mol) of the three isomers of neutral uracil dimercalculated at two levels of theory: IP-CCSD/6-311(+)G(d,p) (bold) andωB97X-D/6-311(+)G(d,p) (italic).

isomer, with the stacked and t-shaped dimers lying 6.8 and 8.8 kcal/mol higher in

energy. Excluding the proton-transferred dimer, the lowest-energy cation structure is the

t-shaped one. The energy spacing between the t-shaped and the stacked and h-bonded

cations is 4.4 and 8.4 kcal/mol, respectively. Upon the proton transfer the total energy

of the h-bonded cation is lowered by 15.8 kcal/mol, so that it lies 7.4 kcal/mol below

than the t-shaped cation.

The calculated binding energies for the h-bonded, stacked and t-shaped neutral

dimers are 17.9, 11.1 and 9.1 kcal/mol, respectively. The DFT-D and CCSD values

are within 1 kcal/mol from each other. TheDe for the stacked and h-bonded isomer are

also in good agreement with the recent CCSD(T)/CBS values of 20.4 and 9.7 kcal/mol

from Ref. 8.

Note that the interaction of the fragments in the neutral uracil dimers is much

stronger than in the benzene dimers, where the typical interaction energies lie in range

71

TU2+

C1

SU2+

C2 HU2+(TS)

C2h

HU2+(PT)

Cs

-De, kcal/mol

De = 24.6 / 27.0

De = 20.2 / 24.2

De = 16.2 / 20.2

De = 32.0 / 31.2De′ = 33.7 / 38.2

Figure 4.6: The binding energies (kcal/mol) of the three isomers of uracil dimer cationcalculated at two levels of theory: IP-CCSD/6-311(+)G(d,p) (bold) andωB97X-D/6-311(+)G(d,p) (italic). For the proton-transfered h-bonded uracil dimer cation, the bind-ing energies corresponding to the two dissociation limits are presented.

of 1.5-3.0 kcal/mol for all isomers [14, 15]. The binding energies increase upon ion-

ization, in agreement with the DMO-LCFMO predictions. In the t-shaped, stacked and

symmetric h-bonded cations the fragments are bound by 24.6, 20.2 and 16.2 kcal/mol,

respectively. For comparison, in the benzene dimer cation the binding energies are 20

and 12 kcal/mol for the sandwich and t-shaped isomers, respectively [9, 10]. However,

the strongest interaction is observed in the proton-transfered h-bonded cation, where the

binding energy corresponding to the U0+U+ dissociation channel is 32.0 kcal/mol (this

channel lies 1.8 kcal/mol below an alternative (U-H)0+UH+ channel).

In conclusion, when the uracil dimer is ionized the interaction between the fragments

increases almost two-fold for the stacked and h-bonded isomers and more than two-fold

for the t-shaped isomer. Such a strong increase in interaction in the t-shaped structure

is very different from the benzene dimer cation and can be explained by electrostatic

72

interactions rather than orbital overlap considerations. The h-bonded isomer is stabilized

by the proton transfer.

Free energy profile

It has been argued that the entropy contribution to the stability can be important in the

nucleobase dimer systems favoring stacked isomers over h-bonded ones [16]. Thus, we

performed the vibrational analysis usingωB97X-D. Moreover, we wanted to quantify

the zero point energy (ZPE) corrections to the dissociation energies. The calculated

dissociation energies and the standard thermodynamic quantities for the dissociation of

the neutral and the ionized dimers are given in Table 4.4.

Table 4.4: The dissociation energies (kcal/mol) and standard thermodynamic quantitiesof the neutral and the cation uracil dimers calculated at theωB97X-D/6-311(+)G(d,p)level. For the proton-transfered cation the values corresponding to the two differentdissociation limits are given.

Reaction De D0 ∆H0, kcal/mol ∆S0, cal/mol×K ∆G0, kcal/mol

SU02 → U0 + U0 10.5 9.8 8.4 31.5 -1.0

SU+2 → U0 + U+ 24.4 22.7 20.9 40.4 8.8

HU02 → U0 + U0 19.4 18.2 16.8 38.1 5.4

HU+2 (TS)→ U0 + U+ 20.2 21.8 23.2 40.5 11.1

HU+2 (TS)→ HU+

2 (PT) 11.0 13.1 -8.8 2.7 -9.6

HU+2 (PT)→ U0 + U+ 31.2 30.6 -0.7 37.7 18.7

HU+2 (PT)→ (U −H)0 + UH+ 38.2 37.0 -1.3 38.6 24.2

TU02 → U0 + U0 8.3 7.6 6.2 29.6 -2.6

TU+2 → U0 + U+ 27.0 25.1 23.0 38.8 11.4

Among the neutral uracil dimers, only the h-bonded isomer is predicted to be stable

under the standard conditions (∆G0 = 5.4 kcal/mol). Standard Gibbs free energies,

∆G0, of the stacked and t-shaped are -1.0 and -2.6 kcal/mol, respectively. The data in

Table 4.4 shows that the entropy contribution is similar for all three isomers:∆S0 of

dissociation is 31.5, 38.1 and 29.6 cal/mol×K for the stacked, h-bonded and t-shaped

73

isomers, respectively. However, more appropriate treatment including anharmonicities

may discriminate between the isomers more. The enthalpy contribution is different: for

the h-bonded uracil dimer the enthalpy of dissociation is 16.8 kcal/mol, whereas the

corresponding values for the stacked and t-shaped isomers are 8.4 and 6.2 kcal/mol,

respectively.

Unlike neutrals, all of the dimer cation isomers are stable under the standard con-

ditions. The most stable isomer is the proton-transfered h-bonded cation with∆G0 of

18.7 kcal/mol. In order of the decreasing stability, the proton-transferred dimer is fol-

lowed by the t-shaped, symmetric h-bonded (TS) and the stacked isomers. Again, the

∆S0 values are very close for all of the isomers being 40.4, 40.5, 37.7 and 38.8 for

SU+2 , HU+

2 (TS), HU+2 (PT) and TU+

2 , respectively, whereas the∆H0 contributions are

different.

Thus, we conclude that the enthalpy determines the relative stability of the neutral

and ionized uracil dimers to a high degree, while the entropy contribution has a less

pronounced effect.

Lastly, the ZPE corrections lower the dissociation energy estimates by 0.6–1.9

kcal/mol for all the neutral and ionized dimers, except for the symmetric h-bonded

dimer. In the symmetric h-bonded dimer, the ZPE correction has the opposite sign

and increases the dissociation energy by 1.6 kcal/mol, which is because this structure is

a transition state with one imaginary frequency.

4.3.4 The electronic spectra of the uracil dimer cations

This section presents the calculated electronic spectra of the uracil dimer cations.

The spectra of the stacked and h-bonded isomers at the geometry of the neutral were

74

described in a detail in the previous work [11], therefore, we focus on the effect of geom-

etry relaxation on the spectroscopic properties. For the h-bonded dimer, we present the

spectra of both the symmetric (TS) and the proton-transfered structures.

Figures 4.7-4.9 present the electronic spectra of the stacked, h-bonded and t-shaped

uracil dimers, respectively, calculated by IP-CCSD/6-31(+)G(d) at the neutral and the

cation geometries. Figures 4.7-4.9 also show the character of the electronic states cor-

responding to the three most intense transitions in each spectra. The transition energies,

transition dipole moments and oscillator strengths are provided in Tables 4.5– 4.8.

The spectrum of the stacked dimer at the neutral geometry is dominated by the three

intense lines at 0.5, 3.5 and 3.8 eV (see Fig. 4.7). The first peak is the CR band, which

is unique to the dimer, while the others are the local excitations (LE) between the states

of cation with the variousπ-orbitals singly occupied. Upon geometric relaxation, the

spectrum shifts to the higher energies by approximately 0.8 eV, so the lines appear at

1.2, 4.4, and 4.6 eV. The intensity of the charge resonance band increases more than

two-fold upon relaxation. The h-bonded dimer cation spectra at the geometry of the

neutral (see Fig. 4.8) features two intense lines at 0.1 and 3.6 eV and a small peak at

1.3 eV. As in the stacked cation, these lines are the CR band and two local excitations

(LE) corresponding to the transition between theπ-orbitals of cation (see Fig. 4.8). The

CR band is less intense than in the stacked cation and the most intense transition is the

LE at 3.6 eV. The spectrum at the transition state structure exhibits only minor differ-

ences, i.e, 0.1 eV blue shifts in peak positions with the intensities remaining the same.

However, the spectrum and the character of states changes dramatically upon proton

transfer. A new band appears at 2.5 eV. The localized character of the states andCs

symmetry make the proton-transfered h-bonded cation spectrum very similar to that of

the uracil cation. In the t-shaped cation spectra at the neutral geometry, the CR and

75

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.00.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

Osc

illat

or S

treng

th

Energy, eV

Ener

gy, e

V

SU20 SU2

+En

ergy

, eV

ΔE = 0.524

ΔE = 3.573

ΔE = 3.844

ΔE = 1.248

ΔE = 4.390

ΔE = 4.622

Figure 4.7: The electronic spectra (top panel) of the stacked uracil dimer cation atthe neutral (solid black) and the cation (dashed blue) geometries calculated with IP-CCSD/6-31(+)G(d) and the electronic states corresponding to the three most intensetransitions (bottom panel).

the two intense LE transitions appear at 0.1, 3.5 and 3.6 eV (see Fig. 4.9). The spec-

trum is very similar to that of the h-bonded isomer at the neutral geometry. As in the

stacked and h-bonded cations, the transitions between theπ-like orbitals are the most

76

Table 4.5: The excitation energies (∆E, eV), transition dipole moments (< µ2 >, a.u.)and oscillator strengths (f ) of the stacked dimer cation at the geometry of the neutraland cation, IP-CCSD/6-31(+)G(d).

neutral cation

Transition ∆E < µ2 > f ∆E < µ2 > f

X2B → 12A 0.524 7.2918 0.0935 1.248 7.4212 0.2269

X2B → 22B 1.023 0.0028 0.0000 1.799 0.0010 0.0000

X2B → 22A 1.081 0.1503 0.0040 1.809 0.0197 0.0009

X2B → 32B 1.349 0.1141 0.0038 2.190 0.0709 0.0038

X2B → 32A 1.406 0.5171 0.0178 2.362 0.4090 0.0237

X2B → 42B 1.906 0.0024 0.0001 2.798 0.0010 0.0000

X2B → 42A 1.952 0.0053 0.0003 2.800 0.0016 0.0001

X2B → 52B 3.573 0.3531 0.0333 4.390 0.7613 0.0819

X2B → 52A 3.844 0.9990 0.0875 4.622 0.2323 0.0263

intense. However, the character of the states is different — the states are more local-

ized. Upon relaxation, the spectrum changes completely, as does the character of the

states. The maximum intensity increases 2.5 times, new intense lines appear in the

1.7-3.0 eV and 4.5-5.0 eV regions. The orbital picture is now much more complex —

the DMOs become combinations of several FMOs. Thus, the electronic transitions can

no longer be described as CR or LE excitations. The most intense bands correspond

to the transitions between the cation states with theπCC orbital and thelp(O) orbital

singly occupied and are of charge-transfer character. To summarize, the three isomers

have distinctly different spectra, which can be used to distinguish between them exper-

imentally. Moreover, significant changes upon relaxation may be exploited to monitor

ionization-induced dynamics in a pump-probe experiment. Immediately upon the ion-

ization, the isomers will exhibit the intense lines in the three regions: 0.0-0.7 eV, 1-1.5

eV and 3.0-4.0 eV. While the spectra of the h-bonded and t-shaped dimers at the neu-

tral geometry are similar, the stacked cation can be distinguished by the two peaks of

77

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.50.00

0.02

0.04

0.06

0.08

0.10

0.12

Osc

illat

or S

treng

th

Energy, eV

HU20 HU2

+(TS) HU2+(HT)

Ener

gy, e

V

Ener

gy, e

V

Ener

gy, e

V ΔE = 0.113

ΔE = 1.358

ΔE = 3.615

ΔE = 0.121

ΔE = 1.632

ΔE = 3.835

ΔE = 2.475

ΔE = 3.650

ΔE = 3.984

Figure 4.8: The electronic spectra (top panel) of the h-bonded uracil dimer cation at theneutral (solid black), symmetric transition state (dashed blue) and the proton-transferredcation (dash-dotted pink) geometries calculated with IP-CCSD/6-31(+)G(d) and theelectronic states corresponding to the three most intense transitions (bottom panel).

moderate intensity in the 0.5-0.7 eV 3.5-4.0 eV regions. Upon the relaxation, the most

intense CR band of the stacked isomer shifts to 1.2 eV and acquires additional intensity.

The relaxation of the t-shaped cation manifests itself by significant growth of intensity

78

Table 4.6: The excitation energies (∆E, eV), transition dipole moments (< µ2 >, a.u.)and oscillator strengths (f ) of the symmetric h-bonded dimer cation at the geometry ofthe neutral and cation, IP-CCSD/6-31(+)G(d).

neutral cation

Transition ∆E < µ2 > f ∆E < µ2 > f

X2Au → 12Bg 0.113 27.4607 0.0763 0.121 28.7406 0.0849

X2Au → 12Bu 0.871 0.0000 0.0000 1.064 0.0000 0.0000

X2Au → 12Ag 0.915 0.0003 0.0000 1.123 0.0003 0.0000

X2Au → 22Bg 1.358 0.2527 0.0084 1.632 0.3048 0.0122

X2Au → 22Au 1.391 0.0000 0.0000 1.683 0.0000 0.0000

X2Au → 22Bu 1.867 0.0000 0.0000 1.954 0.0000 0.0000

X2Au → 22Ag 2.232 0.0000 0.0000 2.381 0.0000 0.0000

X2Au → 32Au 3.501 0.0000 0.0000 3.740 0.0000 0.0000

X2Au → 32Bg 3.615 1.3026 0.1154 3.835 1.2053 0.1133

in the 2.5-3.0 eV region. The hydrogen-bonded complex is more difficult to distinguish

because of the overlap of its spectral lines with the stacked and t-shaped spectra. Still,

the signature of proton transfer is the 0.3-0.4 eV blue shift of the intense transition in

the 3.5-4.0 eV region.

4.4 Conclusions

We characterized the electronic structure of the three representative isomers of the ion-

ized uracil dimers: h-bonded, stacked, and t-shaped. The interactions between the frag-

ments lower vertical IEs by 0.13-0.35 eV, the largest drop in IE being observed for the

stacked and t-shaped isomers. Interestingly, the character of the ionized states and the

origin of the IE change is different in these two isomers. In the stacked dimer, the hole

is delocalized between the two fragments, and orbital overlap determines the change in

79

Table 4.7: The excitation energies (∆E, eV), transition dipole moments (< µ2 >,a.u.) and oscillator strengths (f ) of the h-bonded dimer cation at the optimized proton-transferred geometry, IP-CCSD/6-31(+)G(d).

Transition ∆E < µ2 > f

X2A′′ → 12A′ 1.702 0.0004 0.0000

X2A′′ → 22A′′ 2.475 0.7690 0.0466

X2A′′ → 22A′ 2.782 0.0040 0.0003

X2A′′ → 32A′ 3.325 0.0024 0.0002

X2A′′ → 32A′′ 3.650 0.0605 0.0054

X2A′′ → 42A′′ 3.984 1.1704 0.1142

X2A′′ → 42A′ 4.493 0.0001 0.0000

X2A′′ → 52A′′ 5.343 0.0162 0.0021

X2A′′ → 52A′ 6.082 0.0039 0.0006

IE. In the t-shaped isomer, the hole is localized, and the change in IE is due to elec-

trostatic interactions between the “ionized” and the “spectator” fragment. The change

in IE for the symmetric h-bonded dimer is small, because neither overlap nor electro-

static interactions can stabilize the hole, however, larger changes are expected for the

non-symmetric h-bonded dimers [4].

The geometric relaxation is also different for the three isomers. The stacked isomer

relaxes to tighter structure with more efficient overlap between the FMOs, and the hole

remains delocalized between the fragments. The h-bonded isomer undergoes proton

transfer forming lowest-energy structure on the cation’s surface in which the charge and

the unpaired electron are localized on different moieties. Finally, the t-shaped dimer

relaxes to the structure with the localized hole. The respective binding energies of the

cation isomers are 20.2, 32.0 and 24.6 kcal/mol.

Finally, we characterized the electronic spectra of the cations at the neutral and the

relaxed geometries. At the neutral geometry, the h-bonded and stacked isomers feature

intense CR bands at 0.1 and 0.5 eV, respectively. The CR band in the t-shaped isomer is

80

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.00.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

0.11

0.12

0.13

Osc

illat

or S

treng

th

Energy, eV

TU20 TU2

+

Ener

gy, e

V

ΔE = 0.108

ΔE = 3.561

Ener

gy, e

V

ΔE = 3.613

ΔE = 2.622

ΔE = 2.945

ΔE = 4.757

Figure 4.9: The electronic spectra (top panel) of the t-shaped uracil dimer cation atthe neutral (solid black) and the cation (dashed blue) geometries calculated with IP-CCSD/6-31(+)G(d) and the electronic states corresponding to the three most intensetransitions (bottom panel).

less intense, and appears at the same energy as in the h-bonded dimer (0.1 eV). For all

three isomers, the spectra change dramatically upon relaxation. In the stacked isomer,

the intense CR band shifts to higher energies (i.e., from 0.5 to 1.3 eV) and becomes even

81

Table 4.8: The excitation energies (∆E, eV), transition dipole moments (< µ2 >, a.u.)and oscillator strengths (f ) of the t-shaped dimer cation at the geometry of the neutraland cation, IP-CCSD/6-31(+)G(d).

neutral cation

Transition ∆E, eV < µ2 >, a.u. f ∆E, eV < µ2 >, a.u. f

X2A1 → 22A1 0.108 18.4996 0.0488 1.866 0.5715 0.0261

X2A1 → 32A1 0.725 0.1761 0.0031 2.384 0.7506 0.0438

X2A1 → 42A1 0.841 0.0436 0.0009 2.622 1.8376 0.1180

X2A1 → 52A1 1.031 0.1376 0.0035 2.750 0.0428 0.0029

X2A1 → 62A1 1.176 0.5961 0.0172 2.945 1.1927 0.0861

X2A1 → 72A1 1.609 0.0095 0.0004 3.324 0.0042 0.0003

X2A1 → 82A1 1.776 0.0261 0.0011 3.584 0.3711 0.0326

X2A1 → 92A1 3.561 0.6475 0.0565 4.757 0.6759 0.0788

X2A1 → 102A1 3.613 0.6276 0.0555 5.539 0.0295 0.0040

more intense. In the h-bonded isomer, the CR bands (present at the neutral geometry at

0.1 eV) disappears upon proton transfer, and the spectrum becomes very similar to that

of the monomer. In the t-shaped isomer, new intense lines corresponding to the charge-

transfer transitions develop at 2.5-3.0 eV. Thus, the spectra evolution in these isomers is

rather different, which may be exploited for their experimental determination.

Postscript: Performance ofωB97X-D for the structures and energet-

ics of non-covalent neutral and ionized dimers

Self-interaction corrected functionals provide more reliable (although not fully satis-

factory) description of the ionized non-covalent dimers than the standard non-corrected

82

functionals. To investigate the performance of theωB97X-D functional [17] as an inex-

pensive alternative to more reliable wave function methods, we benchmarked this func-

tional using the stacked uracil isomer. We compared the intra and inter-fragment struc-

tural parameters of theωB97X-D/6-311(+)G(d,p) optimized geometries of the neutral

and cation to the best available geometries. For the neutral system, the geometry from

the S22 set of Hobza and coworkers was used as a benchmark [3]. For the cation, we

used the IP-CISD/6-31(+)G(d) optimized geometry for comparison. The average abso-

lute errors and the standard deviations for the bond lengths and angles in the DFT-D

optimized geometries were calculated. In the neutral, the average absolute error and the

standard deviation for bond lengths were 0.004 and 0.003A, respectively; the average

absolute error and standard deviation for angles were 0.247 and 0.182 Degree. In the

cation, the corresponding values were 0.010 and 0.005A, 0.377 and 0.233 Degree. As

of the inter-fragment parameters, in the neutral the DFT-D parameters (C5C6 and O2N1)

differ by less than 0.05A from the geometry from the S22 set, while in the cation the

DFT-D overestimated them by 0.15A comparing to the IP-CISD/6-31(+)G(d) value.

Given the tendency of IP-CISD to overestimate the inter-fragment distances in weakly

bound systems by 0.2-0.3A (as compared to more accurate IP-CCSD [18]), the DFT-D

geometry of the cation may be more accurate than the IP-CISD one. We conclude that

theωB97X-D structures are reasonably accurate, which validates the use of this method

for geometry optimizations of our system.

To assess the performance of theωB97X-D functional for the energetics, we com-

puted the dissociation energies for all isomers of the neutral and cation dimers and com-

pared them to the IP-CCSD/6-311(+)G(d,p) values. The results are summarized in Fig-

ures 4 and 5.ωB97X-D predicts the correct relative ordering of the neutral and cation

isomers. Quantitatively, the DFT-D errors in dissociation energies with respect to the IP-

CCSD values are in 1-2 kcal/mol range for the neutral dimers and in 1-5 kcal/mol range

83

for the cations. The errors inDe are non-systematic. Therefore, DFT-D withωB97X-D

functional provides a correct qualitative picture for energetics; the quantitative predic-

tions are of moderate accuracy, so a more reliable approach should be employed.

4.5 Reference list





[5] D. Roca-Sanjuan, M. Merchan, and L. Serrano-Andres, Modelling hole-transferin DNA: Low-lying excited states of oxidized cytosine homodimer and cytosine-adenine heterodimer, Chem. Phys.349, 188 (2008).

[6] G. Olaso-Gonzales, D. Roca-Sanjuan, L. Serrano-Andres, and M. Merchan,Toward understanding of DNA fluorescence: The singlet excimer of cytosine, J.Chem. Phys.125, 231002 (2006).

[7] K. Bravaya, Private communication.

[8] M. Pitonak, K.E. Riley, P. Neogrady, and P. Hobza, Highly accurate CCSD(T) andDFT-SAPT stabilization energies of H-bonded and stacked structures of the uracildimer, Comp. Phys. Comm.9, 1636 (2008).


84

[10] P.A. Pieniazek, S.E. Bradforth, and A.I. Krylov, Charge localization and Jahn-Teller distortions in the benzene dimer cation, J. Chem. Phys.129, 074104 (2008).


[12] P.A. Pieniazek, J. VandeVondele, P. Jungwirth, A.I. Krylov, and S.E. Bradforth,Electronic structure of the water dimer cation, J. Phys. Chem. A112, 6159 (2008).


[14] M.O. Sinnokrot and C.D. Sherrill, Highly accurate coupled cluster potential energycurves for the benzene dimer: Sandwich, t-shaped, and parallel-displaced config-urations, J. Phys. Chem. A108, 10200 (2004).

[15] M.O. Sinnokrot and C.D. Sherrill, High-accuracy quantum mechanical studies ofpi-pi interactions in benzene dimers, J. Phys. Chem. A110, 10656 (2006).

[16] M. Kratochvil, O. Engkvist, J. Sponer, P. Jungwirth, and P. Hobza, Uracil dimer:Potential energy and free energy surfaces. Ab initio beyond Hartree-Fock andempirical potential studies, J. Phys. Chem. A102, 6921 (1998).


[18] A.A. Golubeva, P.A. Pieniazek, and A.I. Krylov, A new electronic structuremethod for doublet states: Configuration interaction in the space of ionized 1hand 2h1p determinants, J. Chem. Phys.130, 124113 (2009).

85

Chapter 5

Ionized states of dimethylated uracil

dimers

5.1 Overview

Electronic structure, equillibrium geometries and properties of 1,3-dimethyluracil and

its dimer are characterized by electronic structure calculations. Section 5.3.1 discusses

the structures and binding energies of several low-lying neutral isomers. We investigate

the effect of methylation on the ionized states of the monomer and the dimers, and

quantify the changes in IEs due toπ-stacking interactions (Section 5.3.2). The structural

relaxation in the ionized systems and the binding energies of the cations are discussed

in Section 5.3.3, as well as the electronic spectra of the monomer and the lowest-energy

dimer isomer.


In this study, we employed a variety ofab initio techniques. The structures were

obtained as follows. For the monomer, we employed the RI-MP2/cc-pVTZ and IP-

CISD/6-31(+)G(d) methods [1, 2] in the neutral and the cation optimizations, respec-

tively. Different starting geometries were used in optimizations including theCs andC1

conformers with different angles of rotation of the CH3 groups. We found that both the

86

neutral and the ionized 1,3-dimethyluracil haveCs structures in which only the hydro-

gens of the CH3 groups lie out of plane.

By considering the two main factors contributing to the stability of the stacked

dimers, i.e., electrostatic interactions and steric repulsion, five starting geometries were

generated for the optimization, which employed a DFT-D method with theωB97X-D

functional [3], the 6-311(+,+)G(2d,2p) basis set [4], and the EML(75,302) grid. The

basis set and grid combination was chosen based on the numerical tests, which showed

that calculations with smaller bases, e.g., 6-311(+,+)G(d,p), and smaller grids fail to

reproduce the degeneracy of enantiomeric structures. Tight convergence criteria were

enforced in all optimizations, with the gradient and energy tolerance set to3 · 10−5 and

1.2 · 10−4, respectively, and the maximum energy change1 · 10−7. For the only sym-

metric isomer we carried out additional optimization without the symmetry constraint,

which proved that the minimum-energy structure is indeedCi symmetric.

The same level of theory was used in the dimer cation optimizations. We used the

neutral structures as the starting geometries. All cation optimizations employed the

spin-unrestricted references. The spin-contamination of the doublet Kohn-Sham deter-

minant was low with the typical〈S2〉 values within the 0.76 - 0.77 range. Just like in

the neutrals, theCi symmetry of the only symmetric isomer was tested by additional

optimizations without theCi constraint.

The dissociation and ionization energies and the electronic spectra of the cations

were then calculated with the IP-CCSD method and a moderate 6-31(+)G(d) basis set. In

the monomer calculations, we also employed a larger 6-311(+)G(d,p) basis to investigate

the basis set effect on ionization energies. Core electrons were frozen in the single-point

IP-CCSD energy and spectra calculations.

Optimized geometries, relevant total energies, and harmonic frequencies are given in

the Supporting Materials of Ref. 102. The data on the non-methylated uracil monomer

87

and dimer to which we frequently refer in this work are from Refs. 9,17. All calculations

were performed using theQ-CHEM electronic structure program [5].

5.3 Results and Discussion

5.3.1 Potential energy surface of the neutral dimers: Structures and

energetics

Nucleobase dimers form numerous isomers [6–8], which can be described as the

stacked, t-shaped and h-bonded structures. Three representative isomers from each man-

ifold have been characterized in our recent study of the uracil dimer [9]. The h-bonded

structure corresponds to the global energy minimum in non-methylated species.

Methylation at nitrogens reduces polarity of the molecule, eliminates hydrogens that

can participate in h-bonding, and introduces bulky groups. These factors destabilize

the t-shaped and h-bonded structures of the 1,3-dimethyluracil dimers. The molecular

dynamics study by Hobza and coworkers [10] showed that the potential energy sur-

face (PES) of the 1,3-dimethyluracil dimers is dominated by the stacked structures, the

t-shaped isomers lying 5-6 kcal/mol higher in energy and h-bonded isomers being unsta-

ble. Our calculations usingωB97X-D/6-311(+)G(d,p) found an h-bonded-like structure

(which is better described as a van der Waals dimer) about 10 kcal/mol above the stacked

manifold. Thus, we focus on the stacked isomers of the 1,3-dimethyluracil dimer.

The five optimized structures of the neutral stacked 1,3-dimethyluracil are shown

in Figure 5.1; the corresponding binding and relative energies calculated withωB97X-

D/6-311(+,+)G(2d,2p) and CCSD/6-31(+)G(d) are summarized in Tables 5.1 and 5.2,

respectively. The lowest-energy structure of the dimethylated uracil dimer is non-

symmetric isomer 1, which is similar to the minimum-energy stacked uracil structure

88

Isomer 1 (0)

De=13.8 / 15.9

Isomer 2 (+1.2)

De=12.6

CiC1

De=12.4

Isomer 3 (+1.5)

De=11.7

Isomer 4 (+2.2)

C1

C1

De=10.9

Isomer 5 (+2.9)C1

Figure 5.1: Five isomers of the stacked neutral 1,3-dimethyluracil dimer and their bind-ing energies (kcal/mol). The energy spacings (kcal/mol) between the lowest-energystructure and other isomers are given in the parenthesis. All values were obtained withωB97X-D/6-311(+,+)G(2d,2p) except for theDe value of isomer 1 shown in bold, whichis the IP-CCSD/6-31(+)G(d) estimate.

from the S22 set by Hobza and coworkers [11]. This isomer is followed by isomers 2

(Ci), 3 (C1), 4 (C1) and 5 (C1) lying 1.2, 1.5, 2.2, and 2.9 kcal/mol higher in energy,

respectively. The energy gaps between the isomers are very small: the five isomers lie

in just 2.9 kcal/mol range, and some of them are nearly degenerate, i.e., separated by

0.3 kcal/mol. These energy differences are of the order of kT(298.18 K) = 0.6 kcal/mol,

which suggests significant populations of all these isomers at the standard conditions.

The denseπ-stacked manifold and structural motifs are similar to stacked thymine

dimers [12], where five isomers lie within 2.2 kcal/mol. Interestingly, no low-energy

stacked isomers were identified for dimers of another pyrimidine, cytosine dimer [13].

The binding energies of the neutral stacked 1,3-dimethyluracil dimers lie in the range

of 10.9-13.8 kcal/mol, as computed by DFT-D. For the lowest-energy isomer we also

89

Table 5.1: The total (hartree) and dissociation energies (kcal/mol) of the neutraland ionized 1,3-dimethyluracil monomer and dimers calculated at theωB97X-D/6-311(+,+)G(2d,2p) level of theory.

Complex EtotDFT−D DDFT−D

e

mU0 -493.431022 –

mU+ -493.111429 –

S(mU)02, isomer 1 -986.884084 13.8

S(mU)02, isomer 2 -986.882142 12.6

S(mU)02, isomer 3 -986.881741 12.4

S(mU)02, isomer 4 -986.880611 11.7

S(mU)02, isomer 5 -986.879409 10.9

S(mU)+2 , isomer 1 -986.587029 28.0

S(mU)+2 , isomer 2 -986.570893 17.9

S(mU)+2 , isomer 3 -986.578185 22.4

S(mU)+2 , isomer 4 -986.576570 21.4

T(mU)+2 , isomer 5 -986.572944 19.1

computed the CCSD/6-31(+)G(d) value. The resulting binding energy of 15.9 kcal/mol

is in a good agreement with 13.8 kcal/mol computed withωB97X-D/6-311(+)G(d,p).

Based on our results for uracil [9], using larger basis set in CCSD calculations lowers

the CCSD binding energy and improves the agreement between the methods.

The binding energy of the lowest energy isomer (13.8 kcal/mol) is larger than that

of the stacked non-methylated uracil dimer for whichDe = 10.5 kcal/mol (these are

DFT-D values, but the similar trend is observed for the CCSD/6-31(+)G(d) binding

energies, which are 15.9 and 12.2 kcal/mol). For comparison, the binding energy of the

lowest stacked thymine and adenine homodimers are 12.5 kcal/mol and 10.6 kcal/mol,

respectively [12].

An increase in binding energy upon methylation is somewhat surprising, as methy-

lated uracil is less polar than uracil (the RI-MP2/cc-pVTZ dipole moments are 4.19 D

versus 4.02 D) and, therefore, one may expect weaker electrostatic interaction between

90

Table 5.2: The total (hartree) and dissociation energies (kcal/mol) of the neutral andionized 1,3-dimethyluracil and its dimer (lowest energy isomer) calculated at the IP-CCSD/6-31(+)G(d) level of theory. For the monomer and the dimer cations, the relax-ation energy (∆ECCSD

relax , kcal/mol) is provided.a The uracil and uracil dimer IP-CCSD/6-31(+)G(d) resultsb are included for comparison.

Complex EtotCCSD DCCSD

e ∆ECCSDrelax

mU0 -492.032033 – –

mU+ -491.715681 – -3.8

S(mU)02, isomer 1 -984.089466 15.9 –

S(mU)+2 , isomer 1 -983.798612 31.9 -11.2

U0 -413.683919 – –

U+ -413.345482 – -4.1

SU02 -827.387312 12.2 –

SU+2 -827.069011 24.9 -8.7

a The difference between the total energies of the cation at the vertical and the relaxedgeometries.

b For these estimates, we employed same structures as in Ref. 9 For the stacked uracildimer cation, the DFT-D/ωB97X-D/6-311(+)G(d,p) optimized geometry was used.

the fragments in the 1,3-dimethyluracil dimer. However, this difference appears to be

too small, and local electrostatic interactions play a more important role. The anal-

ysis of the structures reveals that the (NCH2)Hδ+· · ·Oδ−(C) distance in the stacked

1,3-dimethyluracil dimer is shorter than the (N)Hδ+· · ·Oδ−(C) distance in the stacked

uracil dimer, which results in stronger electrostatic interaction between the fragments

in the former complex. A tighter structure of the methylated dimer is also counterin-

tuitive because of the presence of the bulky methyl groups. The observed increase in

binding energy upon substitution is consistent with the results of Sherrill and cowork-

ers [14, 15], who demonstrated that the electrostatic considerations alone are not suffi-

cient to explain the changes in binding inπ-stacked systems upon substitution and that

differential changes in dispersion interactions play an important role.

91

5.3.2 The effect of methylation on the ionized states of the monomer

and the dimers

1,3-dimethyluracil

Figure 5.2 presents the five highest occupied MOs of 1,3-dimethyluracil and uracil and

the corresponding VIEs calculated at the IP-CCSD/6-311(+)G(d,p) level. The shapes

of the MOs are similar in the two molecules, except for theσCH electronic density on

the CH3 groups of 1,3-dimethyluracil. Another minor difference can be seen in the

lp(N) + πCC + πCO orbital, which is more localized in dimethylated uracil.

The order of the ionized states in methylated uracil is the same as in uracil. The

HOMO is theπ-like MO centered at the C–C double bond, and the corresponding IE

is 8.87 eV. This state is followed by ionization from the two lone pair and twoπ-like

orbitals with VIEs of 9.74 (lp(O1)), 9.77 (lp(O) + lp(N)), 10.66 (lp(O2)) and 12.16 eV

(lp(N) + πCC + πCO).

However, the values of IEs and the spacings between the ionized states are different.

Methylation lowers the first IE by 0.6 eV relative to uracil. Similar effect is observed

for other states: the VIEs of12A′, 12A′′, 22A′ and22A′′ states decrease by 0.37, 0.74,

0.43 and 0.86 eV, respectively. Note that for the oxygen lone-pair states, the magnitude

of the effect is smaller than for the states derived from ionization fromπ-like orbitals.

The largest shifts are observed for the states with large contributions from lone pairs of

nitrogens, which are primary substitution sites. As a result, the12A′ and12A′′ states that

are separated by 0.4 eV in uracil become almost degenerate in 1,3-dimethyluracil. The

IEs are lowered due to electron-donating CH3 groups increasing electron density in the

ring (destabilization of the respective MOs) and due to a larger size of the methylated

species contributing to hole stabilization. The effect is larger in the states derived from

ionization from delocalizedπ orbitals, in which the CH3 group donates the electron

92

8.87

9.77

9.74

10.66

12.16

πCC / a´´

lp(N)+lp(O) / a´´

lp(O1) / a´

lp(O2) / a´

lp(N)+πCC+ πCO / a´´

Ioni

zatio

n En

ergy

, eV

9.48

10.51

10.11

11.09

13.02

πCC / a´´

lp(N)+lp(O) / a´´

lp(O1) / a´

lp(O2 ) / a´


Ioni

zatio

n En

ergy

, eV

Figure 5.2: The five lowest ionized states and the molecular orbitals of dimethyluracil(top) and uracil (bottom) calculated by IP-CCSD/6-311(+)G(d,p).

density to theπ system via thelp(N) component, whereas the in-planelp(O) orbitals

are affected less.

93

Table 5.3: The five lowest ionized states and the corresponding IEs (eV) of the 1,3-dimethyluracil at the vertical geometry calculated by IP-CCSD with the 6-31(+)G(d)and 6-311(+)G(d,p) bases. The IE shifts (eV) with respect to the uracil values are givenin parenthesis.

Basis X2A′′ 12A′ 12A′′ 22A′ 22A′′

6-31(+)G(d) 8.77 (-0.61) 9.67 (-0.38) 9.69 (-0.75) 10.58 (-0.45) 12.07 (-0.88)

6-311(+)G(d,p) 8.87 (-0.61) 9.74 (-0.37) 9.77 (-0.74) 10.66 (-0.43) 12.16 (-0.86)

Dimethyluracil dimers

Similarly to otherπ-stacked dimers [9, 12, 16, 17], the electronic structure and ionized

states of the 1,3-dimethyluracil dimer can be described within the DMO-LCFMO frame-

work [16]. The molecular orbitals of the dimer (DMOs) shown in Figure 5.3 are the in-

and out-of-phase combinations of the FMOs. Figure 5.3 also presents the correspond-

ing IEs. Because of the lower symmetry, some of the electronic states of the methylated

uracil dimer are localized on individual fragments. The first IE of the 1,3-dimethyluracil

dimer corresponds to ionization from theπCC(F1) − πCC(F2) DMO. Stacking inter-

action lowers it by 0.37 eV relative to the monomer, i.e, 8.40 eV versus 8.77 eV as

calculated at the IP-CCSD/6-31(+)G(d) level. Thus, the magnitude of the effect is com-

parable to that in the non-methylated stacked uracil dimer and the stacked thymine dimer

(both have 0.35 eV decrease in IE), whereas the shift in adenine dimer is smaller (0.2

eV) [12].

The order of the ionized states in the 1,3-dimethyluracil dimer is different from the

uracil dimer. In the latter (as well as in the stacked thymine dimer, see Ref. 12), the

states corresponding to the in- and out-of-phase FMO combinations appear pair by pair

in the same order as the respective monomer states. In the methylated uracil dimer,

the states arising from ionization fromlp(O1) FMOs lie in between the pair of states

corresponding to thelp(O) + lp(N) FMOs.

94

Ioni

zatio

n En

ergy

, eV

9.42 9.669.69

9.85

10.51 10.46

11.8811.67

8.40

8.81

Figure 5.3: The ten lowest ionized states and the corresponding MOs of the lowest-energy isomer of the neutral stacked 1,3-dimethyluracil computed with IP-CCSD/6-31(+)G(d).

The largest splittings between the pairs of states are observed for the states derived

from theπ-like FMOs owing to their larger overlap. Compare, for example, the 0.41,

0.43 and 0.21 eV splittings for the states derived from ionization from theπ-like orbitals

to the 0.06 and 0.03 eV splittings for the lone-pair states. Overall, the magnitude

of the splittings in methylated and non-methylated dimers is similar, except for the

lp(O) + lp(N) pair of states (0.43 eV vs. 0.06 eV in the 1,3-dimethyluracil and uracil

dimers, respectively). Due to large weight oflp(N), these MOs are most affected by the

electron-donating CH3 groups. The increased electron density in theπ-system results in

larger overlap and, consequently, larger splittings. This large splitting is responsible for

different state ordering. So far, this is the first example of that type — in all other model

95

systems we have studied (benzene, water, uracil, and adenine dimers) the stacking inter-

actions did not change the relative order of the ionized states, even though the splittings

in different pairs of states were quite different.

5.3.3 Ionization-induced changes in the monomer and the dimers:

Structures and properties

Ionization induces considerable structural changes. For the lowest ionized state, relax-

ation pattern is consistent with the MO character. In the uracil monomer, double CC

bond elongates inducing the changes in an entire bond-alternation pattern [9]. In the

dimer, these changes are accompanied by the rings re-orienting to increase the over-

lap between the respective FMOs [9]. Methylated species show very similar behavior.

Below we discuss changes in binding energies and relative order of the isomers and

characterize spectroscopic signatures of the structural relaxation.

Binding energies of the dimer cations

Figure 5.4 presents five relaxed structures of the 1,3-dimethyluracil dimer cations. The

total and dissociation energies of the dimer cations estimated byωB97X-D are given

in Table 5.1; and the CCSD/6-31(+)G(d) estimates for the lowest-energy isomer are

provided in Table 5.2. Similarly to the neutral dimers, the global minimum corresponds

to isomer 1 (C1). However, in all other aspects the PES of the dimer cation differs

drastically from that of the neutral.

The order of the isomers and the energy gaps between them change upon ionization.

Following isomer 1, isomers 3, 4, 5 and 2 lie 5.6, 6.6, 8.8 and 10.1 kcal/mol higher in

energy. In contrast to the neutral, the five minima on the cation PES are well-separated

in energy. For example, the two lowest-energy structures are more than 5 kcal/mol

apart, whereas all five neutral isomers lie within 2.9 kcal/mol interval. Thus, we expect

96

Isomer 1 (0)

De= 28.0 / 31.9

Isomer 2 (+10.1)

De= 17.9

CiC1

De= 22.4

Isomer 3 (+5.6)

De= 21.4

Isomer 4 (+6.6)

C1

C1

De=19.1

Isomer 5 (+8.8)

C1

Figure 5.4: Five low-lying isomers of the 1,3-dimethyluracil dimer cation and the disso-ciation energies (kcal/mol). The energy spacings (kcal/mol) between the lowest-energystructure and other isomers are given in the parenthesis. All values were obtained withωB97X-D/6-311(+,+)G(2d,2p) except for theDe value of isomer 1 (shown in bold),which is the IP-CCSD/6-31(+)G(d) estimate.

dominant population of the lowest-energy structure (isomer 1) of the cation under the

standard conditions. Another difference is the appearance of the t-shaped dimer cation

(isomer 5) among low-lying structures. It is 8.8 kcal/mol above the isomer 1 (but 1.5

kcal/mol below one of the stacked structures).

The dissociation energies of 1,3-dimethyluracil cations fall within the 17.9-28.0

kcal/mol range, as computed with DFT-D. Therefore, the fragments in ionized dimers

are bound 1.4 to 2.0 times stronger than in the neutral dimers with the largest and the

smallest increases observed for isomers 1 and 2, respectively. The magnitude of the

increase is similar to that observed in the uracil dimers. Note that, similarly to the neu-

tral dimers, the interaction between the fragments is stronger in the methylated dimers

than in the non-methylated analogues. The best estimate of the binding energy for the

97

lowest-energy cation structure (isomer 1) is 31.9 kcal/mol (at IP-CCSD/6-31(+)G(d)

level), which is 7.0 kcal/mol larger than that of the stacked uracil dimer (24.9 kcal/mol

at IP-CCSD/6-31(+)G(d) level). The binding energy of the ionized stacked thymine

dimer is similar to that of uracil, i.e., 19.8 kcal/mol. The increase of binding energy

upon methylation can be explained by the increased electron density in theπ-system

resulting in larger overlap, and is consistent with a slightly larger change of IE due to

dimerization. Another contribution into the binding energy comes from the geometric

relaxation, which is larger in the methylated dimer relative to the non-methylated species

(11.2 versus 8.7 kcal/mol). The corresponding relaxation energies in both monomers are

about 3-4 kcal/mol (see Table 5.2). Larger geometric relaxation in the methylated dimer

is similar to the results for the stacked thymine and adenine homodimers [12], where the

difference between VIE and AIE was 15.0 kcal/mol and 11.3 kcal/mol for TT and AA,

respectively, and the corresponding monomer values were 5-6 kcal/mol.

Equilibrium geometries of the cations

The ionization-induced changes in geometry and the electronic structure of isomers 1-5

of the 1,3-dimethyluracil dimer are illustrated in Figures 5.5- 5.9. In each picture, the

neutral and the cation geometries and the two highest MOs of the dimer are shown. The

analysis of these five cases reveals two distinct trends. In isomers 1,2 and 4 (Group 1),

the relaxation results in the increased FMO overlap and, consequently, the delocalized

DMOs at the cation geometry. Isomers 3 and 5 (Group 2) exhibit a different pattern:

the DMOs are localized on one of the fragments at the cation geometry and no signifi-

cant FMO overlap develops upon the relaxation. In both structureslp(O) of one of the

fragments moves toward the hole centered onπCC MO of the other fragment. Thus,

Group 2 cations are stabilized by the favorable electrostatic interaction of the localized

hole and the negative charge onlp(O). This motif, which is similar to the t-shaped

98

uracil dimer [9], demonstrates that electrostatic interactions can be competitive with

the hole delocalization effects even in the stacked systems. Therefore, two factors

(mU)20

isomer 1(mU)2

+

isomer 1

De=28.0 / 31.9 De=13.8 / 15.9

(mU)20

isomer 1(mU)2

+

isomer 1

Figure 5.5: The ionization-induced changes in geometry, binding energies (kcal/mol)and the MOs of isomer 1 of the stacked 1,3-dimethyluracil dimer. TheωB97X-D/6-311(+,+)G(2d,2p) optimized structures, dissociation energies and the HF/6-31(+)G(d)MOs are presented.

are responsible for the stabilization of the ionized 1,3-dimethyluracil dimer cations: the

DMO-LCFMO mechanism in which the stabilization of the ionized state is proportional

to the FMO overlap [16], and the electrostatic mechanism [9,12,13]. The magnitude of

99

(mU)20

isomer 2(mU)2

+

isomer 2

De=17.9De=12.6

(mU)20

isomer 2(mU)2

+

isomer 2


relaxation is comparable for the two mechanisms, e.g., in Group 1 the binding energy

increases 1.4 to 2.0 times relative to the neutrals, and for Group 2 the increase is 1.7

to 1.8 fold. However, one may expect that the DMO-LCFMO stabilization is more

sensitive to relative orientation of the fragments than electrostatic interactions and that

the constrained environments (e.g., DNA) may discriminate between the two effects,

100

(mU)20

isomer 3(mU)2

+

isomer 3

De=22.4De=12.4

(mU)20

isomer 3(mU)2

+

isomer 3


although it is clear how strong perturbation by the backbone can affect relative strengths

of these interactions.

Let us now compare the absolute values of the binding energies for isomers 1-5.

For the Group 1 isomers stabilized via DMO-LCFMO mechanism, the strongest and the

101

(mU)20

isomer 4(mU)2

+

isomer 4

De=21.4De=11.7

(mU)20

isomer 4(mU)2

+

isomer 4


weakest inter-fragment interaction is observed in isomer 1 (28.0 kcal/mol) and symmet-

ric isomer 2 (17.9 kcal/mol), respectively. The difference between these two cases is

apparent from Figures 5.5 and 5.6. In isomer 1, the DMOs look more like a bonding

orbital, whereas isomer 2 fails to develop significant FMO overlap. Isomer 4 (see Fig-

ure 5.8) lies in between these two limiting cases with the moderate overlap and binding

102

(mU)20

isomer 5

De=19.1De=10.9

(mU)2+

isomer 5

(mU)20

isomer 5(mU)2

+

isomer 5

Figure 5.9: The changes in geometry, binding energies (kcal/mol) and the MOs ofisomer 5 of the stacked 1,3-dimethyluracil dimer at ionization. TheωB97X-D/6-311(+,+)G(2d,2p) optimized structures, dissociation energies and the HF/6-31(+)G(d)MOs are presented.

energy of 21.4 kcal/mol. In Group 2, the values of binding energies are less diverse,

which is consistent with the electrostatic stabilization mechanism. In isomers 3 and 5

the fragments are bound by 22.4 and 19.1 kcal/mol, respectively

103

Electronic spectra of the cations

1,3-dimethyluracil The electronic spectra of the methylated uracil and uracil cations

at the vertical and relaxed geometries calculated by IP-CCSD/6-31(+)(d) are shown in

Figure 5.10. Table 5.4 provides the values of transition energies, dipole moments and

oscillator strengths. Owing to the similarity in their structures and MOs, the spectra of

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.50.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14O

scill

ator

Stre

ngth

Energy, eV

πCC / a´´

lp(N)+lp(O) / a´´


0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.50.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

Osc

illat

or S

treng

th

Energy, eV

πCC / a´´

lp(N)+lp(O) / a´´


Figure 5.10: The electronic spectra of 1,3-dimethyluracil (left) and uracil (right) atthe vertical (solid black) and the relaxed (dashed blue) geometries calculated by IP-CCSD/6-31(+)G(d).

104

Table 5.4: The electronic spectrum of the 1,3-dimethyluracil cation at the vertical andrelaxed geometries calculated at the IP-CCSD/6-31(+)G(d) level.

neutral cation

Transition ∆E, eV < µ2 >, a.u. f ∆E, eV < µ2 >, a.u. f

X2A′′ → 12A′ 0.899 0.0004 0.0000 1.269 0.0004 0.0000

X2A′′ → 12A′′ 0.917 0.5222 0.0117 1.557 0.3996 0.0152

X2A′′ → 22A′ 1.809 0.0000 0.0000 2.399 0.0000 0.0000

X2A′′ → 22A′′ 3.297 1.6952 0.1369 3.822 1.4258 0.1335

methylated and non-methylated uracil cation are very similar (see Figure 5.10). In both

cases, the two bright transitions correspond to the transitions between the states of the

cations with theπ-orbitals singly-occupied. The methylated uracil spectrum is slightly

blue-shifted. The effect of the geometry relaxation on the spectra is larger in the uracil

cation than in the 1,3-dimethyluracil cation with the line shifts of +0.7-0.8 eV for the

former and +0.5-0.6 eV for the latter. This can be explained by the electron-donating

properties of the CH3 groups which reduce the effect of ionization on the structure.

1,3-dimethyluracil dimer cation Table 5.5 presents IEs of isomer 1 computed at the

vertical and relaxed geometries. The respective MOs are shown in Figure 5.3. Due

to low symmetry and large size of the methylated dimer we only computed the exci-

tation energies, as calculations of the oscillator strengths for the electronic transitions

in the cation are more computationally expensive than just energy calculations. How-

ever, the intensities of the peaks can be estimated based on the intensities in the uracil

dimer cation [9, 17] and DMO-LCFMO analysis (see Ref. 16 for the DMO-LCFMO

nomenclature), as explained below. These results are visualized in Figure 5.11. In

105

Table 5.5: The ionization energies (eV) and the DMO charactera corresponding to theten lowest ionized states of the stacked 1,3-dimethyluracil dimer at the vertical geometry(isomer 1) calculated at the IP-CCSD/6-31(+)G(d) level.

neutral cation

State DMO IE DMO Eex

X2A1 ψ−(πCC) 8.40 (-0.63) ψ−(πCC) 0.00

12A1 ψ+(πCC) 8.81 (-0.75) ψ+(πCC) 1.48

22A1 ψ−(lp(O) + lp(N)) 9.42 (-0.96) ψ−(lp(O) + lp(N)) 1.99

32A1 lp(O1), F1 9.66 (-0.40) ψ−(lp(O1) 2.15

42A1 lp(O1), F2 9.69 (-0.43) ψ+(lp(O1) 2.18

52A1 ψ+(lp(O) + lp(N)) 9.85 (-0.59) ψ+(lp(O) + lp(N)) 2.44

62A1 lp(O2), F1 10.46 (-0.48) ψ−(lp(O1) 3.07

72A1 lp(O2), F2 10.51 (-0.48) ψ+(lp(O1) 3.09

82A1 ψ−(lp(N) + πCC + πCO) 11.67 (-0.94) ψ−(lp(N) + πCC + πCO) 4.25

92A1 ψ+(lp(N)+πCC+πCO) 11.88 (-1.00) ψ+(lp(N) + πCC + πCO) 4.37a In the DMO-LCFMO notations [16], theψ+(ν) andψ−(ν) represent the bonding and

antibonding combinations of the MOs of fragments 1 and 2 (νF1 andνF2).b The shifts of IEs (eV) of the dimethylated uracil dimer relative to the non-methylatedanalogue are given in parenthesis. For the relaxed cation, the excitation energies (eV)

calculated at IP-CCSD/6-31(+)G(d) level are presented.

the stacked uracil dimer cation, theψ−(π) → ψ+(π) andψ−(π) → ψ−(π) transi-

tions (i.e. the transitions between the electronic states derived from the ionization from

the DMOs composed out ofπ-like FMOs) are intense, whereas theψ−(π) → ψ+(lp)

andψ−(π) → ψ−(lp) transitions are weak. Analogously to the stacked uracil dimer,

in the methylated dimer cation spectrum at the vertical geometry, we expect at least

three intense peaks: at 0.41, 1.45 and 3.27 eV. The former peak is the CR band, and

the latter two are the local excitations (LE) involving otherπ-like DMOs, i.e. the

106

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.50.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

Osc

illat

or s

treng

th

Energy, eV

12A1

52A1

X2A1

82A1

Figure 5.11: The three most intense transitions in the electronic spectrum of the lowestisomer of stacked 1,3-dimethyluracil cation at vertical (solid black) and cation (dashedblue) geometries. The DMOs corresponding to the ground state (framed) and excitedstates (regular) are shown. The positions of the peaks were calculated at IP-CCSD/6-31(+)G(d) level, while the intensities are from the non-methylated dimer calculations.

ψ+(lp(O)+lp(N) andψ−(lp(N)+πCC +πCO). The transition dipole moment is related

to sνF1νF2, the overlap of the FMOs on fragments 1 and 2, by the following equation:

I(ψ−(ν) → ψ+(ν)) ∝ RAB√1− sνF1νF2

, (5.1)

whereRAB is the inter-fragment distance.

Upon the geometry relaxation, the states of the dimer become more delocalized, as

can be seen in Fig. 5.5 showing the two highest-occupied DMOs at the neutral and

cation geometries. The states derived from thelp(O1) andlp(O2) FMOs are no longer

localized on one of the fragments, as they were at the vertical geometry (not shown).

Thus, we expect the following changes in the spectrum. The increasing overlap between

107

theψ+(πCC) andψ−(πCC) DMOs leads to the growth of the intensity of CR band, which

shifts to 1.48 eV upon the relaxation. Based on the similarity of the methylated and non-

methylated systems, we expect the intensity of the CR band to (at least) double at the

relaxed geometry. The position of the LE band that appears at 1.45 eV at the vertical

geometry shifts to 2.44 eV; however, as follows from the FMO overlaps and splittings

no considerable increase of intensity is expected. Finally, the LE transition at 3.27 eV

in the vertical spectrum shifts by +1.0 eV and its intensity decreases upon relaxation.

5.4 Conclusions

The structures, binding energies, properties of several isomers of the neutral and ionized

1,3-dimethylated uracil dimers are characterized usingab initio methods. The methyla-

tion suppresses the formation of hydrogen-bonded and t-shaped neutral structures, how-

ever, theπ-stacked manifold is rather dense. Five lowest isomers of the stacked dimer

lie within the 2.9 kcal/mol range, which suggests that all of the isomers will be present

at the standard conditions. The binding energies of the neutral dimers are in the range

of 10.9-13.8 kcal/mol (DFT-D). Surprisingly, in sterically-constrained and less polar

methylated species the fragments are bound stronger than in the non-methylated analogs

(the corresponding DFT-D estimate for the stacked uracil dimer is 10.5 kcal/mol).

The MOs of the uracil are only slightly perturbed by the CH3 group; however, the

effect is significant for the values of IEs. The methylation lowers the first IE of the 1,3-

dimethyluracil by 0.6 eV as compared to uracil; the higher-lying states also exhibit red

shifts of a varying magnitude (0.37-0.86 eV). This IE lowering is due to the electron-

donating CH3 groups, which increase the electron density in the ring and stabilize the

ionized state. The effect is bigger in the states derived from ionization from the delocal-

izedπ orbitals, in which the electron density is efficiently donated to theπ-system via

108

the lp(N) component. The magnitude of the effect correlates with the weight oflp(N)

in the leading MO, which is not surprising as nitrogens are the primary substitution sites.

Similarly to uracil dimer, the electronic structure of the methylated uracil dimer is

well described by DMO-LCFMO. The stacking interactions lower the first IE by 0.37

eV in the methylated dimers, which is very similar to 0.35 eV lowering in the non-

methylated system (and the stacked dimer of thymine). Another important finding is the

0.6 eV lowering of the IE in the methylated dimer due to the methylation: the effect

is the same as in the monomer. It implies that the effect of substitutions can be incor-

porated into the qualitative DMO-LCFMO picture as a constant shifts of the dimer and

monomer levels, whereas the splittings between the in-phase and out-of-phase DMOs

are surprisingly insensitive to the substitution, except for the states derived from orbitals

with large weights oflp(N). These states exhibit much larger splittings than in non-

methylated species (i.e., 0.43 versus 0.06 eV), which ultimately results in changes in the

states ordering. This is different from other model systems that we have studied (ben-

zene, water, uracil, and adenine dimers) where the stacking interactions do not change

the relative order of the ionized states, even though the splittings in different pairs of

states are quite different.

Ionization changes the bonding pattern inducing considerable changes in structures

and binding energies. The energy separation between the isomers increases, so one

can expect dominant population of the lowest isomer at the standard conditions. The

binding energies increase 1.4-2.0 fold upon ionization and lie in 17.9-28.0 kcal/mol

range (DFT-D); for the lowest-energy dimer cation structure, the IP-CCSD value ofDe

is 31.9 kcal/mol. This binding energy is larger than that in the non-methylated uracil and

thymine dimers. Similarly to the neutrals, the methylation increases the inter-fragment

interaction in the dimer.

109

The relaxation of the cation structures is governed by two distinct mechanisms: the

hole delocalization (and the FMO overlap) and the electrostatic stabilization (interaction

of thelp(O) with the localized hole).

Finally, we presented electronic spectra of the ionized species. Significant changes

in the spectra upon relaxation can be exploited to monitor the ionization-induced dynam-

ics in dimethylated uracils. At the vertical geometry, there are three intense transitions:

at 0.41, 1.45 and 3.27 eV, the CR band at 0.41 eV and LE at 1.45 eV being the most

intense. Upon relaxation, these bands are blue-shifted, and their intensities change to

1.48 (CR), 2.44 (LE) and 4.25(LE) eV. The CR band at 1.48 eV is expected be the most

intense and can be used to monitor the relaxed stacked dimer cation formation.

5.5 Reference list





[5] Y. Shao, L.F. Molnar, Y. Jung, J. Kussmann, C. Ochsenfeld, S. Brown, A.T.B.Gilbert, L.V. Slipchenko, S.V. Levchenko, D.P. O’Neil, R.A. Distasio Jr, R.C.Lochan, T. Wang, G.J.O. Beran, N.A. Besley, J.M. Herbert, C.Y. Lin, T. VanVoorhis, S.H. Chien, A. Sodt, R.P. Steele, V.A. Rassolov, P. Maslen, P.P. Koram-bath, R.D. Adamson, B. Austin, J. Baker, E.F.C. Bird, H. Daschel, R.J. Doerksen,A. Drew, B.D. Dunietz, A.D. Dutoi, T.R. Furlani, S.R. Gwaltney, A. Heyden, S.

110

Hirata, C.-P. Hsu, G.S. Kedziora, R.Z. Khalliulin, P. Klunziger, A.M. Lee, W.Z.Liang, I. Lotan, N. Nair, B. Peters, E.I. Proynov, P.A. Pieniazek, Y.M. Rhee, J.Ritchie, E. Rosta, C.D. Sherrill, A.C. Simmonett, J.E. Subotnik, H.L. WoodcockIII, W. Zhang, A.T. Bell, A.K. Chakraborty, D.M. Chipman, F.J. Keil, A. Warshel,W.J. Herhe, H.F. Schaefer III, J. Kong, A.I. Krylov, P.M.W. Gill, M. Head-Gordon,Advances in methods and algorithms in a modern quantum chemistry programpackage, Phys. Chem. Chem. Phys.8, 3172 (2006).

[6] K. M uller-Dethlefs and P. Hobza, Noncovalent interactions: A challenge for exper-iment and theory, Chem. Rev.100, 143 (2000).

[7] J. Sponer, J. Leszczynski, and P. Hobza, Electronic properties, hydrogen bonding,stacking, and cation binding of DNA and RNA bases, Biopolymers61, 3 (2002).

[8] H. Saigusa, Excited-state dynamics of isolated nucleic acid bases and their clusters,Photochem. Photobiol.7, 197 (2006).


[10] M. Kratochvıl, O. Engkvist, J. Vacek, P. Jungwirth, and P. Hobza, Methylateduracil dimers: Potential energy and free energy surfaces, Phys. Chem. Chem.Phys.2, 2419 (2000).




[14] M.O. Sinnokrot and C.D. Sherrill, Unexpected substituent effecst in face-to-faceπ-stacking interactions, J. Phys. Chem. A107, 8377 (2003).

[15] M.O. Sinnokrot and C.D. Sherrill, Substituent effects inπ− π interactions: Sand-wich and t-shaped configurations, J. Am. Chem. Soc.126, 7690 (2004).

111



112

Chapter 6

Ionized non-covalent dimers: Outlook

and future research directions

6.1 Overview

The non-covalent ionized clusters pose a challenge to theory; at the same time, this very

complexity makes them an exicting and rewarding research topic. Closely-lying elec-

tronic states result in multi-configurational wave functions and rich electronic structure

with large number of states and multiple conical intersections. Weak dispersion inter-

actions and large number of degrees of freedom together make the geometry search dif-

fucult, but produce potential energy surfaces with a variety of distinct structures, both

minima and transition states. In this chapter, two of the numerous possible research

directions will be explored.

6.2 Conical intersections in ionized non-covalent

dimers: Benzene dimer cation revisited

It has been shown that the radiationless decay through the conical intersections between

the electronic states of the nucleobase dimers contributes to the DNA’s intrinsic stabil-

ity [1], pariticipates in the DNA charge transfer process [2–4] and can be responsible

for some mutations [4] (see Ref. 52 for the most recent review). For instance, based on

the calculations Merchan and coworkers [2,3] proposed the cooperative micro-hopping

113

mechanism of the hole transfer in DNA. According to this mechanism, the hole migra-

tion is a series of transitions between the intersecting electronic states of the nucleobase

dimers facilitated by the thermal fluctuations of the flexible DNA chain.

In connection with the CI theme, we revisited the familiar benzene dimer [5]. This

system was a subject of extensive theoretical [5–9] and experimental [10–14] investiga-

tion for several decades. However, not all of the questions have been answered yet.

In the previous study of the benzene dimer cation [5], the excited states and proper-

ties of the three isomers of the Bz+2 (thex-dispaced (XD) sandwich,y-displaced (YD)

sandwich and t-shaped) were investigated using EOM-IP-CCSD. The minimum corre-

sponds to the displaced isomers, which are nearly-degenerate, and the t-shaped cation

was estimated to lie 6 kcal/mol higher in energy. The calculated electronic spectrum of

the cation agrees well with the gas-phase [10–13] and condensed phase [14,15] experi-

ments: the position of the CR band at 1.35 eV was predicted with a remarkable 0.02 eV

accuracy. However, the theory underestimated the intensity of the secondary CR peak

at 1.07 eV in the experimental spectrum by more than two orders of magnitude, and the

reason for this was unclear. Based on the experimental observations [13], this feature

was assigned as one of the two CR transitions corresponding to the single isomer of

Bz+2 .

Motivated by discussion with Prof. Bally from the University of Fribourg, we con-

sidered three alternative benzene dimer cation structures: the two strongly-displaced

sandwich isomers (XSD and YSD, which are displaced along thex- andy-axis, respec-

tively) and the fused structure (FD) that were proposed in Ref. 82. The ground-state

geometries of XSD, YSD and FD were optimized at IP-CISD/6-31(+)G(d) level; the

XD, YD and TS structures were obtained previously [5] employing the IP-CCSD opti-

mization with the 6-31(+)G(d) basis. The optimized ground state geometries of the

six isomers of Bz+2 and the estimated energy gaps are presented in Fig. 6.1. Table 6.1

114

YDXD

XSDTS

FD

0.23/ 0.20 6.37 / 5.89 7.42 / 7.79

33.28 / 27.29

E, kcal/mol

YSD

4.43 / 3.80

Figure 6.1: The six optimized geometries of the benzene dimer cation and the cor-responding energy gaps calculated at the IP-CCSD(dT)/6-31(+)G(d) (italic) and IP-CCSD/6-311(+,+)G(d,p) (bold) levels of theory.

provides the ground state total energies calculated at three different levels of theory.

Table 6.2 summarizes the characteristic geometric parameters, which are explained in

Figure 6.2, for the six isomers. As follows from Table 6.2, the displacement cordi-

nate values for the XSD and YSD structure are more than 2A larger relative to the

moderately-displaced XD and YD structures. Surprisingly, the separation coordinate

and the distance between the centers of mass of the fragments are 0.2-0.4A smaller

for the XSD and YSD isomers relative to the XD and YD isomers, respectively. As

IP-CISD tends to overestimate the intermolecular separations relative to IP-CCSD by

0.2-0.3A the actual difference for moderately and strongly-displaced structures may be

even more pronounced. In the fused structure FD, the two covalent bonds are formed,

which can be seen from the smallh anddCOM values.

115

Table 6.1: The ground state total energies (in hartree) of the six isomers of Bz+2 calcu-

lated at three levels of theory: IP-CCSD/6-31(+)G(d), IP-CCSD(dT)/6-31(+)G(d) andIP-CCSD/6-311(+,+)G(d,p)+FNO(99.25%)

Isomer Ground StateEtotCCSD/6−31(+)G(d) Etot

CCSD(dT )/6−31(+)G(d) EtotCCSD/6−311(+,+)G(d,p)

XD X2Bg -462.717304 -462.910464 -462.727685

YD X2Bg -462.717660 -462.910781 -462.728058

TS X2B2 -462.705866 -462.898372 -462.716231

XSD X2Bu -462.707551 -462.901399 -462.717910

YSD X2Bu -462.710547 -462.904717 -462.720998

FD X2Au -462.664903 -462.867298 -462.675027

dCOM

Δ

h

Figure 6.2: The definitions of structural parameters for the benzene dimer cation. Thedistance between the centers of mass of the fragmentsdCOM , separationh and slidingcoordinates∆ are shown.

In accord with the previous study [5], the two lowest structures of Bz+2 are the nearly-

degenerate XD and YD sandwich isomers, which lie more than 7 kcal/mol below the TS

structure (see Fig. 6.1). Not surprisingly, the fused FD structure lies much higher in

energy, so we omit it from further consideration. However, the two strongly-displaced

116

Table 6.2: The characteristic geometric parameters of the six ground-state structures ofthe benzene dimer cation. The distances between the centers of mass of the fragmentsdCOM (in A), separationh (in A) and sliding coordinate∆ (in A) values are presented.

Isomer dCOM h ∆

XD 3.27 3.09 1.07

YD 3.29 3.10 1.10

TS 4.57 – –

XSD 3.01 2.91 3.16

YSD 2.81 2.77 3.22

FD 1.64 1.49 3.15

structures - XSD and YSD - were found to lie in between the sandwich and t-shaped

structures, the lowest one less than 4 kcal/mol apart from the XD and YD isomers. It

is unclear whether the XSD and YSD are the minima or transition states. Note that the

discussed energy differences are estimated at IP-CCSD/6-311(+)G(d,p) level. Our tests

showed that the effect of triple contributions is almost neglegible and changes the energy

differences by only 0.01-0.03 kcal/mol for four low-lying isomers and 0.17 kcal/mol for

FD structure. At the same time, increasing the basis set to 6-311(+)G(d,p) at IP-CCSD

level results in 0.02, 0.66, 0.45, 0.39 and 5.82 kcal/mol changes in energy differences

for XD, YSD, XSD, TS and FD isomers, respectively. Therefore, we expect the IP-

CCSD/6-311(+)G(d,p) estimates to be of better quality than IP-CCSD(dT)/6-31(+)G(d).

This finding shows that the PES of the benzene dimer cation (as well as other ionized

non-covalent dimers) is shallow and rugged. What consequences does it have for the

electronic structure?

Consider Figure 6.3, which depicts the evolution of the four lowest electronic states

of Bz+2 along thex- (top panel) andy- (bottom panel) displacement coordinates. The

corresponding singly-occupied MOs of the cation and the calculated enegy spacings (the

ground state of the XD and YD structures are chosen as the zero-level) are presented.

117

0.27 eV

0.51eV

1.28 eV

1.40 eV

0.86 eV

1.23 eV

1.25 eV

Bg

Bu

Ag

AuAu

Ag

Bg

Bu

Displacement along x axis

E, eV

0 eV

XD XSD

CI?

ΔE

E, eV

0.19 eV

1.07 eV

1.28 eV

1.43 eV

0.91 eV

1.25 eV

1.29 eV

Bg

Bu

Ag

Au

Au

Ag

Bg

Bu

Displacement along y axis

0 eV

ΔE

CI?

YD YSD

Figure 6.3: The evolution of the four lowest electronic states of the benzene dimer cationalong thex- (top panel) andy- (bottom panel) displecement coordinates calculated withIP-CCSD/6-31(+)G(d). Two moderately (XD, YD) and two strongly-displaced (XSD,YSD) fully-optimized ground-state structures were employed. The blue arrows depictthe CR transitions at four geometries and the dashed lines interconnect the related elec-tronic states.

118

The dashed lines connect the related electronic states in moderately and strongly-

displaced sandwich isomers; the blue arrows mark the CR transitions. As it appears,

the electronic states change the order along thex- andy- displacement coordinate. For

instance, in the XSD structure the states, when ordered by the increasing energy, appear

asX2Bu, 12Bg, 12Ag and12Au as opposed to theX2Bg, 12Ag, 12Bu and12Au order

in the XD isomer. This points to the presense of the conical intersections between the

surfaces, for example, the12Bg and12Bu states of thex-displaced structures; moreover,

the intersection point is likely to be located along thex-coordinate. Interestingly, the

optimization of the geometry of the excited12Bg state of XSD converges to the ground

state XD geometry. Analogously, in they-displaced structures, the CI point between

theX2Bg and12Bu states may exist along they-axis. In theC2h group theBg → Bu

transitions are allowed by symmetry, so the interconversion between the ground states of

moderately (XD, YD) and the corresponding strongly-displaced (XSD, YSD) structures

can occur.

These findings suggest an alternative explanation of the origin of the broad peak

at 1.07 eV observed in the gas-phase experiment. As the authors point out [13], the

two-photon ionization leads to a large excess of energy in the experimental system.

The estimate of the lowest IE of the benzene dimer is significantly lower than the 12

eV available to the system and is in the range of 8.59-8.79 eV for all the isomers [5].

Some of the energy dissipates in the evaporative cooling process, but it is still likely

that the hot ionized dimers are produced in this experiment. If the height of the barrier

for theX2Bg → X2Bu interconversion through the CI is significantly smaller than the

energy excess, the strongly-displaced structures will be populated at the experimental

conditions along with XD and YD. Therefore, four CR bands will be observed in the

spectrum — at 0.96, 1.10, 1.40 and 1.43 eV (see Fig. 6.3 and Tables 6.4 and 6.3) —

consistently with the experimental findings. The relative intensity of the two arising

119

Tabl

e6.

3:T

hesi

xlo

wes

tsym

met

ry-a

llow

edtr

ansi

tions

inth

eel

ectr

onic

spec

trum

ofth

ebe

nzen

edi

mer

catio

nat

the

XD

and

XS

Dop

timiz

edge

omet

ries.

Cal

cula

ted

with

IP-C

CS

D/6

-31(

+)G

(d).

XD

XS

D

Tra

nsiti

on∆E

,eV

<µ

2>

,a.u

.f

Tra

nsiti

on∆E

,eV

<µ

2>

,a.u

.f

X2B

g→

12B

u1.

280.

0036

0.00

01X

2B

u→

12B

g0.

590.

0055

0.00

00

X2B

g→

12A

u1.

406.

3050

0.21

68X

2B

u→

12A

g0.

9611

.152

20.

2619

X2B

g→

22B

u3.

320.

6052

0.04

93X

2B

u→

22A

g3.

560.

0001

0.00

00

X2B

g→

22A

u3.

740.

0040

0.00

04X

2B

u→

22B

g3.

640.

0000

0.00

00

X2B

g→

32B

u3.

800.

0057

0.00

05X

2B

u→

32A

g4.

280.

4044

0.04

24

X2B

g→

32A

u5.

960.

0003

0.00

00X

2B

u→

32B

g6.

040.

0001

0.00

00

120

Tabl

e6.

4:T

hesi

xlo

wes

tsym

met

ry-a

llow

edtr

ansi

tions

inth

eel

ectr

onic

spec

trum

ofth

ebe

nzen

edi

mer

catio

nat

the

YD

and

YS

Dop

timiz

edge

omet

ries.

Cal

cula

ted

with

IP-C

CS

D/6

-31(

+)G

(d).

YD

YS

D

Tra

nsiti

on∆E

,eV

<µ

2>

,a.u

.f

Tra

nsiti

on∆E

,eV

<µ

2>

,a.u

.f

X2B

g→

12B

u1.

280.

0029

0.00

01X

2B

u→

12B

g0.

730.

0115

0.00

02

X2B

g→

12A

u1.

436.

2174

0.21

84X

2B

u→

12A

g1.

1010

.615

70.

2871

X2B

g→

22B

u3.

340.

6055

0.04

95X

2B

u→

22B

g3.

580.

0000

0.00

00

X2B

g→

32B

u3.

760.

0069

0.00

06X

2B

u→

22A

g3.

700.

0024

0.00

02

X2B

g→

22A

u3.

820.

0034

0.00

03X

2B

u→

32A

g4.

390.

3794

0.04

09

X2B

g→

32A

u5.

960.

0005

0.00

01X

2B

u→

32B

g6.

090.

0002

0.00

00

121

features in 1.4-1.5 eV and 0.9-1.1 eV spectral regions will be determined by the ratio

of moderately- and strongly-displaced structures at experimental conditions rather than

the calculated intensities of the elementary transitions (which are similar for all CR

bands). The 0.14 eV spacing between the two lowest CR transitions even explains the

broadening of the experimental band at 1.07 eV.

Quite a few questions remain unanswered. Where is the PES crossing point located

and how large is the interconversion barrier? Are the XSD and YSD true minima or

transition states? What is the effect of the entropic contribution on the barriers and

energy gaps? The last point is particularly important when interpreting the results of

finite-temperature experiments, like the one discussed above. The DFT-D vibrational

analysis with theωB97X-D functional can address the latter two questions (for the

ground states). However, one should be careful as the harmonic approximation used

in frequency calculations is likely to be of limited accuracy. As of the former, using the

minimum-energy crossing point search procedure implemented in Q-Chem for EOM-

CC family of methods [16], we can locate the PES crossing point and estimate the barrier

of interconversion.

6.3 The effect of substituents in ionized non-covalent

dimers: Electronic structure and properties

The electronic structure and properties of the chemically-modified nucleobase dimers

is another promising research direction, which is attractive from both the fundamental

and the applied viewpoints. It was shown that the conductivity of the DNA decreases

sufficiently with the increase of the A-T base pair’s content [17–19]. This imposes the

restrictions on the sequence and composition of the DNA molecules that may be suc-

cessful candidates for molecular electronics applications. Another issue is the oxidative

122

degradation of guanine in the chain that is associated with the charge transport [20]. To

overcome these difficulties, synthetic analogs of the DNA can be used in the device con-

struction. In these analogs the target properties can be modified by the introduction of

substituents, like alkyl, halogen groups, additional aromatic rings or heteroatoms in the

”native” nucleobase structures. The latter approach was successfully used by Majima

and coworkers [21]. In their experimental study, the 7-Deazaadenine (Z) (i.e. adenine

with one of the N heteroatoms replaced by the C atom) was introduced in the DNA

sequence instead of the adenine. This increased the efficiency of the charge transport

more than two-fold relative to the original sequence. This effect was explained by the

smaller gap between the HOMOs of the ZT and GC base pairs as compared to AT and

GC. Okamoto and coworkers [20] used another approach, i.e. they extended the nucle-

obase aromatic system. The Benzodeazaadenine was incorporated in the DNA instead

of the native adenine nucleobase. The modified DNA samples exhibited a remarkably

high hole transport ability. The authors indicated that the orderedπ-stacking array, low

oxidation potentials of the nucleobases and suppressed oxidative degradation are the

three essential factors for the successfull design of the synthetic DNA nanowire.

To facilitate the search of promising synthetic DNA analogs, a systematic approach

is needed. A qualitative theory, which would be able to predict the effect of chemical

modifications on the electronic structure, ionization energies and states of the nucle-

obase and nucleobase clusters, would be of great value. We have already investigated the

effect of methylation on the ionized states and electronic structure of the monomer and

dimers of one of the nucleobases. The results showed that the qualitative trends for IEs

of the modified nucleobase can be predicted by classifying the introduced perturbation

as stabilizing or destabilizing for the corresponding ionized state. The simple analysis

of the molecular orbitals of the original nucleobase in conjuction with the qualitative

123

organic chemistry considerations (i.e. inductive and resonance effects, electron-donor

and electron-acceptor groups) can provide an insight.

An interesting question is whether or not the effect of substitutions can be extrap-

olated from the monomer to the dimer system. For instance, in the 1,3-dimethylated

uracils, the effect of methylation on the lowest IE of the dimer was comparable to that in

the monomer: -0.61 and -0.63 eV shifts in the first IE, respectively. For other states, the

methylation-related shifts were also similar (see Table 5.5), unless there was an exces-

sive electron density overlap in the methylated dimer attributed to the CH3 groups, e.g.

as for the22A1 and52A1 states, where theσCH MO component of one of the fragments

overlapped with thelp(O) component of the other. The DMO-LCFMO splittings of

states were also similar in the methylated and non-methylated dimers (0.37 vs. 0.35 eV,

respectively), again excluding the22A1 and52A1 states. Thus, for most states the DMO-

LCFMO overlap and the effect of substituents on the IEs are additive, so the electronic

structure of the substituted dimer cation can be extrapolated from the prototype dimer

using the substituted monomer results. In terms of the qualitative DMO-LCFMO frame-

work, the levels of modified dimers are just shifted up or down by constants equal to the

state shifts observed in the substituted monomer. Such extrapolation schemes can be

useful for approximate estimates when the full calculation is too expensive. It should be

noted, however, that the CH3 groups represent a relatively small perturbation, such that

the shapes of MOs and structures are similar for the methylated- and non-methylated

systems. It is likely that the introduction of strong electron-acceptors, like NO2 and

halogens, or bulk aromatic rings will significantly perturb the structure, MOs and the

states, so that such simplified considerations will be of limited value.

Back to the DNA nanowire design, according to the micro-hopping mechnanism pro-

posed by Merchan and coworkers [2], the hole transfer along the single DNA strand is a

series of hole hops betwen the pairs of adjacentπ-stacked nucleobases, which involves

124

the transitions through the conical intersections. How can we control the efficiency

of such process? First, the low-lying ionized states of the adjacent nucleobase dimers

should be nearly-degenerate. Second, there should exist a low-energy CI between the

PES of the two dimer systems (i.e. the CI on the tetramer surface along the separation

coordinate of the dimers).

Consider Table 6.5 presenting some of the available theoretical estimates of the first

VIE of the DNA and RNA nucleobases and stacked nucleobase dimers. The first VIEs

Table 6.5: Theoretical estimates of the lowest VIE (in eV) of the nucleobase monomersandπ-stacked dimers.

Monomers Stacked dimers

VIE, eV VIE, eV

A 8.37a, 8.37b A2 8.18b

T 9.07a, 9.13b AT2 8.28b

C 8.73a T2 8.78b

G 8.09a U2 9.21c

U 9.42a, 9.55ca Empirically corrected (IPEA=0.25) CASPT2/ANO-L 431/21 from Ref. 22.

b The EOM-IP-CCSD/cc-pVTZ from Ref. 23. For dimers, the extrapolation was used.c The EOM-IP-CCSD/cc-pVTZ from Ref. 24. For dimers, the extrapolation was used.

of the DNA bases lie in the 8.1 - 9.1 eV range, with guanine and adenine ionizing at

lower energies than thymine and cytosine [22, 23]. In RNA, thymine is replaced with

uracil that extends this range to 9.55 eV [24]. The stacked dimer data is incomplete,

and includes three homodimer (U2, T2, A2) and one heterodimer (AT) structure (i.e 4

structures out of 15 possible) [23, 24]. For effective CT, we need to tighten the lowest

VIE range. From the DMO-LCFMO considerations, it follows that homodimers com-

posed from the hard-to-ionize thymine and uracil should affect the CT in DNA and RNA

the most (because for the heterodimers, like AT or TC, VIEs are expected to be lower).

The synthetic RNAs with dimethylated uracils could be one of the possible solutions.

125

However, in such case the double-helix structure of RNA could be perturbed, as the AU

hydrogen-bonding interactions will be suppressed. In the DNA, thymine could also be

methylated at one of the nitrogens to decrease its VIE. Alternatively, another approach

can be exploited, in which the VIEs of the lower-ionizing bases - guanine and adenine

- are altered by the introduction of the electron-acceptors like halogen groups (or NO2).

Therefore, the ionized methylated thymine dimer and halogen-substituted adenine could

be an intriguing target for future studies.

Of course, the above discussion only applies to the single-strand DNA charge trans-

port. In the DNA and RNA double-helices the charge-trapping by the proton-transfer

and other mechanisms affectinging CT need to be considered. Therefore, it would be of

interest to investigate the effect of substituents on the symmetric and proton-transfered

H-bonded structures and the barriers of the proton transfer.

6.4 Reference list

[1] T. Schultz, E. Samoylova, W. Radloff, I. V. Hertel, A. L. Sobolewski, and W. Dom-cke, Efficient deactivation of a model base pair via excited-state hydrogen transfer.,Science306, 1765 (2004).

[2] D. Roca-Sanjuan, M. Merchan, and L. Serrano-Andres, Modelling hole transferin DNA: Low-lying excited states of oxidized cytosine homodimer and cytosine-adenine heterodimer., Chem. Phys.349, 188 (2008).

[3] D. Roca-Sanjuan, G. Olaso-Gonzalez, P. B. Coto M. Merchan, and L. Serrano-Andres, Modelling hole transfer in DNA. II. Molecular basis of charge transportin the DNA chain., Theor. Chim. Acta (2009).

[4] I. Gonzalez-Ramırez, T. Climent, J. J. Serrano-Perez, R. Gonzalez-Luque,M. Merchan, and L. Serrano-Andres, The role of pyrimidine nucleobase excimersin DNA photophysics and photoreactivity, Pure Appl. Chem.81, 1695 (2009).


126

[6] K. Hiraoka, S. Fujimaki, K. Aruga, and S. Yamabe, Stability and structure ofbenzene dimer cation (C6H6)

+2 in the gas phase, J. Chem. Phys.95, 8413 (1991).

[7] E. Miyoshi, T. Ichikawa, T. Sumi, Y. Sakai, and N. Shida, Ab initio CASSCF andMRSDCI calculations of the (C6H6)

+2 radical, Chem. Phys. Lett.275, 404 (1997).

[8] E. Miyoshi, N. Yamamoto, M. Sekiya, and K. Tanaka, Structure and bonding ofthe (C6H6)

+2 radical, Mol. Phys.101, 227 (2003).

[9] M. Rusyniak, Y. Ibrahim, E. Alsharaeh, M. Meot-Ner (Mautner), and M.S. El-Shall, Mass-selected ion mobility studies of the isomerization of the benzene radi-cal cation and binding energy of the benzene dimer cation. Separation of isomericions by dimer formation, J. Phys. Chem. A107, 7656 (2003).

[10] K. Ohashi and N. Nishi, Photodissociation spectroscopy of benzene clusterions:(C6H6)

+2 and (C6H6)

+3 , J. Chem. Phys.95, 4002 (1991).

[11] K. Ohashi and N. Nishi, Photodepletion spectroscopy on charge resonance bandof (C6H6)

+2 and (C6H6)

+3 , J. Phys. Chem.96, 2931 (1992).

[12] K. Ohashi, Y. Nakai, T. Shibata, and N. Nishi, Photodissociation spectroscopy of(C6H6)

+2 , Laser Chem.14, 3 (1994).

[13] K. Ohashi, Y. Inokuchi, and N. Nishi, Pump-probe photodepletion spectroscopy of(C6H6)

+2 . Identification of spectrum in the charge resonance band region, Chem.

Phys. Lett.263, 167 (1996).

[14] Y. Inokuchi, Y. Naitoh, K. Ohashi, K. Saitow, K. Yoshihara, and N. Nishi, For-mation of benzene dimer cations in neat liquid benzene studied by femtosecondtransient absorption spectroscopy, Chem. Phys. Lett.269, 278 (1997).

[15] T. Shida and W. H. Hamill, Molecular ions in radiation chemistry. 3. Absorptionspectra of aromatic-hydrocarbon cations and anions in organic glasses, J. Chem.Phys.44, 4372 (1966).

[16] E. Epifanovsky and A.I. Krylov, Direct location of the minimum point on intersec-tion seams of potential energy surfaces with equation-of-motion coupled-clustermethods, Mol. Phys.105, 2515 (2007).

[17] K. Nakatani, C. Pohno, and I. Saito, Chemistry of sequence-dependent remoteguanine oxidation: Photoreaction of duplex DNA containing cyanobenzophenone-substituted uridine, J. Am. Chem. Soc.121, 10854 (1999).

[18] B. Giese, Long-distance charge transport in DNA: The hopping mechanism, Acc.Chem. Res.33, 631 (2000).

127

[19] C. Wan, T. Fiebig, O. Schiemann, J.K. Barton, and A. Zewail, Femtosecond directobservation of charge transfer between bases in DNA, Proc. Natl. Acad. Sci. USA97, 14052 (2000).

[20] A. Okamoto, K. Tanaka, and I. Saito, Rational design of a DNA wire possessingan extremely high hole transport ability, J. Am. Chem. Soc.125, 5066 (2003).

[21] K. Kawai, H. Kodera, Y. Osakada, and T. Majima, Sequence-independent andrapid long-range charge transfer through DNA, Nature Chemistry1, 156 (2009).




128

Bibliography

[1] P.W. Atkins and R.S. Friedman.Molecular Quantum Mechanics. New York:Oxford University Press, 2005.

[2] R. N. Barnett, C. L. Cleveland, A. Joy, U. Landman, and G.B. Schuster. Chargemigration in DNA: Ion-gated transport.Science, 294:567–571, 2001.

[3] L. Belau, K.R. Wilson, S.R. Leone, and M. Ahmed. Vacuum-ultravioled pho-toionization studies of the microhydration of DNA bases (guanine, cytosine, ade-nine, and thymine).J. Phys. Chem. A, 111:7562–7568, 2007.

[4] E.R. Bittner. Lattice theory of ultrafast excitonic and charge-transfer dynamics inDNA. J. Chem. Phys., 125:094909, 2006.

[5] M. Bixon and J. Jortner. Hole trapping, detrapping, and hopping in DNA.J. Phys.Chem. A, 105:10322–10328, 2001.

[6] K. Bravaya. Private communication.

[7] K.B. Bravaya, O. Kostko, M. Ahmed, and A.I. Krylov. The effect ofπ-stacking,h-bonding, and electrostatic interactions on the ionization energies of nucleic acidbases: Adenine-adenine, thymine-thymine and adenine-thymine dimers.Phys.Chem. Chem. Phys., 2010. in press, DOI:10.1039/b919930f.

[8] E. Cauet, D. Dehareng, and J. Lievin. Ab initio study of the ionization of the DNAbases: Ionization potentials and excited states of the cations.J. Phys. Chem. A,110:9200–9211, 2006.

[9] E. Cauet and J. Lievin. Radical cations of the nucleic bases and radiation damageto DNA: Ab initio study. Adv. Quantum Chem., 52:121–147, 2007.

129

[10] J.-D. Chai and M. Head-Gordon. Long-range corrected hybrid density function-als with damped atom-atom dispersion interactions.Phys. Chem. Chem. Phys.,10:6615–6620, 2008.

[11] A.-O. Colson, B. Besler, and M.D. Sevilla. Ab initio molecular orbital calcula-tions on DNA base pair radical ions: Effect of base pairing on proton-transferenergies, electron affinities, and ionization potentials.J. Phys. Chem., 96:9787–9794, 1992.

[12] A.-O. Colson, B. Besler, and M.D. Sevilla. Ab initio molecular orbital calcula-tions on DNA radical ions. 4. Effect of hydration on electron affinities and ion-ization potentials of base pairs.J. Phys. Chem., 97:13852–13859, 1993.

[13] M.S. Cooke, M. D. Evans, M. Dizdaroglu, and J. Lunec. Oxidative DNA damage:Mechanisms, mutation and disease.The FASEB Journal, 17:1195–1214, 2003.

[14] D. Dougherty, K. Wittel, J. Meeks, and S. P. McGlynn. Photoelectron spec-troscopy of carbonyls. Ureas, uracils, and thymine.J. Am. Chem. Soc., 98:3815,1976.

[15] T.H. Dunning. Gaussian basis sets for use in correlated molecular calculations.I. The atoms boron through neon and hydrogen.J. Chem. Phys., 90:1007–1023,1989.

[16] K. Emrich. An extension of the coupled-cluster formalism to excited states (I).Nucl. Phys., A351:379–396, 1981.

[17] E. Epifanovsky and A.I. Krylov. Direct location of the minimum point on inter-section seams of potential energy surfaces with equation-of-motion coupled-cluster methods.Mol. Phys., 105:2515–2525, 2007.

[18] J. Geertsen, M. Rittby, and R.J. Bartlett. The equation-of-motion coupled-clustermethod: Excitation energies of Be and CO.Chem. Phys. Lett., 164:57–62, 1989.

[19] F.L. Gervasio, A. Laio, M. Parrinello, and M. Boero. Charge localization in DNAfibers.Phys. Rev. Lett., 94:158103, 2005.

[20] B. Giese. Long-distance charge transport in DNA: The hopping mechanism.Acc.Chem. Res., 33:631–636, 2000.

[21] B. Giese. Long-distance electron tranfer through DNA.Annu. Rev. Biochem.,71:51–70, 2002.

[22] B. Giese, J. Amaudrut, A.-K. Kohler, M. Spormann, and S. Wessely. Directobservation of hole transfer through DNA by hopping between adenine bases andby tunnelling.Nature, 412:318–320, 2001.

130

[23] E.D. Glendening, J.K. Badenhoop, A.E. Reed, J.E. Carpenter, J.A. Bohmann,C.M. Morales, and F. Weinhold. NBO 5.0. Theoretical Chemistry Institute, Uni-versity of Wisconsin, Madison, WI, 2001.

[24] A.A. Golubeva and A.I. Krylov. The effect ofπ-stacking and H-bonding onionization energies of a nucleobase: Uracil dimer cation.Phys. Chem. Chem.Phys., 11:1303–1311, 2009.

[25] A.A. Golubeva, P.A. Pieniazek, and A.I. Krylov. A new electronic structuremethod for doublet states: Configuration interaction in the space of ionized 1hand 2h1p determinants.J. Chem. Phys., 130(12):124113, 2009.

[26] I. Gonzalez-Ramırez, T. Climent, J. J. Serrano-Perez, R. Gonzalez-Luque,M. Merchan, and L. Serrano-Andres. The role of pyrimidine nucleobase excimersin DNA photophysics and photoreactivity.Pure Appl. Chem., 81:1695–1705,2009.

[27] S. Grimme. Accurate description of van der Waals complexes by density func-tional theory including empirical corrections.J. Comput. Chem., 25:1463–1473,2004.

[28] S. Grimme. Semiempirical GGA-type density functional constructed with a long-range dispersion correction.J. Comput. Chem., 27(15):1787–1799, 2006.

[29] W.J. Hehre, R. Ditchfield, and J.A. Pople. Self-consistent molecular orbital meth-ods. XII. Further extensions of gaussian-type basis sets for use in molecularorbital studies of organic molecules.J. Chem. Phys., 56:2257, 1972.

[30] T. Helgaker, P. Jørgensen, and J. Olsen.Molecular electronic structure theory.Wiley & Sons, 2000.

[31] P.T. Henderson, D. Jones, G. Hampikian, Y. Kan, and G.B. Schuster. Long-distance charge transport in duplex DNA: The phonon-assisted polaron-like hop-ping mechanism.Proc. Nat. Acad. Sci., 96(15):8353–8358, 1999.

[32] K. Hiraoka, S. Fujimaki, K. Aruga, and S. Yamabe. Stability and structure ofbenzene dimer cation (C6H6)

+2 in the gas phase.J. Chem. Phys., 95:8413–8418,

1991.

[33] P. Hobza, J.Sponer, and T. Reschel. Density functional theory and molecularclusters.J. Comput. Chem., 16(11):1315, 1995.

[34] H.R. Hudock, B.G. Levine, A.L. Thompson, H. Satzger, D. Townsend, N. Gador,S. Ulrich, A. Stolow, and T.J. Martınez. Ab initio molecular dynamics and time-resolved photoelectron spectroscopy of electronically excited uracil and thymine.J. Phys. Chem. A, 111:8500–8598, 2007.

131

[35] G.R. Hutchison, M.A. Ratner, and T.J. Marks. Intermolecular charge transferbetween heterocyclic oligomers. Effects of heteroatom and molecular packing onhopping transport in organic semiconductors.J. Am. Chem. Soc., 127:16866–16881, 2005.

[36] Y. Inokuchi, Y. Naitoh, K. Ohashi, K. Saitow, K. Yoshihara, and N. Nishi. For-mation of benzene dimer cations in neat liquid benzene studied by femtosecondtransient absorption spectroscopy.Chem. Phys. Lett., 269:278–304, 1997.

[37] P. Jurecka, J.Sponer, J.Cerny, and P. Hobza. Benchmark database of accurate(MP2 and CCSD(T) compl ete basis set limit) interaction energies of small modelcomplexes, DNA base pairs, and amino acid pairs.Phys. Chem. Chem. Phys.,8:1985, 2006.

[38] K. Kawai, H. Kodera, Y. Osakada, and T. Majima. Sequence-independent andrapid long-range charge transfer through DNA.Nature Chemistry, 1:156–159,2009.

[39] S.K. Kim, W. Lee, and D.R. Herschbach. Cluster beam chemistry: Hydrationof nucleic acid bases; Ionization potentials of hydrated adenine and thymine.J.Phys. Chem., 100:7933–7937, 1996.

[40] O. Kostko, K.B. Bravaya, A.I. Krylov, and M. Ahmed. Ionization of cytosinemonomer and dimer studied by VUV photoionization and electronic structurecalculations.Phys. Chem. Chem. Phys., 2010. In press, DOI: 10.1039/B921498D.

[41] K. Kowalski and P. Piecuch. The active space equation-of-motion coupled-clustermethods for excited electronic states: the EOMCCSDt approach.J. Chem. Phys.,113(19):8490–8502, 2000.

[42] M. Kratochvil, O. Engkvist, J. Sponer, P. Jungwirth, and P. Hobza. Uracil dimer:Potential energy and free energy surfaces. Ab initio beyond Hartree-Fock andempirical potential studies.J. Phys. Chem. A, 102(35):6921–6926, 1998.

[43] M. Kratochvıl, O. Engkvist, J. Vacek, P. Jungwirth, and P. Hobza. Methylateduracil dimers: Potential energy and free energy surfaces.Phys. Chem. Chem.Phys., 2:2419–2424, 2000.

[44] R. Krishnan, J.S. Binkley, R. Seeger, and J.A. Pople. Self-consistent molecularorbital methods. XX. A basis set for correlated wave functions.J. Chem. Phys.,72:650, 1980.

[45] S. Kristyan and P. Pulay. Can (semi)local density functional theory account forthe London dispersion forces?Chem. Phys. Lett., 229:175–180, 1994.

132

[46] A.I. Krylov. Size-consistent wave functions for bond-breaking: The equation-of-motion spin-flip model.Chem. Phys. Lett., 338:375–384, 2001.

[47] A.I. Krylov. Spin-flip configuration interaction: An electronic structure modelthat is both variational and size-consistent.Chem. Phys. Lett., 350:522–530,2001.

[48] A.I. Krylov. Equation-of-motion coupled-cluster methods for open-shell andelectronically excited species: The hitchhiker’s guide to Fock space.Annu. Rev.Phys. Chem., 59:433–462, 2008.

[49] G. Lauer, W. Schafer, and A. Schweig. Functional subunits in the nucleic acidbases uracil and thymine.Tetrahedron Lett., 16(45):3939, 1975.

[50] S.V. Levchenko and A.I. Krylov. Equation-of-motion spin-flip coupled-clustermodel with single and double substitutions: Theory and application to cyclobu-tadiene.J. Chem. Phys., 120(1):175–185, 2004.

[51] R.A. Marcus and N. Sutin. Electron transfers in chemistry and biology.Biochim.Biophys. Acta, 811:265–322, 1985.

[52] C.T. Middleton, K. de La Harpe, C. Su, Y.K. Law, C.E. Crespo-Hernandez, andB. Kohler. DNA excited-state dynamics: From single bases to the double helix.Annu. Rev. Phys. Chem., 60:217–239, 2009.

[53] E. Miyoshi, T. Ichikawa, T. Sumi, Y. Sakai, and N. Shida. Ab initio CASSCF andMRSDCI calculations of the (C6H6)

+2 radical. Chem. Phys. Lett., 275:404–408,

1997.

[54] E. Miyoshi, N. Yamamoto, M. Sekiya, and K. Tanaka. Structure and bonding ofthe (C6H6)

+2 radical.Mol. Phys., 101:227–232, 2003.

[55] K. Muller-Dethlefs and P. Hobza. Noncovalent interactions: A challenge forexperiment and theory.Chem. Rev., 100:143–167, 2000.

[56] K. Nakatani, C. Pohno, and I. Saito. Chemistry of sequence-dependentremote guanine oxidation: Photoreaction of duplex DNA containingcyanobenzophenone-substituted uridine.J. Am. Chem. Soc., 121:10854–10855,1999.

[57] M.E. Nu nez, D.B. Hall, and J.K. Barton. Long-range oxidative damage to DNA:Effects of distance and sequence.Chem. and Biol., 6(2):85–97, 1999.

[58] M. Nooijen and R.J. Bartlett. Equation of motion coupled cluster method forelectron attachment.J. Chem. Phys., 102:3629–3647, 1995.

133

[59] D. T. Odom and J. K. Barton. Long-range oxidative damage in DNA/RNAduplexes.Biochemistry, 40:8727–8737, 2001.

[60] K. Ohashi, Y. Inokuchi, and N. Nishi. Pump-probe photodepletion spectroscopyof (C6H6)

+2 . Identification of spectrum in the charge resonance band region.

Chem. Phys. Lett., 263:167–172, 1996.

[61] K. Ohashi, Y. Nakai, T. Shibata, and N. Nishi. Photodissociation spectroscopy of(C6H6)

+2 . Laser Chem., 14:3–14, 1994.

[62] K. Ohashi and N. Nishi. Photodissociation spectroscopy of benzene clusterions:(C6H6)

+2 and (C6H6)

+3 . J. Chem. Phys., 95:4002–4009, 1991.

[63] K. Ohashi and N. Nishi. Photodepletion spectroscopy on charge resonance bandof (C6H6)

+2 and (C6H6)

+3 . J. Phys. Chem., 96:2931–2932, 1992.

[64] A. Okamoto, K. Tanaka, and I. Saito. Rational design of a DNA wire possessingan extremely high hole transport ability.J. Am. Chem. Soc., 125:5066–5071,2003.

[65] G. Olaso-Gonzales, D. Roca-Sanjuan, L. Serrano-Andres, and M. Merchan.Toward understanding of DNA fluorescence: The singlet excimer of cytosine.J. Chem. Phys., 125:231002, 2006.

[66] S. Pal, M. Rittby, R.J. Bartlett, D. Sinha, and D. Mukherjee. Multireferencecoupled-cluster methods using an incomplete model space — application toionization-potentials and excitation-energies of formaldehyde.Chem. Phys. Lett.,137:273–278, 1987.

[67] P.A. Pieniazek, S.A. Arnstein, S.E. Bradforth, A.I. Krylov, and C.D. Sherrill.Benchmark full configuration interaction and EOM-IP-CCSD results for proto-typical charge transfer systems: Noncovalent ionized dimers.J. Chem. Phys.,127:164110, 2007.

[68] P.A. Pieniazek, S.E. Bradforth, and A.I. Krylov. Charge localization and Jahn-Teller distortions in the benzene dimer cation.J. Chem. Phys., 129:074104, 2008.

[69] P.A. Pieniazek, A.I. Krylov, and S.E. Bradforth. Electronic structure of the ben-zene dimer cation.J. Chem. Phys., 127:044317, 2007.

[70] P.A. Pieniazek, J. VandeVondele, P. Jungwirth, A.I. Krylov, and S.E. Bradforth.Electronic structure of the water dimer cation.J. Phys. Chem. A, 112:6159–6170,2008.

134

[71] M. Pitonak, K.E. Riley, P. Neogrady, and P. Hobza. Highly accurate CCSD(T)and DFT-SAPT stabilization energies of H-bonded and stacked structures of theuracil dimer.Comp. Phys. Comm., 9:1636–1644, 2008.

[72] F. Prat, K.N. Houk, and C.S. Foote. Effect of guanine stacking on the oxidationof 8-oxoguanine in B-DNA.J. Am. Chem. Soc., 120:845, 1998.

[73] D. Roca-Sanjuan, M. Merchan, and L. Serrano-Andres. Modelling hole transferin DNA: Low-lying excited states of oxidized cytosine homodimer and cytosine-adenine heterodimer.Chem. Phys., 349:188–196, 2008.

[74] D. Roca-Sanjuan, M. Merchan, and L. Serrano-Andres. Modelling hole-transferin DNA: Low-lying excited states of oxidized cytosine homodimer and cytosine-adenine heterodimer.Chem. Phys., 349:188–196, 2008.

[75] D. Roca-Sanjuan, G. Olaso-Gonzalez, P. B. Coto M. Merchan, and L. Serrano-Andres. Modelling hole transfer in DNA. II. Molecular basis of charge transportin the DNA chain.Theor. Chim. Acta, 2009.

[76] D. Roca-Sanjuan, M. Rubio, M. Merchan, and L. Serrano-Andres. Ab initiodetermination of the ionization potentials of DNA and RNA nucleobases.J.Chem. Phys., 125:084302, 2006.

[77] D.J. Rowe. Equations-of-motion method and the extended shell model.Rev. Mod.Phys., 40:153–166, 1968.

[78] M. Rusyniak, Y. Ibrahim, E. Alsharaeh, M. Meot-Ner (Mautner), and M.S. El-Shall. Mass-selected ion mobility studies of the isomerization of the benzeneradical cation and binding energy of the benzene dimer cation. Separation of iso-meric ions by dimer formation.J. Phys. Chem. A, 107:7656–7666, 2003.

[79] H. Saigusa. Excited-state dynamics of isolated nucleic acid bases and their clus-ters.Photochem. Photobiol., 7:197–210, 2006.

[80] H. Satzger, D. Townsend, and A. Stolow. Reassignment of the low lying cationicstates in gas phase adenine and 9-methyl adenine.Chem. Phys. Lett., 430:144–148, 2006.

[81] C.D. Scherrill. Reviews in Computational Chemistry, chapter Chapter 1: Com-putations of noncovalentπ interactions, pages 1–38. Jon Wiley & Sons, 2009.

[82] K. Schroeter, D. Schroder, H. Schwarz, G. D. Reddy, O. Wiest, C. Carra, andT. Bally. Ion chemistry ofanti-o,o′-Dibenzene. Chem. Eur. J., 6:4422–4430,2000.

135

[83] T. Schultz, E. Samoylova, W. Radloff, I. V. Hertel, A. L. Sobolewski, andW. Domcke. Efficient deactivation of a model base pair via excited-state hydro-gen transfer.Science, 306:1765–1768, 2004.

[84] S. Schumm, M. Prevost, D. Garcia-Fresnadillo, O. Lentzen, C. Moucheron, andA. Krisch-De Mesmaeker. Influence of the sequence dependent ionization poten-tials of guanines on the luminescence quenching of Ru-labeled oligonucleotides:A theoretical and experimental study.J. Phys. Chem. B, 106:2763–2768, 2002.

[85] H. Sekino and R.J. Bartlett. A linear response, coupled-cluster theory for excita-tion energy.Int. J. Quant. Chem. Symp., 26:255–265, 1984.

[86] T. Shida and W. H. Hamill. Molecular ions in radiation chemistry. 3. Absorptionspectra of aromatic-hydrocarbon cations and anions in organic glasses.J. Chem.Phys., 44:4372, 1966.

[87] M.O. Sinnokrot and C.D. Sherrill. Unexpected substituent effecst in face-to-faceπ-stacking interactions.J. Phys. Chem. A, 107:8377–8379, 2003.

[88] M.O. Sinnokrot and C.D. Sherrill. Highly accurate coupled cluster potentialenergy curves for the benzene dimer: Sandwich, t-shaped, and parallel-displacedconfigurations.J. Phys. Chem. A, 108:10200–10207, 2004.

[89] M.O. Sinnokrot and C.D. Sherrill. Substituent effects inπ−π interactions: Sand-wich and t-shaped configurations.J. Am. Chem. Soc., 126:7690–7697, 2004.

[90] M.O. Sinnokrot and C.D. Sherrill. High-accuracy quantum mechanical studies ofpi-pi interactions in benzene dimers.J. Phys. Chem. A, 110:10656–10668, 2006.

[91] J. Sponer, J. Leszczynski, and P. Hobza. Electronic properties, hydrogen bonding,stacking, and cation binding of DNA and RNA bases.Biopolymers, 61:3–31,2002.

[92] J.F. Stanton and R.J. Bartlett. The equation of motion coupled-cluster method.A systematic biorthogonal approach to molecular excitation energies, transitionprobabilities, and excited state properties.J. Chem. Phys., 98:7029–7039, 1993.

[93] H. Sugiyama and I. Saito. Theoretical studies of GC-specific photocleavage ofDNA via electron transfer: Significant lowering of ionization potential and 5’-localization of HOMO of stacked GG bases in B-form DNA.J. Am. Chem. Soc.,118:7063–7068, 1996.

[94] T. Takada, K. Kawai, M. Fujitsuka, and T. Majima. Direct observation ofhole transfer through double-helical DNA over 100a. Proc. Nat. Acad. Sci.,101:14002–14006, 2004.

136

[95] G.S. Tschumper.Reviews in Computational Chemistry, chapter Chapter 2: Reli-able electronic structure computations for weak noncovalent interactions in clus-ters, pages 39–90. Jon Wiley & Sons, 2009.

[96] J. Cerny and P. Hobza. Non-covalent interactions in biomacromolecules.Phys.Chem. Chem. Phys., 9:5291–5303, 2007.

[97] S. Urano, X. Yang, and P.R. LeBrenton. UV photoelectron and quantum mechani-cal characterization of DNA and RNA bases: Valence electronic structures of ade-nine, 1,9-dimethylguanine, 1-methylcytosine, thymine and uracil.J. Mol. Struct.,214:315, 1989.

[98] C. Wan, T. Fiebig, O. Schiemann, J.K. Barton, and A. Zewail. Femtoseconddirect observation of charge transfer between bases in DNA.Proc. Natl. Acad.Sci. USA, 97:14052–14055, 2000.

[99] Y. Shao, L.F. Molnar, Y. Jung, J. Kussmann, C. Ochsenfeld, S. Brown, A.T.B.Gilbert, L.V. Slipchenko, S.V. Levchenko, D.P. O’Neil, R.A. Distasio Jr, R.C.Lochan, T. Wang, G.J.O. Beran, N.A. Besley, J.M. Herbert, C.Y. Lin, T. VanVoorhis, S.H. Chien, A. Sodt, R.P. Steele, V.A. Rassolov, P. Maslen, P.P. Koram-bath, R.D. Adamson, B. Austin, J. Baker, E.F.C. Bird, H. Daschel, R.J. Doerksen,A. Drew, B.D. Dunietz, A.D. Dutoi, T.R. Furlani, S.R. Gwaltney, A. Heyden, S.Hirata, C.-P. Hsu, G.S. Kedziora, R.Z. Khalliulin, P. Klunziger, A.M. Lee, W.Z.Liang, I. Lotan, N. Nair, B. Peters, E.I. Proynov, P.A. Pieniazek, Y.M. Rhee,J. Ritchie, E. Rosta, C.D. Sherrill, A.C. Simmonett, J.E. Subotnik, H.L. Wood-cock III, W. Zhang, A.T. Bell, A.K. Chakraborty, D.M. Chipman, F.J. Keil, A.Warshel, W.J. Herhe, H.F. Schaefer III, J. Kong, A.I. Krylov, P.M.W. Gill, M.Head-Gordon. Advances in methods and algorithms in a modern quantum chem-istry program package.Phys. Chem. Chem. Phys., 8:3172–3191, 2006.

[100] C. Yu, T.J. O’Donnel, and P.R. LeBreton. Ultraviolet photo-electron studies ofvolatile nucleoside models - vertical ionization-potential measurements of methy-lated uridine, thymidine, cytidine, and adenosine.J. Phys. Chem., 85:3851–3855,1981.

[101] A.A. Zadorozhnaya and A.I. Krylov. Ionization-induced structural changes inuracil dimers and their spectroscopic signatures.J. Chem. Theory Comput., 2010.In press.

[102] A.A. Zadorozhnaya and A.I. Krylov. Zooming into pi-stacked manifolds of nucle-obases: Ionized states of dimethylated uracil dimers.J. Phys. Chem. A, 2010. Inpress.

137

[103] Y. Zhang and W. Yang. A challenge for density functionals: Self-interaction errorincreases for systems with a noninteger number of electrons.J. Chem. Phys.,109(7):2604–2608, 1998.

138

Appendix A

EOM-IP optimized geometries of Bz+2

X-displaced isomer (XD)

Comment: Ground electronic state (X2Bg) optimized with IP-CCSD/6-31(+)G(d) under

C2h symmetry constraint,ENN=647.863144.Atom x y zC 1.577051 -0.344668 -1.391098H 1.596237 -0.355418 -2.480441C 2.242307 0.695416 -0.691513H 2.753735 1.478322 -1.248242C 2.242307 0.695416 0.691513H 2.753735 1.478322 1.248242C 1.577051 -0.344668 1.391098H 1.596237 -0.355418 2.480441C 0.955447 -1.401972 0.694504H 0.500928 -2.220563 1.249090C 0.955447 -1.401972 -0.694504H 0.500928 -2.220563 -1.249090C -2.242307 -0.695416 0.691513H -2.753735 -1.478322 1.248242C -1.577051 0.344668 1.391098H -1.596237 0.355418 2.480441C -0.955447 1.401972 0.694504H -0.500928 2.220563 1.249090C -0.955447 1.401972 -0.694504H -0.500928 2.220563 -1.249090C -1.577051 0.344668 -1.391098H -1.596237 0.355418 -2.480441C -2.242307 -0.695416 -0.691513H -2.753735 -1.478322 -1.248242

139

Y-displaced isomer (YD)

Comment: Ground electronic state (X2Bg) optimized with IP-CCSD/6-31(+)G(d) under

C2h symmetry constraint,ENN=648.359009.Atom x y zC -2.375370 -0.802427 0.000000H -3.000807 -1.692604 0.000000C -1.970007 -0.221982 1.202903H -2.275235 -0.658658 2.152860C -1.180373 0.964775 1.203183H -0.923839 1.432362 2.152829C -0.826193 1.574414 0.000000H -0.257481 2.501418 0.000000C -1.180373 0.964775 -1.203183H -0.923839 1.432362 -2.152829C -1.970007 -0.221982 -1.202903H -2.275235 -0.658658 -2.152860C 1.970007 0.221982 -1.202903H 2.275235 0.658658 -2.152860C 2.375370 0.802427 0.000000H 3.000807 1.692604 0.000000C 1.970007 0.221982 1.202903H 2.275235 0.658658 2.152860C 1.180373 -0.964775 1.203183H 0.923839 -1.432362 2.152829C 0.826193 -1.574414 0.000000H 0.257481 -2.501418 0.000000C 1.180373 -0.964775 -1.203183H 0.923839 -1.432362 -2.152829

140

T-shaped isomer (TS)

Comment: Ground electronic state (X2B2) optimized with IP-CCSD/6-31(+)G(d) under

C2v symmetry constraint,ENN=600.842133.Atom x y zC 0.000000 -1.399973 -2.278360H 0.000000 -2.488962 -2.299023C -1.217379 -0.699252 -2.285733H -2.158362 -1.246985 -2.316611C 1.217379 -0.699252 -2.285733H 2.158362 -1.246985 -2.316611C -1.217379 0.699252 -2.285733H -2.158362 1.246985 -2.316611C 1.217379 0.699252 -2.285733H 2.158362 1.246985 -2.316611C 0.000000 1.399973 -2.278360H 0.000000 2.488962 -2.299023C 0.000000 0.000000 0.907763C 1.244445 0.000000 1.609353H 2.172257 0.000000 1.041906H 0.000000 0.000000 -0.174517C 1.244368 0.000000 2.986650H 2.173847 0.000000 3.551289C 0.000000 0.000000 3.681626H 0.000000 0.000000 4.770875C -1.244368 0.000000 2.986650H -2.173847 0.000000 3.551289C -1.244445 0.000000 1.609353H -2.172257 0.000000 1.041906

141

Strongly x-displaced isomer (XSD)

Comment: Ground electronic state (X2Bu), optimized with IP-CISD/6-31(+)G(d) under

C2h symmetry constraint,ENN=614.903162.Atom x y zC 1.150552 0.969722 0.707571H 0.419080 1.555055 1.234935C 2.136379 0.279022 1.407161H 2.149267 0.295308 2.481720C 3.108690 -0.404995 0.705527H 3.883640 -0.932554 1.232270C 3.108690 -0.404995 -0.705527H 3.883640 -0.932554 -1.232270C 2.136379 0.279022 -1.407161H 2.149267 0.295308 -2.481720C 1.150552 0.969722 -0.707571H 0.419080 1.555055 -1.234935C -1.150552 -0.969722 -0.707571H -0.419080 -1.555055 -1.234935C -2.136379 -0.279022 -1.407161H -2.149267 -0.295308 -2.481720C -3.108690 0.404995 -0.705527H -3.883640 0.932554 -1.232270C -3.108690 0.404995 0.705527H -3.883640 0.932554 1.232270C -2.136379 -0.279022 1.407161H -2.149267 -0.295308 2.481720C -1.150552 -0.969722 0.707571H -0.419080 -1.555055 1.234935

142

Strongly y-displaced isomer (YSD)

Comment: Ground electronic state (X2Bu) optimized with IP-CISD/6-31(+)G(d) under

C2h symmetry constraint,ENN=617.531975.Atom x y zC -0.948544 1.036858 0.000000H -0.094961 1.691125 0.000000C -1.541681 0.660690 1.221958H -1.103733 0.987375 2.147873C -2.691245 -0.097191 1.218022H -3.158457 -0.383562 2.142498C -3.265501 -0.478245 0.000000H -4.169692 -1.060908 0.000000C -2.691245 -0.097191 -1.218022H -3.158457 -0.383562 -2.142498C -1.541681 0.660690 -1.221958H -1.103733 0.987375 -2.147873C 0.948544 -1.036858 0.000000H 0.094961 -1.691125 0.000000C 1.541681 -0.660690 1.221958H 1.103733 -0.987375 2.147873C 2.691245 0.097191 1.218022H 3.158457 0.383562 2.142498C 3.265501 0.478245 0.000000H 4.169692 1.060908 0.000000C 2.691245 0.097191 -1.218022H 3.158457 0.383562 -2.142498C 1.541681 -0.660690 -1.221958H 1.103733 -0.987375 -2.147873

143

Fused isomer (FD)

Comment: Ground electronic state (X2Au), optimized with IP-CISD/6-31(+)G(d) under

C2h symmetry constraint,ENN=656.211616.Atom x y zC -0.561504 0.600372 0.764805H -0.141109 1.492488 1.205667C -1.817295 0.192585 1.428685H -1.835554 0.189867 2.505310C -2.900883 -0.171726 0.725565H -3.807561 -0.444572 1.235457C -2.900883 -0.171726 -0.725566H -3.807561 -0.444572 -1.235457C -1.817295 0.192585 -1.428685H -1.835554 0.189867 -2.505310C -0.561504 0.600372 -0.764805H -0.141109 1.492488 -1.205667C 0.561504 -0.600372 0.764805H 0.141109 -1.492488 1.205667C 1.817295 -0.192585 1.428685H 1.835554 -0.189867 2.505310C 2.900883 0.171726 0.725565H 3.807561 0.444572 1.235457C 2.900883 0.171726 -0.725566H 3.807561 0.444572 -1.235457C 1.817295 -0.192585 -1.428685H 1.835554 -0.189867 -2.505310C 0.561504 -0.600372 -0.764805H 0.141109 -1.492488 -1.205667

144

ELECTRONIC STRUCTURE OF IONIZED NON …iopenshell.usc.edu/people/thesis-golubeva.pdfProf. Anna...

Documents

Transcript of ELECTRONIC STRUCTURE OF IONIZED NON …iopenshell.usc.edu/people/thesis-golubeva.pdfProf. Anna...