Calculation of Molecular Properties: How, What and Why? Dr. Vasile Chiş, Faculty of Physics,...

Calculation of Molecular Properties:

How, What and Why?

Dr. Vasile Chiş , Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca

Dr. Vasile ChiDr. Vasile Chişş

Biomedical Physics Department, Biomedical Physics Department, Faculty of Physics Faculty of Physics

BabeBabeşş-Bolyai University, Cluj-Napoca-Bolyai University, Cluj-Napoca

"Many experimental chemists use various kinds of spectroscopy in their research even though they are not spectroscopists. In a similar manner, more and more scientists are applying computational techniques as another weapon in their arsenal"

Delano P. Chong in Recent Advances in Density Functional Methods, Part I, World Scientific, 1995


Outline

1. Introduction

2. Hartree-Fock-Roothaan-Hall Theory

3. Basis Sets

4. Electron Correlation

5. ABC of DFT

6. Predictible Molecular Properties

7. Examples of Calculationsvibrational, NMR and ESR spectraconformers, tautomers, relative energies, molecular orbitals


Ab Initio Electronic Structure Theory

Hartree-FockDFT

Molecular Structures

Molecular Properties

Spectroscopic Observables

Benchmarks for parametrizations

Transition StatesReaction Coordinates

Prodding and Helping the Experimentalists

Calculation of Molecular Properties: Why?


“We are perhaps not far removed from the time when we shall be able to submit the bulk of chemical phenomena to calculation”

Joseph Louis Gay-Lussac, Memoires de la Societe d’Arcueil, 2,207(1808)

“The more progress physical science make, the more they enter the domain of mathematics, which is a kind of centre to which they all converge. We may even judge the degree of perfection to which a science has arrived by the facility with which it may be submitted to calculation.”

Adolphe Quetelet, Instructions Populaires sur le Calcul des Probabilities, Tarlier, Brussels, 1828, p. 230

“Every attempt to employ mathematical methods in the study of chemical questions must be considered profoundly irrational and contrary to the spirit of chemistry. If mathematical analysis should ever hold a proeminent place in chemistry – an aberration which is almost impossible – it would occasion a rapid widespread degeneration of that science”

A. Compte, Philosophie Positive, 1830

A short history

J.L. Gay-Lussac

A. Quetelet

A. Compte


Quantum Wave Mechanics, 1926

HH=E

“The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble.”

P.A.M. Dirac, Proc. Roy. Soc(London) 123, 714(1929)

E.R.J.A. Schrödinger W.K. Heisenberg

P.A.M. Dirac


nneeenne V

M

1A

M

AB AB

BA

V

N

1i

N

ij ij

V

N

1i

M

1A iA

A

T

M

1A

2A

A

T

N

1i

2i R

ZZr1

rZ

2M1

21

H

Hartree-Fock-Roothaan Theory

M. Born

R. Oppenheimer


D. Hartree


D. Hartree

V. Fock


D. Hartree

V. Fock C. Roothaan


Basis Sets

K

1μμμii cΦ

)(...)()(

)(...)()(

)(...)()(

)!(222

111

2/1

NKNjNi

Kji

Kji

xxx

xxx

xxx

N

)()()( jjiji rx

=LCBF {μ} – a set of known

functions

),(),,;,,,( 1 lm

rni YeNrrmln Slater Type Orbitals (STO)

zyx lllrf zyxNezyxfnmlg22

),,;,,,,( Gaussian Type Orbitals (GTO)


0

5

10

15

0 2 4 6

GTOallow a more rapidly and efficiently calculation of the two-electron integrals

have different functional behavior with respect to known functional behavior of AOs.

L

pAp

GFppA

CGTO d1

),()( RrRr

S. F. Boys, Proc. Roy. Soc. (London) A200 (1950) 542.


Standard basis: 6-31G (6D, 7F) Basis set in the form of general basis input: 1 0 S 6 1.00 .3047524880D+04 .1834737130D-02 .4573695180D+03 .1403732280D-01 .1039486850D+03 .6884262220D-01 .2921015530D+02 .2321844430D+00 .9286662960D+01 .4679413480D+00 .3163926960D+01 .3623119850D+00 SP 3 1.00 .7868272350D+01 -.1193324200D+00 .6899906660D-01 .1881288540D+01 -.1608541520D+00 .3164239610D+00 .5442492580D+00 .1143456440D+01 .7443082910D+00 SP 1 1.00 .1687144782D+00 .1000000000D+01 .1000000000D+01 **** 2 0 S 3 1.00 .1873113696D+02 .3349460434D-01 .2825394365D+01 .2347269535D+00 .6401216923D+00 .8137573262D+00 S 1 1.00 .1612777588D+00 .1000000000D+01 **** ...

6-31G Basis set for CH4 molecule

HF limit: mono-determinantal wave-function + infinite basis set

STO-3G

3-21G

6-31G(d)

6-311++G(2df,p)

…

zyx lllrf zyxNezyxfnmlg22

),,;,,,,(

L

pAp

GFppA

CGTO d1

),()( RrRr

Electron Correlation


HF method: electron-electron interaction is replaced by an average interaction

HFHFc EEE 0

E0 – exact ground state energyEHF – HF energy for a given basis set

0HFcE

- represents a measure for the error introduced by the HF approximation


Types of electronic correlationTypes of electronic correlation

Exchange EnergyExchange Energy

Spin correlationSpin correlation - effect of the Pauli exclusion principle(Fermi correlation)(Fermi correlation) (Fermi hole)

Dynamical correlationDynamical correlation – related to the movements of the individual electrons (Coulomb correlation)(Coulomb correlation) (Coulomb hole)

Non-dynamical correlationNon-dynamical correlation - related to the fact that in certain circumstances the ground state SD wave-function is not a good

approximation to the true ground state because there are other Slater determinants with comparable energies (near degeneracy problem)

Correlation EnergyCorrelation Energy


Correlation Energy: Is it important?Correlation Energy: Is it important?

0

10

20

30

40

50

60

70

80

90

100

Total electronicenergy

Correlation energy

N2 molecule:CE ~ 0.5% of the EE ~ 50% of the binding

energy!


multideterminantal wave-function

i

iiHF

0 ΨaΨaΨ

ESD – obtained by replacing MOs which are occupied in the HF determinant by unoccupied MOs

- singly, doubly, triply, quadruply, etc. excited relative to the HF determinant

ESDΨi

How to take it into account?


Electron correlated methods:

Configuration Interaction (CIS, CID, CISD, CISDT, etc.)

Multi-Configuration Self-Consistent Field Method (MCSCF) n,m-CASSCF

Moller-Pleset Theory MP2, MP4, etc.

Coupled Cluster Theory CCD, CCSD, etc.


ABC of DFT

Why a new theory?

HF method scales as K4 (K - # of basis functions)CI methods scale as K6-K10

MPn methods scale as >K5

CC methods scale as >K6

Correlated methods are not feasible for medium and large sized molecules!

The electron density

1927 L.H. Thomas, E. Fermi1964 P. Hohenberg, W. Kohn, L.J. Sham1992 Gaussian®

DFT is presently the most successful and also the most promising approach to compute the electronic structure of matter.

Applicability: atoms, molecules, solids

DFT is less computationally expensive than traditional Hartree-Fock methods but it gives similar accuracy.



ρ(r)

ν(r)

H

E

N

Nρ(r)dr

EΨΨH ˆ

First HK Theorem:First HK Theorem:

P. Hohenberg

W. Kohn


The explicit form of T[ρ] and Enon-cl[ρ] is the major challenge of DFT

FHK ???

Modern DFTModern DFT

eeHK

HKNeeeNe

E]T[ρ][ρF

with

][ρFr)dr()Vrρ(][ρE]T[ρ][ρE]E[ρ

][ρE]J[ ρ][ρErdrdr

)r()ρr(ρ

21

][ρE non_clnon_cl2112

21ee

Only J[ρ] is known!


T[ρ] – kinetic energy of a real interacting electron system with density ρ(r)

N

1ii

2iKS ΨΨ

21

TTKS – kinetic energy of a fictitious non-interacting

system of the same density ρ(r)Ψi - are the orbitals for the non-interacting system (KS orbitals)

][ρE]J[ ρ][ρT][ρF cl-nonKSHK

T=TKS+(T-TKS)

][ρE

drdr)(rr1

)(r21

21

dr)(rrZ

-

][ρE]J[ ρ][ρT][ρE]E[ρ

xc

N

1i

N

1j21

2

2j12

2

1i

N

1ii

2i

N

1i

M

1A1

2

1i1A

A

xcKSNe

Exc[ρ] includes everything which is unknown:

-exchange energy

-correlation energy

-correction of kinetic energy (T-TKS)


Variational Principle in DFTVariational Principle in DFT

Minimize E[ρ] with the conditions:

ijji δ

Nρ(r)dr

Kohn-Sham Equations:Kohn-Sham Equations:

iii

M

1A 1A

A1xc2

12

22 εrZ

)(rvdrr

)ρ(r21

with:

i

2i

xcxc

(r)ρ(r)

δρρδE

(r)v

][

Second HK Theorem

W. Kohn L.J. Sham


Kohn-Sham Formalism

jjji

i2 ε(r)Kdr'

r'r)ρ(r'

v(r)21

Hartree-Fock equations

Kohn-Sham equations

W. Kohn L.J. Sham


EExcxc[[ρρ] = ??] = ??

Local Density Approximation (LDA)

(r))dr(ρρ(r)ε][ρE xcxc εxc only depends on the density at r

Generalized Gradient Approximation (GGA)

(r),...)drρ(r),(ρρ(r)ε][ρE xcxc εxc depends on the density and its gradient at r

Hybrid Functionals

GGAxc

KSx

hyb α)E(1αE][ρExc


DFT: a new and powerful tool in chemical physics


Predictible Molecular Properties


Examples of Calculations

pyrazinamide

meta-benzosemiquinone anion free radical

5-pBBTT


analogue of nicotinamide

very important drug used to treat tuberculosis

some transition metal(II) molecular complexes of this molecule are recognized and used as antimycobacterial agents

Pyrazinamide Pyrazinamide (PZA)(PZA)


Optimized geometries (B3LYP/6-31G(d))

of the two conformers of PZA

C1

C2

Possible contributions from both conformers (in gas or liquid phase)


HB – moderate strength

- predominant electrostatic

character

(B)E(A)E(AB)EΔE ABBA

ABAB

ABAB

CP00

(M)E(D)EΔE DD

DD

CP 2

E(B)]E(A)E(AB)ΔE [Interaction energy:

ΔEuncorrected = 16.14 Kcal/mol

ΔECP corrected = 13.82 Kcal/mol

Basis set superposition error

C1 C2 Dimer

Dihedral angles

H13N8C7C2 20.5 0 25.6 0

H14N8C7C2 177.1 180 173.5 180

Hydrogen bond parameters

N8...O9' 2.905 - - 2.895

H14...O9' 2.034 - - 1.871

N8H14...O9' 178.4 - - 174.3

ExperimentalCalculated (B3LYP/6-31G(d))

G.A. Jeffrey, An Introduction to Hydrogen Bonding, Oxford University Press, New York, 1997

Optimized geometry (B3LYP/6-31G(d)) Optimized geometry (B3LYP/6-31G(d))

of the PZA dimerof the PZA dimer


Selected experimental and calculated vibrational bands of

PZA

NH2 – important role in the conformation of peptides or Watson-Crick complexes

- intermediates the hydrogen bonds (intra and inter)


Experimental and calculated NMR spectrum of PZA

HB

4.0 8.9


[1H, 1H] COSY45 NMR spectrum of pyrazinamide in DMSO solution


For a reliable assignment of experimental spectra

- intermolecular interactions must be considered!

- minimal computational strategy:

vibrational spectra

DFT (B3LYP ++ BLYP)

monomer ++ dimer calculations

6-31G(d) basis set

NMR spectra

DFT (B3LYP)

dimer calculations

cc-pVDZ basis set


Quinones (and related radicals) are involved in many biophysical processes:

cellular respiration (ubiquinone = coenzyme Q10)

- also, an essential nutrient

blood clotting (menaquinones = vitamin K2)

aging (tocoquinones = vitamin E2)

microbial controlling agentsquinone-type radicals important cofactors for electron transfer in photosynthesis

ESR spectra of ortho-, meta- and para-benzosemiquinone radicals

para

ortho

meta

very accessible to experimental and theoretical analyses


BSQ anion radicals: energetics, structures and symmetriesBSQ anion radicals: energetics, structures and symmetries

-381.60

-381.58

-381.56

-381.54

-381.52

-381.50

-381.48

ortho meta para

Tota

l energ

ies (

a.u

.)

6-31+G(d) EPR-II

7.38Kcal/mol7.15Kcal/mol

B3LYP/6-31+G(d)

Cs symmetry


BSQ anion radicals: HOMO and LUMO’s energiesBSQ anion radicals: HOMO and LUMO’s energies

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

HOMO LUMO ΔE

Fro

nti

er o

rbit

als

ener

gy

(eV

)

ortho meta para

B3LYP/6-31+G(d)

Cs symmetry


ortho

HOMO LUMO

meta

para

USD Distribution

BSQ anion radicals: HOMOs, LUMOs, USDsBSQ anion radicals: HOMOs, LUMOs, USDs


meta-BSQ optimized structures

B3LYP/EPR-II


UB3LYP/EPR-IIGas-phase

A2 A4,6 A5

Experimental*(water)

0.68 11.44 2.43

Cs(2A”) 0.27 -11.76 2.85

C2v(2A2) 0.27 -11.76 2.85

C2v(2B1) -16.32 0.32 -0.72

* absolute values

Calculated hyperfine coupling constants of the

meta-BSQ anion radical in

gas-phase, for the three minimum structures


Gas-phase meta-benzosemiquinone anion radical

B3LYP/EPR-II (grid ultrafine) 0.27 -11.76 2.87

Marked non uniformity of the electron density in C1C2C3 region

+ - +


(cm-1) I ntensity Assignment

533 medium CCC bend

970 very weak CCC bend

1070 weak CH bend

1093 strong CO stretch

1227 weak CH bend

1314 weak CC stretch



1519 strong CO stretch

1570 very weak CC stretch

calculated*

527

962

1090/1048

! 1133/1089

1237/1189

1332/1281

1473/1416

1497/1439

1573/1512

! 1596/1534

Experimental and calculated wave-numbers for m-BSQ anion radical

*B3LYP/6-31+G(d) Cs symmetry

CO stretch

CH bend

G.N.R.Tripathi, D.M.Chipman, C.A.Miderski, H.F.Davis, R.W.Fessenden, R.H. Schuler, J.Phys.Chem., 90,3968(1986)

present work


dipole moments: (ortho)> (meta)>(para)=0 number of minimum energy conformers: 2 for ortho and para, 3 for meta total energies: Emeta>Eortho>Epara

hfcc’s: ortho - strong influence of the solvation effects

meta - marked non-uniformity in the electron density

para – easilly reproduced even in gas-phase vibrational spectra:

ortho – no experimental data available

meta – reassignment of two bands in the IR spectrum

para – very good agreement between experiment and theory

Conclusions


Molecular structure and atom numbering scheme for 5-para-bromo-benzilidene- thiazolidine-2-thion-4-one molecule

Vibrational, NMR and DFT investigation of 5-pBBTT


5-pBBTT Conformers and Tautomers

C1 C2

C1 Thiol

C1 Thiol 1

C2 Thiol

C2 Thiol 1


Unit cell parameters

a = 4.4597(7) Å b = 12.5508(19) Å c = 13.727(2)Å α = 90.751(2) β = 96.230(2) γ = 97.865(3)

Crystal System: Triclinic Space group: P-1

X-ray diffraction


1H NMR Spectrum of 5-pBBTT in DMSOLooking for a proton


Thione Thiol ThioneH-bonded

ThioneH-bonded

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

7.13 3.50 11.74 14.14

Different tautomers in liquid state?

Experimental: 3.4ppm and 13.9 ppm

Thiolic ConformerThione Conformer

Thiol: 66%

Thione: 33%

Calculated chemical shift for N-H and S-H protons in thione and thiol tautomers


m1 corrected

-20.00

-15.00

-10.00

-5.00

0.00

5.00

10.00

15.00

20.00

gas-phase water DMSO

thione

thiol

enol

SCRF-PCM continuum solvation model

Solvent

Thione Thiol Enol

5pBr-BTT

Vacuo0.002.63

14.962.41

15.805.39

Water-17.612.81

18.293.25

6.499.07

DMSO-4.273.36

3.133.54

11.637.81

5pF-BTT

Vacuo0.002.56

15.072.69

15.805.78

Water-12.735.22

9.923.94

-0.7910.51

DMSO-3.724.09

3.374.01

11.308.37


• Proposed molecular structure is confirmed by experimental and theoretical results.

• The most stable conformer was proposed based on theoretical results and was confirmed by vibrational, NMR and X-ray diffraction results.

• Based on NMR and theoretical data, the coexistence of thiolic and thione tautomers is proved in liquid state. Moreover, thiolic conformer is prevailing in this case and thione conformer still remains H-bonded in liquid phase.

Conclusions:


From the beginning: Calculation of Molecular

Properties

Why?

How?

What?

HF, UHF, MPn, CI, CC, DFT, AM1, PM3, etc.6-31G(d), cc-pVDZ, Lanl2DZ(ECP), etc.

well… almost everything!

can we live without? (designing new materials, pharmaceuticals, etc)


Publications: closed-shell systems

Molecular and Vibrational Structure of 2,4-Dinitrophenol: FT-IR, FT-Raman and Quantum Chemical Calculations

V.Chiş Chem.Phys., 300, 1-11 (2004)

Vibrational Spectroscopy and Theoretical Studies on 2,4-dinitrophenylhydrazineV.Chiş, V.Miclăuş, A.Pîrnău, C.Tănăselia, V.Almăşan, M.VasilescuJ.Mol.Struct., 744-747 363-368 (2005)

NIR Surface Enhanced Raman Spectroscopy and Band Assignment by DFT Calculations of Non-Natural -amino acids

T. Iliescu, D. Maniu, V. Chiş, F.D. Irimie, Cs. Paizs and M. Tosa Chem.Phys., 310, 189-199 (2005)

Adsorption of 6-Mercaptopurine and 6-Mercaptopurine-Riboside on Silver Colloid: A pH Dependent Surface Enhanced Raman Spectroscopy and Density Functional Theory Study. Part I. 6-MercaptopurineA. V. Szeghalmi, L. Leopold, S. Pînzaru, V. Chiş, I. Silaghi-Dumitrescu, M. Schmitt, J. Popp, W. KieferJ.Mol.Struct., 735-736, 103-113 (2005)

Adsorption of 6-mercaptopurine and 6-mercaptopurine-riboside on silver colloid: A pH dependent surface enhanced

Raman spectroscopy and density functional theory study. Part II. 6-mercaptopurine-ribosideV. Szeghalmi, L. Leopold, S. Pînzaru, V. Chiş, I. Silaghi-Dumitrescu, M. Schmitt, J. Popp, W. KieferBiopolymers, 78, 298-310 (2005)

Experimental and DFT Study of PyrazinamideV. Chiş, A. Pîrnău, T. Jurcă, M. Vasilescu, S. Simon, O. Cozar, L. DavidChem. Phys., 316, 153-163 (2005)

Molecular and Vibrational Structure of 5-Para-Bromo-Benziliden–Tiazolidin-2-Tion-4-Ona. Experimental and Theoretical InvestigationA.Pîrnău, M. Baias, O.Oniga, V.Chiş, M.Vasilescu, O.CozarStudia Physica, Special Issue, NANOSPEC, 2005


Publications: open-shell systems (free radicals)

Ab Initio and DFT calculations of the hyperfine structure of OH, HO2 and H2O+ radicalsV.Chiş, L.David, O.Cozar, A.Chiş Rom.J.Phys., 48, 413-428 (2003)

Ab Initio and DFT Study on Hyperfine Structure of 1,2-Benzosemiquinone Anion RadicalV.Chiş, A.Nemeş, L.David, O.CozarStudia UBB, Physica, 47(1) 157-170 (2002)

AM1/INDO Semiempirical Calculations on Tyrosyl RadicalV.ChişStudia UBB, Physica, 47(1), 147-156 (2002)

Which radicals are formed by electrochemical reduction of Dihydrazid-Hydrazone? An ESR and DFT Investigation.

V.Chiş, V.Miclăuş, L.Mureşan, G.Damian, L.David, O.CozarStudia UBB, Physica, XLXIII, Special Issue, 123-134 (2003)

Theoretical ESR Spectrum of 1,3-Benzosemiquinone RadicalV.Chiş, R.Marcu, M.Oltean, L.David, O.CozarAnalele Universităţii din Oradea, A XIII, 123-142 (2003)

Density Functional Calculations of Hyperfine Coupling Constants in Glycine-Derived RadicalsRaluca Marcu, Vasile ChişStudia Physica, Special Issue, NANOSPEC, 2005


Publications: wave-functions for small molecules

The effect of target representation in positron-impact ionization of molecular hydrogen R. I. Campeanu, V. Chiş, L. Nagy and A. D. StaufferPhys.Lett. A, 310(5-6),445 - 450(2003)

Positron impact ionization of molecular nitrogen R.I. Campeanu, V.Chiş, L. Nagy, A. D. StaufferNucl. Instrum. Meth. B 221 (2004) 21-23

Positron impact ionization of molecular oxygen R.I. Campeanu, V. Chiş, L. Nagy, A. D. Stauffer Phys. Lett. A 325 (1) 66-69 (2004)

Positron impact ionization of CO and CO2R.I. Campeanu, V. Chiş, L. Nagy, A.D. StaufferPhys.Lett. A, 344 (2-4): 247-252 (2005)


Prof. L. Nagy, Prof. T. Iliescu, Prof. S. Astileandr. N. Leopold, dr. D. Maniu, dr. S. Cinta Pinzaru, dr. C. Craciun, dr. M. VasilescuBabes-Bolyai University, Faculty of Physics

Acknowledgments

dr. V. Miclaus, dr. M. Venter Babes-Bolyai University, Faculty of Chemistrydr. T. Jurca University of Oradea, Faculty of Medicine and PharmacyProf. O.OnigaUMF Cluj-Napoca, Dept. of Pharmaceutical ChemistryA. Pirnau, R. Marcu, M. Baias, M. Oltean, C. Tanaselia, L. Szabo, S. Botond Babes-Bolyai University, Faculty of Physics

Calculation of Molecular Properties: How, What and Why? Dr. Vasile Chiş, Faculty of Physics,...

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