Exploring Potential Energy Surfaces Using Ab Initio Molecular Dynamics

Prof. H. Bernhard SchlegelDepartment of ChemistryWayne State University

Current Research GroupDr. Peng Tao Dr. Barbara MunkJia Zhou Jason SonkBrian Psciuk Adam Birkholz

Recent Group MembersProf. Xiaosong Li Dr. Hrant Hratchian Prof. Jason Sonnenberg Dr. Stan SmithProf. Smriti Anand Dr. Jie (Jessy) LiDr. John Knox Michael Cato

Canadian Conference on Computational Chemistry

Halifax, July 19 - 24, 2009

Overview

AIMD study of non-statistical behavior acetone radical cation and 2,4-pentanedione radical cation dissociation

AIMD study of a Coulomb explosion: dissociation of CH2=NHn+, (n=0,1,2,3)

Electronic response of molecules in short, intense laser pulses

Applications of Ab Initio Molecular Dynamics

Jia Zhou

ChemistryWayne State U.

Prof. Smriti Anand

Northern VirginiaCommunity College

Dr. Jie Li

Genome CenterUC Davis

Ab Initio Molecular Dynamics (AIMD)

AIMD – electronic structure calculations combined with classical trajectory calculations

Every time the forces on the atoms in a molecule are needed, do an electronic structure calculation

Born – Oppenheimer (BO) method: converge the wavefunction at each step in the trajectory

Extended Lagrangian methods: propagate the wavefunction along with the geometry

Car-Parrinello – plane-wave basis, propagate MO’s

ADMP – atom centered basis, propagate density matrix

Ab Initio Classical Trajectory on theBorn-Oppenheimer Surface Using Hessians

Calculate the energy,gradient and Hessian

Solve the classicalequations of motion on a

local 5th order polynomial surface

Millam, J. M.; Bakken, V.; Chen, W.; Hase, W. L.; Schlegel, H. B.; J. Chem. Phys. 1999, 111, 3800-5.

Dissociation of Acetone Radical Cation

Dissociation of C3H6O+• has been of interest for many years now The enol ion is produced via the McLafferty rearrangement.

The enol form isomerizes to the keto form, activating the newly formed methyl group, and dissociates to form an acetyl cation and methyl radical

Dissociation behaves in a non-statistical manner favoring the loss of newly formed methyl group by 1.1-1.7 to 1

H3C CH3

O

CH3CO + CH3H3C CH2

OH

*

O CH2R H transfer O CHRH

OH CHR+ _

H2C CHR

H3C CH2

OH+

Energy Dependence of the Branching Ratio

Osterheld, T. H.; Brauman, J. I.; J. Am. Chem. Soc. 1993, 115, 10311-10316.

Potential Energy Profile (CBS-APNO)

-25

-15

-5

5

15

25

35

45

Re

lati

ve

En

erg

y (

kc

al/

mo

l)

Ketene/Methane complex

TS for Methane Elimination

CH3CO+/ CH3

• complex

Anand, S.; Schlegel, H. B. Phys. Chem. Chem. Phys. 2004, 6, 5166.

Improved Potential Energy Surfaces using Bond Additivity Corrections (BAC)

The most important corrections needed for acetone radical cation dissociation reaction are for C-C bond stretching potentials.

BAC (bond additivity correction) add simple corrections to get better energetics for the reaction E = E′+ ∆E ∆E = AC-C Exp{-αC-C RC-C1} + AC-C Exp{- αC-C RC-C2} add the corresponding corrections to gradient and hessian

G = G′+ ∂(∆E)/∂x H = H′+ ∂2(∆E)/∂x2

A and α are parameters obtained by fitting to high level energies

Initial Energy

(kcal/mol)

Branching Ratio

Average Etranslation

(kcal/mol)

Average Dissociation

Time (fs)

1

2

1.43

1.88

2.7 / 2.0

3.3 / 2.7

181 / 224

177 / 240

10 1.70 4.2 / 2.3 147 / 186

18 1.50 4.2 / 2.8 140 / 167

Branching Ratios for Microcanonical Ensemble

Energy assigned 3rd mode 6th mode 8th mode

0 1.10:1

1 kcal/mol 1.59:1 1.58:1 1.54:1

2 kcal/mol 1.84:1 2.31:1 1.82:1

4 kcal/mol 1.46:1 1.85:1 2.36:1

8 kcal/mol 1.55:1 2.03:1 2.76:1

* plus 0.5 kcal/mol in transition vector

Effect of Adding Energy to Specific Vibrational Modes

Dissociation of Chemically Activated Pentane-2,4-dione Radical Cation

H3C CH2 (CH2)3R

O O

H3C CH2 CH2

O HO

H3Ca CbH2 CcH3

O O

- e

*

chemically activated intermediate

- RCH=CH2

CaH3C(O)CbH2CO+ + .CcH3

CaH3C(O)CbH2. + CcH3CO+

CaH3CO+ + .CbH2C(O)CcH3

.CaH3 + +OCCbH2C(O)CcH3

The enol radical cation can be produced via the McLafferty rearrangement

Energy is localized in terminal C-C bond, but can flow to the other C-C bonds

Zhou, J.; Schlegel, H. B.; J. Phys. Chem. A 2009, 113, 1453

Potential Energy Surface for Pentanedione Radical Cation

H3C CH2 CH3

O O

29%

45%2.3%

0%

*

Kinetic Scheme for Pentanedione Radical Cation

H3C CH2 CH3

O O

H3C CH2 CH3

O O

H3C CH2 CH3

O O

H3C CH2 CH3

O O

H3C CH2 CH3

O O

*H3C CH2 CH3

O O

*H3C CH2 CH3

O O

*H3C CH2 CH3

O O

*k4 k3'

k1k2

proton transfer andester-like product

k6k6

loss ofactive methyl

loss ofactive acetyl

loss ofspectator methyl

loss ofspectator acetyl

initial activation of the terminal

CC bond

enol

k5

k1k1fast

k3fast

k3

k2k2fast

indicates activated bond*

k1fast = 0.018 fs-1

k2fast = 0.040 fs-1

k3fast = 0.018 fs-1

k1 = 0.00114 fs-1, k2 = 0.012 fs-1

k3=k3' = 0.0032 fs-1, k4 = 0.001 fs-1

k5 = 0.00167 fs-1, k6 = 0.002 fs-1

0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 00

2 0

4 0

6 0

8 0

1 0 0

T im e fs

A c tiv e M e th y l

A c tiv e A c e ty l

S p e c ta to r A c e ty l

Time (fs)

Dissociation of Methanimine and its Cations, CH2=NHn+ (n=0,1,2,3)

Simplest example of a molecule with a CN double bond, also known as methyleneimine and formaldimine

As electrons are removed, bonding should become weaker, finally leading to a Coulomb explosion

CH2NH formed by pyrolysis of amines and azides, and seen in interstellar clouds

Monocation also well studied experimentally, but little or no experimental information on higher cations

Many theoretical studies over the years, but at many different levels of theory

Structures and energetics calculated by CBS-APNO Ab initio molecular dynamics by B3LYP/6-311G(d,p)

Dissociation of H2CNH

Dissociation of H2CNH+

Dissociation of H2NCH2+

Dissociation of H2NCH3+

Direct vs Indirect Dissociation of H2CNH

Direct (no hydrogen rearrangement before dissociation)

Indirect (hydrogen migration before dissociation)

Ab Initio Molecular Dynamicsof CH2=NHn+ Dissociation

Neutral H2CNH (200 kcal/mol initial energy) CH dissociation (28% direct, 4% indirect) NH dissociation (13% direct, 3% indirect) Triple dissociation (22% HCN+H+H, 9% HNC+H+H) Molecular dissociation (9 % HCN+H2, 10% HNC+H2)

Monocation H2CNH+ (150 kcal/mol initial energy) HCNH+ + H (68% direct, 13% indirect) H2CN+ + H HCNH+ + H (10%) Molecular dissociation (3 % HCN++H2, 3% HNC++H2)

Dication H2NCH2+ (120 kcal/mol initial energy) HCNH+ + H+ (51% direct, 24% indirect) H2NC+ + H+ (10%) No reaction (13%)

Time Dependent Simulations of Molecules in Strong Fields

Prof. Xiaosong LiUniversity of Washington

Dr. Stan Smith, Temple U.

Prof. Robert Levis, Temple U.

Jason Sonk, WSU

Electronic Response of Molecules Short, Intense Laser Pulses

For intensities of 1014 W/cm2, the electric field of the laser pulse is comparable to Coulombic attraction felt by the valence electrons – strong field chemistry

Need to simulate the response of the electrons to short, intense pulses

Time dependent Schrodinger equations in terms of ground and excited states

= Ci(t) i i ħ dCi(t)/dt = Hij(t) Ci(t) Requires the energies of the field free states and the transition dipoles between them Need to limit the expansion to a subset of the excitations – TD-CIS, TD-CISD

Time dependent Hartree-Fock equations in terms of the density matrix

i ħ dP(t)/dt = [F(t), P(t)]

For constant F, can use a unitary transformation to integrate analyticallyP(ti+1) = V P(ti) V† V = exp{ i t F }

Fock matrix is time dependent because of the applied field and because of the time dependence of the density (requires small integration step size – 0.05 au)

Hydrogen Moleculeaug-cc-pVTZ basis plus 3 sets of diffuse sp shells

Emax = 0.07 au (1.7 1014 W/cm2), = 0.06 au (760 nm)(a)

(b)

(c)

(b)

(c)

(d)

(e)

(f)

TD-CIS TD-CISD TD-HFInstantaneous dipole response

Fourier transform of the residual dipole response

Energy (au)

Time (0.05×au)

Butadiene

1.75

1.80

1.85

1.90

1.95

2.00

0.00

0.05

0.10

0.15

0.20

0.25

1.982

1.984

1.986

1.988

1.990

1.992

1.994

1.996

1.998

2.000

2.002

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

0.016

0.018

-2 0 2 4 6 8 10 12 14 16 18

1.988

1.990

1.992

1.994

1.996

1.998

2.000

-2 0 2 4 6 8 10 12 14 16 18

0.000

0.002

0.004

0.006

0.008

0.010

HOMO HOMO-1

LUMO LUMO+1

n(a

u)

HOMO-2 HOMO-3

n(a

u)

LUMO+2 LUMO+3

Time (fs)

HOMO-4 HOMO-5

Time (fs)

LUMO+4 LUMO+5

-2 0 2 4 6 8 10 12 14 16 18-0.6-0.4-0.20.00.20.40.6-4

-2

0

2

4-0.06-0.04-0.020.000.020.040.06

q(a

u)

Time (fs)

C1

C2

C3

C4

d(a

u) d

x

dy

(au

)8.75×1013 W/cm2

760 nm

HF/6-31G(d,p)

t = 0.0012 fs

H

H

H

H

H

H

Laser pulse

Dipole

Charges

Populations ofoccupied orbitals

Populations ofunoccupied orbitals

Butadiene, Hexatriene and NaphthaleneTD-CIS/6-31G(d,p), = 0.06 au (760 nm)

Excited state weights in the final wavefunction

RPACISCIS(D)CISDEOM-CCSD

Excited State Energies of Butadiene

* Transition Dipoles for Butadiene (6-31G(d,p) basis)

Response of 2 and 3 Level Systemsto a 3 Cycle Gaussian Pulse

2 4 6 8fs

0.04

0.02

0.02

0.04

I

0.00

0.25

0.00

0.25

0.35

Response of the States of Butadieneto a 3 Cycle Gaussian Pulse

TD-CIS 1Ag (gs) 1Bu 1Ag 1Bu

TD-EOMCC

TD-CIS response vs number of states

A large number of states are needed for the response to be stable

Lowest states are well separated

Higher states form a quasi-continuum

Most of the higher lying states are needed primarily to represent the polarization of the molecule in the field

20 40 60 80 100

0 .2

0 .4

0 .6

0 .8

1 .0

State Number

80 100 120 140 160Number of States

0.01

0.02

0.03

noitcnufevaW

tneiciffeoC

TD-CIS in a Reduced Space

Perturbation theory for the effective polarizability of the low lying states

Finite difference method for the effective polarizability

where D' is the matrix of transition dipoles with the elements between the low lying states set to zero

Integrate TD-CI equations with polarizability

22 | | /( )

high lying

i k ik

i k r

2( ( ) 2 (0) ( )) / ( ) ( ' )Ti i i i i e e e e U H D e U

1

2( ) ( ) ( ) ( ) ( ) ( ) ( )

i ij j ij i ij ij ijii dC t dt H t C t H t t t t e e eD

2 4 6 8 1 0 1 2 1 4 1 6

3

2

1

1

2

3

2 4 6 8 1 0 1 2 1 4 1 6

3

2

1

1

2

3

0 .0 0 .2 0 .4 0 .6 0 .8 1 .00 .000

0 .005

0 .010

0 .015

0 .020

0 .025

TD-CIS in a Reduced SpaceButadiene, TD-CIS/6-31G(d,p)

Emax = 0.05 au (8.75 1013 W/cm2), = 0.06 au (760 nm)

Large CIS space Small CIS space with polarizability

0 .0 0 .2 0 .4 0 .6 0 .8 1 .00 .0 00

0 .0 05

0 .0 10

0 .0 15

0 .0 20

0 .0 25

Instantaneous DipoleInstantaneous Dipole

Wavefunction Coefficients

Wavefunction Coefficients

Time (fs)

Energy (au)

Time (fs)

Energy (au)

Response of Butadieneto a 3 Cycle Gaussian Pulse(=0.6 au, 6-31G(d,p) basis)

RPA

TD-CIS(D)

TD-CIS

TD-EOMCC

Transition Dipoles for Butadiene(CIS)

Response of Butadieneto a 3 Cycle Gaussian Pulse

(=0.6 au, TD-CIS)

6-31G(d,p) 6-31++G(d,p) 6-311++G(2df,2pd)

Current Research GroupDr. Peng Tao Dr. Barbara MunkJia Zhou Jason SonkBrian Psciuk Adam Birkholz

Recent Group MembersProf. Jason Sonnenberg, Stevenson University,Prof. Xiaosong Li, U. of WashingtonProf. Smriti Anand, Northern Virginia CollegeDr. Hrant Hratchian, Gaussian, Inc.Dr. Jie Li, U. California, Davis (Duan group)Dr. Stan Smith, Temple U. (Levis group)Dr. John Knox, GlaxoSmithKline (Singapore)Michael Cato, Jackson State U. (Leszczynski group)

Funding and Resources:National Science FoundationOffice of Naval ResearchNIHGaussian, Inc.Wayne State U.

AcknowledgementsCollaborators:

Dr. T. Vreven, Gaussian Inc.Dr. M. J. Frisch, Gaussian Inc.Prof. John SantaLucia, Jr., WSURaviprasad Aduri (SantaLucia group)Prof. G. Voth, U. of UtahProf. David Case, ScrippsProf. Bill Miller, UC BerkeleyProf. Thom Cheatham, U. of UtahProf. S.O. Mobashery, Notre Dame U.Prof. R.J. Levis, Temple U.Prof. C.H. Winter, WSUProf. C. Verani, WSUProf. E. M. Goldfield, WSUProf. D. B. Rorabacher, WSUProf. J. F. Endicott, WSU Prof. J. W. Montgomery, U. of MichiganProf. Sason Shaik, Hebrew UniversityProf. P.G. Wang, Ohio State U.Prof. Ted Goodson, U. of Michigan Prof. G. Scuseria, Rice Univ.Prof. Srini Iyengar, Indiana UProf. O. Farkas, ELTEProf. M. A. Robb, Imperial, London

Recent Group Members

Current Group Members