Exploring Potential Energy Surfaces for Chemical Reactions

Prof. H. Bernhard SchlegelDepartment of ChemistryWayne State University

Current Research GroupDr. Jason Sonnenberg Dr. Peng TaoBarbara Munk Jia ZhouMichael Cato Jason SonkBrian Psciuk

Recent Group MembersDr. Xiaosong Li Dr. Hrant HratchianDr. Stan Smith Dr. Jie (Jessy) LiDr. Smriti Anand Dr. John Knox

UC - Davis, March 14, 2007

Research overview

With molecular orbital calculations, it is possible to investigate details of chemical reactions and molecular properties that are often difficult to study experimentally

Our group is involved in both the development and the application of new methods in ab initio molecular orbital (MO) methods.

Features of Potential Energy Surfaces

Development of new algorithms

energy derivatives for geometry optimization searching for transition states following reaction paths computing classical trajectories for molecular

dynamics directly from the MO calculations. spin projection methods to obtain more accurate

energetics for open shell systems (radicals) simultaneous optimization of the wavefunction

and the geometry

Applications

Organic systems

Inorganic systems

Biochemistry

Study of materials

Dynamics

Nickel catalyzed three component couplings Reactions involving nitric oxides

Organo-metallic complexes

Interactions in the active site of enzymes Guanine oxidation Amber parameters for modified RNA and DNA bases

CVD studies on TiN and ZnO Organic LED materials Molecules in a nanotube Blue shifted hydrogen bonds

One transition state serving two mechanisms Molecules in intense laser fields Two and three body photo dissociation reactions

Ni Catalyzed Three Component Coupling

W X

Y Z

LnNi(0)Ni

LL

W

X Y

ZW

X Y

Z

Ni

LL

R

X Y

Z

Ni

LL

WZn

Zn W

X Y

Z RLnNi(0)

ZnR

(A)(B)

(C)

+

Montgomery, Acc. Chem. Res. 2000, 33, 467-473.

Hratchian, Chowdhury, Gutierrez-Garcia, Amarasinghe, Heeg, Schlegel,

Montgomery, Organomet. 2004, 23, 4636-4646, 5652.

The mechanism for a family of nickel catalyzed three component coupling reactions has been studied experimentally by Prof. Montgomery (WSU). MO studies provide additional insight into the mechanism.

Reaction Profile for L=H2NCH2CH2NH2

-25

-15

-5

5

15

25

35

Reaction Progress

En

erg

y (

kc

al/m

ol)

Reactant

TS1

37.0 kcal/molbarrier

Intermediate

TS2

20.2 kcal/molbarrier

Product

H MeNi

ONi

Me

O

HN

NHNHHN Ni

HN

NH

Me

H

O

Ligand Exchange with ZnMe2

H MeNi

O

MeZn

Ni

Zn

Me

Me

H

O

Me

Me

Ni

Zn Me

Me

H

O

Me

-15

-10

-5

0

5

10

15

20

25

Reaction Progress

En

erg

y (

kcal/

mo

l)

TS20.0 kcal/mol

barrier

TS8.0 kcal/mol

barrier

Reactant

Product

OXA-10 β-lactamase X-ray structure shows

carboxylated Lys70 Modified Lys70 has

mechanistic role Removes proton

from Ser67 Leads to acylation of

Ser67 by substrate Enzyme shows

biphasic kinetics during substrate turnover

J. Li; J. B. Cross; T. Vreven; S. O. Meroueh; S. Mobashery; H. B. Schlegel; Proteins 2005, 61, 246-257

ONIOM QM/MM Method

The active site region is treated using high-level molecular orbital theory, while the most distant parts of the enzyme are treated using low-cost molecular mechanics.

Carboxylation in Gas Phase and in Solution (B3LYP/6-31G(d,p))

R3 (-8.8)

2.70 1.17

1.181.021.47

2.112.13

0.97

TS3 (12.9)

1.29

1.22

1.201.23

1.28

1.211.561.48

P3 (-5.3)

1.381.22

1.36

0.98

1.86

1.45

Model TS1 P TS2 D TS3 P3 TS4 D4

Gas Phase 38.7 5.4 39.6 -1.0 17.7 0.7 32.5 -6.1

Solution 32.4 -5.6 37.4 -2.4 12.0 -10.6 36.6 -5.0

Rx1: CH3NH2+CO2

Rx2: CH3NH2+HCO3-

Rx3: CH3NH2+CO2+H2O

Rx4: CH3NH2+HCO3-+H2O

QM/MM Calculations of the Transition State for Lys-70 Carboxylation

Trp-154 Lys-70

Ser-67

Trp-154 Lys-70

Ser-67

Stereoview of the TS showing a molecule of water catalyzing the addition of carbon dioxide to the side chain of Lys-70

Carboxylation in the QM/MM model of the active site of OXA-10

Model TS1 P TS2 D TS3 P3 TS4 D4

Gas Phase 38.7 5.4 39.6 -1.0 17.7 0.7 32.5 -6.1

Solution 32.4 -5.6 37.4 -2.4 12.0 -10.6 36.6 -5.0

Enzyme 37.9 -12.0 25.6 -36.1 13.8 -12.7 42.8 -51.8

QM/MM Calculations of the Reactants, TS and Products for Lys-70 Carboxylation

N

O

O O

H

N

H

H

H

OH

HO

H

Trp-154

Lys-70

2.732.95

2.87

2.802.84

QM/MM-R

1.18 1.18

2.26Ser-67

N

O

OO

H

N

H

H

HO

H

HO

H

Trp-154

Lys-70QM/MM-TS

Ser-67

N

O

OO

H

N

H

H

H H

O

H

HO

H

Trp-154

Lys-70

2.682.78

3.003.03

2.74N/A

2.68N/A2.87

2.98

QM/MM-P

1.221.23

1.351.25

1.381.37

Ser-67

H H

1.52

1.27

1.34

2.62

2.78

1.21

2.672.86

3.80 1.30

1.131.30

N

O

O O

H

N

H

H

H

OH

HO

H

Trp-154

Lys-70QM/MM-D

2.74N/A

3.063.03

2.70N/A

2.682.78

2.812.98

1.411.37

1.271.23

1.271.25

Ser-67

QM/MM values in normal text

X-ray values in italics

OXA-10 β-lactamase - Discussion

A water molecule in the active site can catalyze carboxylation of Lys70 with CO2

X-ray structure is most likely the deprotonated carboxylation product

Carboxylation is accompanied by deprotonation Re-protonation of carbamate nitrogen results in

barrierless loss of CO2, accounting for biphasic kinetics of enzyme

B. M. Munk, C. J. Burrows, H. B. Schlegel, Chem. Res. Toxicol. (accepted)

Transformations of 8-hydroxy guanine

radical

B3LYP/6-31+G(d) gas phase optimization

IEF-PCMB3LYP/aug-cc-pVTZ

solution phase energies

Oxidative Damage to DNA

Transformations of 8-hydroxy guanine radicalPath 1: reduction followed by tautomerization and ring opening

Transformations of 8-hydroxy guanine radicalPath 2: tautomerization followed by ring opening and reduction

Transformations of 8-hydroxy guanine radicalPath 3: ring opening followed by reduction and tautomerization

Transformations of 8-hydroxy guanine radicalPath 4: ring opening followed by tautomerization and reduction

Transformations of 8-hydroxy guanine radical

(a) Pathways 2 and 4 are preferred

(b) Barriers for ring opening and tautomerization are lower for the radical than for the closed shell molecule

AMBER Force Field Parameters for the Naturally Occurring Modified Nucleosides in RNA

R. Aduri, B. T. Psciuk, P. Saro, H. B. Schlegel, J. SantaLucia Jr. J. Chem. Theor. Comp. (submitted)

NH

N

N

O

NHCH3N

R

H3CN NH

O

O

R

NH

O

ON

HO2CH2CHNH2C

R

NH

N

C

O

NH2N

CH2

HN

HO

O

HO

O

H

OH

H

OH

HO

HH

HO

R

NH

N

C

O

NH2N

CH2

HN

HO

HO

R

N2-methylguanosine 1-methylpseudouridine 5-carboxymethylamino methyluridine

NH

N

O

N

N

N

CH3

R

4-demethylwyosine galactosyl-queuosine queuosine

Protocol for Determining Atom-centered Partial Charges

Electrostatic Potential (pop=mk)

Geometry Optimization

Restrained Electrostatic Potential

PDB/GaussView structure

Optimized Structure

ESP of the molecule

The atom-centered partial charges

Modular approach to fitting RESP charges

N

NN

N

NH2

O

OHO

HH

HH

PO

O-

O

O-

PO

O-

O-CH3

O

OHOH

HH

HH

HO

+

N

NN

N

NH2

H3C

+ P

O2P

O3' O5'

O1P

H3C CH3

The C3’ endo sugar charge was obtained by multi equivalencing the four natural nucleosides Two stage RESP was used to fit the ESP of the modified bases and sugars Atom types and parameters available in GAFF were sufficient for almost all 103 modifications The “prepin” and “frcmod” files generated for all 103 modifications Parameters can be downloaded from http://ozone3.chem.wayne.edu:8080/Modifieds/index.jsp

Test Application of the Parameters for Modified RNA Bases

H. Shi and P. B. Moore

RNA (2000) 6 1091-2000

5MC

MRGMRC

5MC

7MG

WBG

2MG

M2G

PSU

2MG

DHU

5MU PSU

tRNAPhe

with and without

modified bases

(1EHZ)

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.

A Reaction with Branching after the Transition State

Previous work with S. Shaik (JACS 1997, 119, 9237 and JACS 2001, 123, 130): Common TS for inner sphere ET and SUB(C) reactions. Long C-C bond in TS (ca. > 2.45 Å ) favors ET; shorter favors SUB( C ). A less electronegative halide switches the mechanism from SUB( C ) to ET. Poorer electron donors of radical anions favor SUB( C ). More bulkier alkyl halide or more strained TS favor ET.

O-

H YCH3X

HOX-

YH HH

O

H Y.CH3

CH3

O

YH

OH

X-

HH

YH

O CH3

YH

SUB(C)

SUB(O)

OH

X-

HH

YH

+

+ X-

‡

X-

‡.

.

+

+

X-+

.

..

outer sphere ET

ET.

//

-1.5 -1 -0.5 0 0.5 1

0

0.5

1

1.5

2

Sub(C)

OCH2CH3

+ Cl-

ET

CH2O +

CH3 + Cl-

SUB(C) and ET Reaction Paths for CH2O.- + CH3Cl

TS

(C-C) (bohr)

(C-Cl)

(bohr)

Energetics at the UHF/6-31G(d) level of theory

8.1

-5.8 0.0

-56.4

-66.3

-41.2

ET product complex

SUB(C) product complex

SUB(C)ET TS(with chlorine ion bound)

TS

reactant complex

2.563 2.073

2.717 1.847

3.940 3.395

3.6523.667

2.0923.5923.767

1.519

1.521

2.132

-42.6

-30.3

-58.7

+ +

+

+

ET product

SUB(C)ET TS(without chlorine)

SUB(C) product

Temperature dependence of the branching ratio

Temp=148K

50.25%43.84%

0.49% 3.94%1.48%

SUB(C)SUB(C)-ETDirect ET SUB(O)NR Temp=298K

42.36%

53.20%

0.49% 2.96%0.99%

Temp=448K

40.89%

49.75%

0.99% 3.94%

4.43%

Temp=598K

39.41%

49.75%

0.00% 4.43%

6.40%

0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

60.00%

70.00%

148K 298K 448K 598K

ET

SUB( C )

Li, J.; Li, X.; Shaik, S.; Schlegel, H. B. J. Phys. Chem. A 2004, 108, 8526-8532.

Energetics at the G3 level of theory

10.0

-2.90.0

-27.5

-33.2

-19.1

ET product complex

SUB(C) product complex SUB(C)ET TS

(with chlorine ion bound)

TS

reactant complex

2.538 1.988

2.664 1.823

3.5603.439

2.044

3.3843.726

1.520

1.159

2.071

-12.3

-4.7

-21.2

+ +

+

+

ET product

SUB(C)ET TS(without chlorine)

SUB(C) product3.338 3.706

Improved Potential Energy Surfaces using Bond Additivity Corrections (BAC)

The most important correction needed for this reaction are C-C and C-Cl bond stretching potentials.

BAC (bond additivity correction) add simple corrections to get better energetics for the

reaction E = E′+ ∆E ∆E = AC-CExp{-αC-C RC-C} + AC-ClExp{- αC-Cl RC-Cl} 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 G3 energies

BAC-UHF Dynamics Results

SUB(C) SUB(C)-ET Direct ET SUB(O) NR

UHF/6-31G(d) 42.4% 53.2% 1.0% 0.5% 3.0%

BHandHLYP/6-31G(d) 48.8% 24.1% 15.3% 0.0% 10.3%

BAC-UHF/6-31G(d) 56.2% 35.5% 6.9% 0.0% 1.5%

UHF/6-31G(d)

SUB(C)42%

SUB(C)-ET54%

SUB(O)0%

Direct ET1%

NR3%

BHandHLYP/6-31G(d)

SUB(O)0%

SUB(C)-ET24%

Direct ET16%

NR10%

SUB(C)50%

Table 2. Branching ratios at different levels of theory.

BAC-UHF/6-31G(d)

SUB(C)-ET35%

Direct ET7%

SUB(O)0%

NR1%

SUB(C)57%

Li, J.; Shaik, S.; Schlegel, H. B.; J. Phys. Chem. A 2006, 110, 2801-2806. .

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)

0 50 100 150 200 250 300 350 400

-0.4

-0.2

0.0

0.2

0.4

0.00

0.01

0.02

0.96

0.98

1.00

-0.6

-0.4

-0.2

0.0

0.2

0.4

-0.1

0.0

0.1

Hydrogen 1 Hydrogen 2

(d)

Time (a.u.)

1g

1u

2g

2u

(c)

1g

1u

2g

2u

(b)

(a)

q (

a.u

.)n

(a.

u.)

E (

a.u

.) (

a.u

.)

Test Case

H2 in an intense laser fieldTD-HF/6-311++G(d,p)

Emax = 0.10 au (3.5 1014 W/cm2) = 0.06 au (760 nm)

Test Case(a)

(b)

(c)

H2 in an intense laser fieldTD-HF/6-311++G(d,p)

Emax = 0.12 au (5.0 1014 W/cm2) = 0.06 au (760 nm)

Laser pulse

Instantaneous dipole response

Fourier transform of the residual dipole response

Hydrogen Moleculeaug-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-HF

Butadiene in an intense laser field(8.75 x 1013 W/cm2 760 nm)

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

)HF/6-31G(d,p)

t = 0.0012 fs

The Charge Response of Neutral Butadiene

Butadiene in an intense laser fieldTD-CIS/6-31G(d,p), 160 singly excited states

= 0.06 au (760 nm)

Fourier transform of the residual dipole

Excited state weights in the final wavefunction

Polyacenes in Intense Laser Pulse (Levis et al. Phys. Rev. A 69, 013401 (2004))

1 1014 W·cm-2

Time-of-flight,s

Ion

Sign

al, n

orm

aliz

ed

403020100403020100

2 1014 W·cm-2

5.4 1013 W·cm-2 6 1013 W·cm-2

2.4 1013 W·cm-2 2.7 1013 W·cm-2

4.5 1012 W·cm-2 5.0 1012 W·cm-2

TDHF Simulations for Polyacenes

Polyacenes ionize and fragment at much lower intensities than polyenes

Polyacene experimental data shows the formation of molecular +1 cations prior to fragmentation with 60 fs FWHM pulses

Time-dependent Hartree-Fock simulations with 6-31G(d,p) basis, t = 0.0012 fs, ω=1.55 eV and 5 fs FWHM pulse

Intensities chosen to be ca 75% of the experimental single ionization intensities

Intensities of 8.75 x 1013, 3.08 x 1013, 2.1 x 1013 and 4.5 x1012 for benzene, naphthalene, anthracene and tetracene

Nonadiabatic multi-electron excitation model was used to check that these intensities are non-ionizing

Tetracene: Dipole Response

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

-10-505

10-10-505

10

-3

0

3

-0.009-0.006-0.0030.0000.0030.0060.009

2+ Neutral Geometry

Time (fs)

1+ Neutral Geometry

d(au

)

Neutral

(au)

I = 3.38 x 1012 W/cm2 ω = 1.55eV, 760 nm

Naphthalene+1:Dependence on the Field Strength

-2 0 2 4 6 8 10 12 14 16 18-8-6-4-20246

-6-4-20246

-6-4-20246

Time (fs)

E = 0.0340 au

d(a

u)

E = 0.0296 au

E = 0.0155 au

ω = 1.55eV, 760 nm

10 20 30 40 50 60 70 80

2

4

6

8

10

12

10 20 30 40 50 60 70 80

2

4

6

8

10

12

10 20 30 40 50 60 70 80

2

4

6

8

10

12

Energy (eV) Energy (eV)

1.1 eV

1.1 eV

4.5 eV

7.1 eV

7.1 eV

Tra

nsiti

on

Am

plit

ude

1.1 eV

3.1 eV

(2x1.55 eV)

4.5 eV

7.1 eV

Energy (eV)

E = 0.0155 au E = 0.029 au E = 0.034 au

8.95 eV

Naphthalene+1:Dependence on the Field Strength

ω = 1.55eV, 760 nm

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

-10-8-6-4-202468-8

-6-4-202468-8

-6-4-202468

Time (fs)

= 3.00 eV

n(a

u)

= 2.00 eV

= 1.00 eV

Anthracene+1:Dependence on the Field Frequency

Emax = 0.0183 au

5 10 15 20 25 30 35 40

10

20

30

40

50

Emax = 0.0183 au

5 10 15 20 25 30 35 40

5

10

15

20

25 ω = 1.00 eV1.95 eV

3.63 eV

4.95 eV

6.32 eV

7.79 eV

9.57 eV

5

10

15

20

25

Tra

nsiti

on A

mpl

itude

5 10 15 20 25 30 35 40

10

20

30

40

ω = 2.00 eV

1.95 eV

3.63 eV

6.32 eV

7.97 eV

40

30

20

10

ω = 3.00 eV

2.79 eV

3.63 eV

4.61 eV

5.58 eV

7.97 eV

10.23 eV10

20

30

40

50

Anthracene+1:Dependence on the Field Frequency

Energy Energy Energy

Non-adiabatic behavior increases with length Non-adiabatic behavior is greater for monocation Increasing the field strength increases the non-resonant

excitation of the states with the largest transition dipoles Increasing the field frequency increases the non-resonant

excitation of higher states

Smith, S. M.; Li, X.; Alexei N. Markevitch, A. N.; Romanov, D. A.; Robert J. Levis, R. J.; Schlegel, H. B.; Numerical Simulation of Nonadiabatic Electron Excitation in the Strong Field Regime: 3. Polyacene Neutrals and Cations. (JPCA submitted)

Polyacenes: Summary

Recent Group Members

Current Group Members

Current Research GroupDr. Jason Sonnenberg Dr. Peng TaoBarbara Munk Michael CatoJia Zhou Jason SonkBrian Psciuk

Recent Group MembersProf. Xiaosong Li, U of WashingtonProf. Smriti Anand, Christopher-Newport U.Dr. Hrant Hratchian, Indiana U. (Raghavachari grp)Dr. Jie Li, U. California, Davis (Duan group)Dr. Stan Smith, Temple U. (Levis group)Dr. John Knox (Novartis)

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

Molecular geometriesand orientation of the field

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

-4

0

4-4

0

4-4

0

4

-4

0

4-4

0

4-0.04

0.00

0.04

Time (fs)

2+ Ion Geometry

2+ Neutral Geometry

d(au

)

1+ Ion Geometry

1+ Neutral Geometry

Neutral

(au)

Effect of Charge and Geometry on the Dipole Moment Response: Butadiene

I = 8.75 x 1013 W/cm2

ω = 1.55eV, 760 nm

10 20 30 40 50 60 70 80

5

10

15

20

25

30

Butadiene+1: Fourier Analysis of Residual Oscillations

10 20 30 40 50

5

10

15

20

25

30

35

40

4.10 eV

5.69 eV

Main Transition

(TDHF Coefficient)

Energy

(eV)Transition

Dipole (au)

Oscil.

Stren.

Neutral Geometry

HOMO → SOMO (1.00)

2.53 1.70 0.12

SOMO → LUMO (0.92)

4.87 1.75 0.38

Ion Geometry

HOMO → SOMO (0.95)

4.03 1.94 0.39

HOMO → LUMO (0.83)

5.69 0.23 0.01

Ion Geometry

Tra

nsit

ion

Am

plit

ude

2.32 eV

Neutral Geometry

2.57 eV

4.90 eV

The monocations have lower energy excited states and show greater non-adiabatic behavior than the dications

Relaxing the geometry increases the energy of the lowest excited states and decreases the non-adiabatic behavior

Fourier transform of the residual oscillations in the dipole moment shows that the non-adiabatic excitation involves the lowest excited states

Smith, S. M.; Li, X.; Alexei N. Markevitch, A. N.; Romanov, D. A.; Robert J. Levis, R. J.; Schlegel, H. B.; Numerical Simulation of Nonadiabatic Electron Excitation in the Strong Field Regime: 2. Linear Polyene Cations. J. Phys. Chem. A 2005, 109, 10527-10534.

Polyene Cations: Summary

Ionization Probability using NME

MoleculeExcited

State Energy (Δ)

Transition Dipole

Moment (au)

Ionization Probability

Benzene

Neutral 8.00 1.8700 0.0022+1 Neutral Geometry 5.59 1.0294 0.0052+1 Ion Geometry 5.60 1.1165 0.0054+2 Neutral Geometry 7.53 1.3739 0.00034+2 Ion Geometry 7.41 1.2511 0.00023Naphthalene

Neutral 6.94 3.0104 0.0001+1 Neutral Geometry 6.99 1.7097 0.011+1 Ion Geometry 7.26 2.3353 0.00018+2 Neutral Geometry 6.63 2.3504 0.00025+2 Ion Geometry 6.35 2.3733 0.00026Anthracene

Neutral 6.21 3.9917 0.00015+1 Neutral Geometry 6.37 2.7456 0.00047+2 Neutral Geometry 5.94 3.1693 0.00056Tetracene

Neutral 5.70 4.8840 0.00006+1 Neutral Geometry 6.28 3.3935 0.0011+2 Neutral Geometry 5.44 3.8964 0.00095

Time-dependent HF or DFT propagation of the electron density

Classical propagation of the nuclear degrees of freedom

Novel integration method using three different time scales

Li, X.; Tully, J. C.; Schlegel, H. B.; Frisch, M. J.; Ab Initio Ehrenfest Dynamics. J. Chem. Phys. 2005, 123, 084106

Ehrenfest Dynamics

Potential energy curves for H2C=NH2

+ torsion

0 20 40 60 80 100 120 140 160 1800

1

2

3

4

5

6

7

8

9

S1

En

ergy

(eV

)

Torsional Angle (degree)

S0

1.6 eVC N

H

H H

H

Torsional dynamicsfor H2C=NH2

+

-0.1

0.0

0.1

0.2

0.3

0 20 40 60 80 100 120 140 160 180-0.1

0.0

0.1

0.2

0.3

-0.1

0.0

0.1

0.2

0.3

(b) Ekin

= 5.22 eV

Nat

ura

l Ch

arge

of

NH

2

(b) Ekin

= 9.28 eV

Torsional Angle (degree)

BO Dynamics Ehrenfest Dynamics

(a) Ekin

= 4.39 eV