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Exploring Potential Energy Surfaces by Ab Initio Molecular Dynamics

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### Exploring Potential Energy Surfaces by Ab Initio Molecular Dynamics

### Empirical Valence Bond Models for Reactive Potential Energy Surfaces Using Distributed Gaussians

### Electronic Response of Molecules to Short, Intense Laser Pulses

Molecular Quantum MechanicsAnalytical Gradients and Beyond

A Conference in Honor of Peter Pulay

May 29 – June 3, 2007, Margitsziget, Budapest

Prof. H. Bernhard Schlegel

Department of Chemistry

Wayne State University

Current Research Group

Dr. Jason Sonnenberg Dr. Peng Tao

Barbara Munk Jia Zhou

Michael Cato Jason Sonk

Brian Psciuk

Recent Group Members

Dr. Xiaosong Li Dr. Hrant Hratchian

Dr. Stan Smith Dr. Jie (Jessy) Li

Dr. Smriti Anand Dr. John Knox

Early encounters with Peter Pulay and his work

- During my graduate studies, 1972-75
- HF gradients for s,p basis sets
- Pulay was the external examiner on PhD thesis

- While a postdoc with John Pople, 1977-78
- HF second derivatives and post-SCF gradients with Krishnan Raghavachari

Reactions and Dynamics

- Modeling reactive potential energy surfaces with empirical valence bond methods using distributed Gaussians
- energy derivatives, redundant internal coordinates, DIIS

- Dynamics of the electron density of molecules interacting with intense laser pulses
- TD-HF and TD-CIS simulations of the response prior to ionization

H. B. Schlegel, J. L. Sonnenberg,

J. Chem. Theor. Comp. 2006, 2, 905-911.

J. L. Sonnenberg, H. B. Schlegel,

Mol. Phys. (submitted).

Supported by a grant from ONR to

Voth, Miller, Case, Cheatham and Schlegel

Empirical Valence Bond Models for Potential Energy Surfaces for Reactions

- For condensed phase and enyzmatic systems where extensive dynamics is required, QM/MM calculations may still be too costly.
- EVB provides a simple, systematic way to construct an empirical PES for reactions, calibrated to QM calculations
- PES represented by 2 (or more) valence bond configurations and empirical interaction matrix elements
- Initially employed by Warshel
- Improved by Chang and Miller
- MCMM method by Truhlar

Empirical Valence Bond Models for Potential Energy Surfaces for Reactions

- V11 and V22 can be treated adequately by molecular mechanics
- Need to find a suitable functional form for V12
- Fit V12 to ab initio calculation around the transition state

Empirical Valence Bond Models for Potential Energy Surfaces for Reactions

- Chang – Miller approach:
- Fit V12 to energy, gradient and Hessian at or near transition state

Empirical Valence Bond Models for Potential Energy Surfaces for Reactions

- Our approach:
- Fit V12 to energy, gradient and Hessian at one or more points around the transition state

Empirical Valence Bond Models for Potential Energy Surfaces for Reactions

HCNHNCisomerization PES: effect of coordinate system

Cartesian Harmonic internal Anharmonic internal

Actual PES

Empirical Valence Bond Model using Distributed Gaussians for Reactions

Potential Energy Surface for for Reactions2-Pyridone – 2-Hydroxypyridine Tautomerization

MP2/6-311+G(d,p) optimization, 159 kJ/mol barrier

EVB surface with distributed Gaussians fitted energies, gradients and Hessians at one to nine points along the reaction path

Redundant internal coordinates used: 56 (all), 32 (only bonds and angles), 25 (changes greater than 0.01), 10 (changes greater than 0.1 bohr or rad)

V for Reactions122 along the reaction path for pyridone tautomerization

V122 (au)

V122 difference (au)

Long dashes – 3 Gaussian fit (R, P, TS)

Short dashes – 7 Gaussian fit (R, P, TS, ±½, ±¼ )

Red – ab initio V122 along the path

Energy along the reaction path for for Reactionspyridone tautomerization

Total energy (au)

Energy difference (au)

1 Gaussian fit at TS – max error 7.3 kJ/mol

Long dashes – 3 Gaussian fit (R, P, TS) – max error 4.1 kJ/mol

Short dashes – 7 Gaussian fit (R, P, TS, ±½, ±¼ ) – max error 0.4 kJ/mol

Red – ab initio energy along the path

Gradient along the reaction path for for Reactionspyridone tautomerization

Long dashes – 3 Gaussian fit (R, P, TS)

Short dashes – 7 Gaussian fit (R, P, TS, ±½, ±¼ )

Red – ab initio gradient norm along the path

Potential energy surface for for Reactionspyridone tautomerization

Potential Energy Surface for for ReactionsPyridone + Water Tautomerization

B3LYP/6-31G(d,p) opt., 50 kJ/mol barrier

1 Gaussian fit

V122 using all coord., max error = 4.0 kJ/mol

V122 using only bonds, max error = 2.9 kJ/mol

3 Gaussian fit (R, TS, P)

V122 using all coord., max error = 1.8 kJ/mol

V122 using only bonds, max error = 3.0 kJ/mol

Potential Energy Surface for the for ReactionsClaisen Rearrangment

MP2/6-311+G(d,p) optimization, 99 kJ/mol barrier

EVB surface with 7 Gaussians has a maximum error of 3.3 kJ/mol along the reaction path

Phys. Rev. A. 2003, 68, 011402(R),

Phys. Rev. A. 2004, 69, 013401,

Phys. Chem. Chem. Phys. 2005, 7, 233-239,

J. Phys. Chem. A 2005; 109; 5176-5185,

J. Phys. Chem. A2005, 109, 10527-10534,

J. Phys. Chem. A2007 (accepted),

J. Chem. Phys. 2007 (accepted).

Supported by a grant from NSF

TD-CI and TD-HF simulation of molecules in 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 analytically
P(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)

H laser pulses2 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

Laser pulse laser pulses

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)Test Case

(a)

Instantaneous dipole response

(b)

(c)

Fourier transform of the residual dipole response

Hydrogen Molecule laser pulses

aug-pVTZ basis plus 3 sets of diffuse sp shells

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

(b)

(a)

(c)

TD-CIS TD-CISD TD-HF

(b)

(d)

(c)

(e)

(f)

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

HF/6-31G(d,p)

Dt = 0.0012 fs

The Charge Response of Neutral Butadiene laser pulses

Butadiene in an intense laser field laser pulsesTD-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

Hexatriene in an intense laser field laser pulsesTD-CIS/6-31G(d,p), 200 singly excited states = 0.06 au (760 nm)

Fourier transform of the residual dipole

Excited state weights in the final wavefunction

- 2 laser pulses 1014 W·cm-2

- 6 1013 W·cm-2

- 5.4 1013 W·cm-2

- 2.7 1013 W·cm-2

- 2.4 1013 W·cm-2

- 5.0 1012 W·cm-2

- 4.5 1012 W·cm-2

0

10

20

30

40

0

10

20

30

40

Polyacenes in Intense Laser Pulse (Levis, R. J. et al. Phys. Rev. A2004, 69, 013401)- 1 1014 W·cm-2

Ion Signal, normalized

Time-of-flight, ms

TDHF Simulations for Polyacenes laser pulses

- 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, Dt = 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

Naphthalene in an intense laser field laser pulsesTD-CIS/6-31G(d,p), 200 singly excited states = 0.06 au (760 nm)

Fourier transform of the residual dipole

Excited state weights in the final wavefunction

Anthracene laser pulses+1:Dependence on the Field Frequency

Emax = 0.0183 au

Anthracene laser pulses+1:Dependence on the Field Frequency

Emax = 0.0183 au

3.63 eV

ω = 1.00 eV

ω = 3.00 eV

ω = 2.00 eV

25

1.95 eV

1.95 eV

50

40

2.79 eV

20

40

4.61 eV

3.63 eV

3.63 eV

30

Transition Amplitude

15

5.58 eV

30

4.95 eV

7.97 eV

20

10

6.32 eV

6.32 eV

20

7.79 eV

10

5

10

10.23 eV

7.97 eV

9.57 eV

Energy Energy Energy

Polyacenes: Summary laser pulses

- 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. J. Phys. Chem. A (submitted)

Recent Group Members laser pulses

Current Group Members laser pulses

Collaborators laser pulses:

Dr. T. Vreven, Gaussian Inc.

Dr. M. J. Frisch, Gaussian Inc.

Prof. John SantaLucia, Jr., WSU

Raviprasad Aduri (SantaLucia group)

Prof. G. Voth, U. of Utah

Prof. David Case, Scripps

Prof. Bill Miller, UC Berkeley

Prof. Thom Cheatham, U. of Utah

Prof. S.O. Mobashery, Notre Dame U.

Prof. R.J. Levis, Temple U.

Prof. C.H. Winter, WSU

Prof. C. Verani, WSU

Prof. E. M. Goldfield, WSU

Prof. D. B. Rorabacher, WSU

Prof. J. F. Endicott, WSU

Prof. J. W. Montgomery, U. of Michigan

Prof. Sason Shaik, Hebrew University

Prof. P.G. Wang, Ohio State U.

Prof. Ted Goodson, U. of Michigan

Prof. G. Scuseria, Rice Univ.

Prof. Srini Iyengar, Indiana U

Prof. O. Farkas, ELTE

Prof. M. A. Robb, Imperial, London

Acknowledgements- Current Research Group
- Dr. Jason Sonnenberg Dr. Peng Tao
- Barbara Munk Michael Cato
- Jia Zhou Jason Sonk
- Brian Psciuk

- Recent Group Members
- Prof. Xiaosong Li, U of Washington
- Prof. 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 Foundation
- Office of Naval Research
- NIH
- Gaussian, Inc.
- Wayne State U.

Molecular geometries laser pulsesand orientation of the field

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

I = 8.75 x 1013 W/cm2

ω = 1.55eV, 760 nm

2.32 eV Butadiene

5.69 eV

Butadiene+1: Fourier Analysis of Residual Oscillations4.10 eV

2.57 eV

4.90 eV

Transition Amplitude

Neutral Geometry

Ion Geometry

Polyene Cations: Summary Butadiene

- 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. A2005, 109, 10527-10534.

Ionization Probability using NME Butadiene

Pulse Shaping and Sequencing Butadiene

Test case: HF/6-31++G(d,p) calculations of excitation energies, transition dipoles and time dependent response of H2+

Transition dipole for |1g to |1u is 1.00 au, and for |1u to |2gis 1.57 au, but no transition dipole between |1g to |2g

Ladder-type STIRAP experiment (stimulated Raman adiabatic passage):

A single-photon excitation from |1g |1u and a second single-photon excitation from |1u |2g should populate the |2g state with little or no population in the |1u state if the |1u |2g is pumped first

Electric Field Profiles for H Butadiene 2+ with Counter-Intuitive Pulse Timing

Stokes Pulse

Pump Pulse

FWHM = 120 fs

FWHMP = 85 fs

150 fs delay between pulses

STIRAP Results for H Butadiene 2+

Effects of Detuning for H Butadiene 2+

Ehrenfest Dynamics Butadiene

- 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

Potential energy curves for H Butadiene 2C=NH2+ torsion

Torsional Butadiene dynamicsfor H2C=NH2+

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