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Exploring Potential Energy Surfaces by Ab Initio Molecular Dynamics

Molecular Quantum MechanicsAnalytical Gradients and Beyond A Conference in Honor of Peter Pulay May 29 – June 3, 2007, Margitsziget, Budapest. Exploring Potential Energy Surfaces by Ab Initio Molecular Dynamics. Prof. H. Bernhard Schlegel Department of Chemistry Wayne State University

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Exploring Potential Energy Surfaces by Ab Initio Molecular Dynamics

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  1. Molecular Quantum MechanicsAnalytical Gradients and Beyond A Conference in Honor of Peter Pulay May 29 – June 3, 2007, Margitsziget, Budapest Exploring Potential Energy Surfaces by Ab Initio Molecular Dynamics 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

  2. 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

  3. 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

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

  5. 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

  6. 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

  7. 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

  8. 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

  9. Empirical Valence Bond Models for Potential Energy Surfaces for Reactions HCNHNCisomerization PES: effect of coordinate system Cartesian Harmonic internal Anharmonic internal Actual PES

  10. Empirical Valence Bond Model using Distributed Gaussians

  11. Potential Energy Surface for 2-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)

  12. V122 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

  13. Energy along the reaction path for pyridone 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

  14. Gradient along the reaction path for pyridone 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

  15. Potential energy surface for pyridone tautomerization

  16. Potential Energy Surface for Pyridone + 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

  17. Potential Energy Surface for theClaisen 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

  18. Electronic Response of Molecules to Short, Intense Laser Pulses 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

  19. 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)

  20. 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

  21. Laser pulse 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

  22. Hydrogen Molecule 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)

  23. Butadiene in an intense laser field(8.75 x 1013 W/cm2 760 nm) HF/6-31G(d,p) Dt = 0.0012 fs

  24. The Charge Response of Neutral Butadiene

  25. 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

  26. Hexatriene in an intense laser fieldTD-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

  27. 2  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

  28. 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, 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

  29. Anthracene: Dipole Response I = 1.58 x 1013 W/cm2 ω = 1.55eV, 760 nm

  30. Tetracene: Dipole Response I = 3.38 x 1012 W/cm2 ω = 1.55eV, 760 nm

  31. Naphthalene in an intense laser fieldTD-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

  32. Anthracene+1:Dependence on the Field Frequency Emax = 0.0183 au

  33. Anthracene+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

  34. Polyacenes: Summary • 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)

  35. Recent Group Members

  36. Current Group Members

  37. Collaborators: 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.

  38. Molecular geometriesand orientation of the field

  39. Effect of Charge and Geometry on the Dipole Moment Response: Butadiene I = 8.75 x 1013 W/cm2 ω = 1.55eV, 760 nm

  40. 2.32 eV 5.69 eV Butadiene+1: Fourier Analysis of Residual Oscillations 4.10 eV 2.57 eV 4.90 eV Transition Amplitude Neutral Geometry Ion Geometry

  41. Polyene Cations: Summary • 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.

  42. Ionization Probability using NME

  43. Pulse Shaping and Sequencing Test case: HF/6-31++G(d,p) calculations of excitation energies, transition dipoles and time dependent response of H2+ Transition dipole for |1g to |1u is 1.00 au, and for |1u to |2gis 1.57 au, but no transition dipole between |1g to |2g Ladder-type STIRAP experiment (stimulated Raman adiabatic passage): A single-photon excitation from |1g |1u and a second single-photon excitation from |1u |2g should populate the |2g state with little or no population in the |1u state if the |1u |2g is pumped first

  44. Electric Field Profiles for H2+ with Counter-Intuitive Pulse Timing Stokes Pulse Pump Pulse FWHM = 120 fs FWHMP = 85 fs 150 fs delay between pulses

  45. STIRAP Results for H2+

  46. 0.32 eV 0.1 eV Effects of Detuning in Ladder Type STIRAP for H2+

  47. Effects of Detuning for H2+

  48. Ehrenfest Dynamics • 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

  49. Potential energy curves for H2C=NH2+ torsion

  50. Torsional dynamicsfor H2C=NH2+

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