Exploring Potential Energy Surfaces Using Ab Initio Molecular Dynamics

1. Canadian Conference on Computational Chemistry Halifax, July 19 - 24, 2009 Exploring Potential Energy Surfaces Using Ab Initio Molecular Dynamics Prof. H. Bernhard Schlegel Department of Chemistry Wayne State University Current Research Group Dr. Peng Tao Dr. Barbara Munk Jia Zhou Jason Sonk Brian Psciuk Adam Birkholz Recent Group Members Prof. Xiaosong Li Dr. Hrant Hratchian Prof. Jason Sonnenberg Dr. Stan Smith Prof. Smriti Anand Dr. Jie (Jessy) Li Dr. John Knox Michael Cato

2. 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

3. Applications of Ab Initio Molecular Dynamics Jia Zhou Chemistry Wayne State U. Prof. Smriti Anand Northern Virginia Community College Dr. Jie Li Genome Center UC Davis

4. 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

5. Ab Initio Classical Trajectory on theBorn-Oppenheimer Surface Using Hessians Calculate the energy, gradient and Hessian Solve the classical equations 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.

6. 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

7. Energy Dependence of the Branching Ratio Osterheld, T. H.; Brauman, J. I.; J. Am. Chem. Soc.1993, 115, 10311-10316.

8. Potential Energy Profile (CBS-APNO) • + CH CO / CH complex 3 3 45 35 25 15 Relative Energy (kcal/mol) 5 Ketene/Methane complex TS for Methane Elimination -5 -15 Anand, S.; Schlegel, H. B. Phys. Chem. Chem. Phys. 2004, 6, 5166. -25

9. 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

10. Branching Ratios for Microcanonical Ensemble

11. Effect of Adding Energy to Specific Vibrational Modes * plus 0.5 kcal/mol in transition vector

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

13. Potential Energy Surface for Pentanedione Radical Cation

14. Kinetic Scheme for Pentanedione Radical Cation Number of trajectories Time (fs)

15. 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)

16. Dissociation of H2CNH

17. Dissociation of H2CNH+

18. Dissociation of H2NCH2+

19. Dissociation of H2NCH3+

20. Direct vs Indirect Dissociation of H2CNH Direct (no hydrogen rearrangement before dissociation) Indirect (hydrogen migration before dissociation)

21. 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%)

22. Time Dependent Simulations of Molecules in Strong Fields Prof. Xiaosong Li University of Washington Jason Sonk, WSU Prof. Robert Levis, Temple U. Dr. Stan Smith, Temple U.

23. 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 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)

24. Hydrogen Molecule aug-cc-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 Instantaneous dipole response (b) (d) Time (0.05×au) (c) Fourier transform of the residual dipole response (e) Energy (au) (f)

25. Laser pulse Butadiene Dipole Charges 8.75×1013 W/cm2 760 nm HF/6-31G(d,p) Dt = 0.0012 fs Populations of occupied orbitals Populations of unoccupied orbitals

26. Butadiene, Hexatriene and NaphthaleneTD-CIS/6-31G(d,p),  = 0.06 au (760 nm) Excited state weights in the final wavefunction

27. Excited State Energies of Butadiene RPA CIS CIS(D) CISD EOM-CCSD

28. * Transition Dipoles for Butadiene (6-31G(d,p) basis)

29. Response of 2 and 3 Level Systemsto a 3 Cycle Gaussian Pulse 0.25 0.00 0.35 0.25 0.00

30. Response of the  States of Butadieneto a 3 Cycle Gaussian Pulse TD-CIS 1Ag (gs) 1Bu1Ag1Bu TD-EOMCC

31. 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 Energy (au) State Number

32. 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

33. 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 Instantaneous Dipole Instantaneous Dipole Time (fs) Time (fs) Wavefunction Coefficients Wavefunction Coefficients Energy (au) Energy (au)

34. Response of Butadieneto a 3 Cycle Gaussian Pulse(=0.6 au, 6-31G(d,p) basis) RPA TD-CIS TD-CIS(D) TD-EOMCC (c) (f)

35. Transition Dipoles for Butadiene(CIS)

36. 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) (c) (f)

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. Peng Tao Dr. Barbara Munk • Jia Zhou Jason Sonk • Brian Psciuk Adam Birkholz • Recent Group Members • Prof. Jason Sonnenberg, Stevenson University, • Prof. Xiaosong Li, U. of Washington • Prof. Smriti Anand, Northern Virginia College • Dr. 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 Foundation • Office of Naval Research • NIH • Gaussian, Inc. • Wayne State U.

38. Recent Group Members

39. Current Group Members