1. Yinghua Wu* Xin Chen, Yinghua Wu and Victor S. Batista Department of Chemistry, Yale University, New Haven, CT 06520-8107 Xin Chen * Current address: Department of Chemistry, Tulane University. 228 th ACS National Meeting, August 22-August 26, 2004 Philadelphia Quantum/Classical Calculations in Chemistry and Biophysics Matching-Pursuit Representations for Simulations of Quantum Processes

2. Time-Sliced Simulations of Quantum Processes

3. Wu,Y.; Batista, V.S. J. Chem. Phys. 118, 6720 (2003) Wu,Y.; Batista, V.S. J. Chem. Phys. 119, 7606 (2003) Wu,Y.; Batista, V.S. J. Chem. Phys. 121, 1676 (2004) Chen, X., Wu,Y.; Batista, V.S. J. Chem. Phys. submitted (2004) Wu,Y.; Batista, V.S. J. Chem. Phys. in prep. (2004) MP/SOFT Method Trotter Expansion

7. ESIPT in the keto-enolic tautomerization of 2-(2’-hydroxyphenyl)-oxazole (HPO). Changes in hybridization and connectivity Classical Dynamics (HPMO) Vendrell, O.; Moreno, M.; Lluch J.M.; Hammes-Schiffer, S. J. Phys. Chem. B 108, 6745 (2004) Quantum Dynamics (7-d simulation, related ESIPT system) Petkovic, M.; Kuhn, O. J. Phys. Chem. A 107, 8458 (2003) SC-IVR (HPO) Guallar, V.; Batista, V.S.; Miller, W.H. J. Chem. Phys. 113, 9510 (2000) Batista, V.S.; Brumer, P. Phys. Rev. Lett. 89, 143201 (2002) Batista, V.S.; Brumer, P. Phys. Rev. Lett. 89, 249903 (2002)

8. Reaction Surface 35-dimensional Model V(r 1,r 2,z) = V 0 (r 1,r 2 ) + 1/2 [z- z 0 (r 1,r 2 )] F(r 1,r 2 ) [z-z 0 (r 1,r 2 )] V 0 : Reaction surface z 0 : ab initio geometries F : ab initio force constants r 1,r 2 : reaction coordinates

9. CIS/6-31G* Reaction Surface Potential V 0 (r 1,r 2 )

10. Computation of Observables Time dependent reactant population: Absorption Spectrum:

11. Time-Dependent Survival Amplitude HK SC-IVR vs. Classical Wigner Wigner SC-IVR

12. Time-Dependent Survival Amplitude HK SC-IVR vs. MP/SOFT

13. Time Dependent Reactant Population HK SC-IVR, Classical Wigner (SC/L) and WKB

14. WIGNER, TD-SCF, HK SC-IVR, MP/SOFT Time Dependent Reactant Population Early Time Relaxation Dynamics

15. WIGNER, TD-SCF, HK SC-IVR, MP/SOFT Time Dependent Reactant Population Longer Time Relaxation Dynamics [1] [2] [1] Wu,Y.; Batista, V.S. J. Chem. Phys. in prep. (2004) Guallar, V.; Batista, V.S.; Miller, W.H. J. Chem. Phys. 113, 9510 (2000)

16. Decoherence Dynamics HK SC-IVR vs. MP/SOFT Batista, V.S.; Brumer, P. Phys. Rev. Lett. 89, 143201 (2002) [2] [1] Wu,Y.; Batista, V.S. J. Chem. Phys. in prep. (2004)

17. Thermal Correlation Functions Boltzmann Ensemble Averages Chen, X., Wu,Y.; Batista, V.S. J. Chem. Phys. submitted (2004)

18. Bloch Equation: MP/SOFT Integration Partition Function Boltzmann Matrix:

21. Calculations of Thermal Correlation Functions Time-Dependent Position Ensemble Average Position-Position Correlation Function: Model System:

22. Classical density Quantum density Ground State, V 0 Excited State, V 1 Model System, cont’d

23. Position-Position Correlation Function

24. Time-Dependent Position Ensemble Average

25. Conclusions We have introduced the MP/SOFT method for time-sliced simulations of quantum processes in systems with many degrees of freedom. The MP/SOFT method generalizes the grid-based SOFT approach to non-orthogonal and dynamically adaptive coherent-state representations generated according to the matching-pursuit algorithm. The accuracy and efficiency of the resulting method were demonstrated in simulations of excited-state intramolecular proton transfer in 2-(2’- hydroxyphenyl)-oxazole (HPO), as modeled by an ab initio 35-dimensional reaction surface Hamiltonian. Further, we have extended the MP/SOFT method for computations of thermal equilibrium density matrices (equilibrium properties of quantum systems), finite temperature time-dependent expectation values and time- correlation functions. The extension involves solving the Bloch equation via imaginary-time propagation of the density matrix in dynamically adaptive coherent-state representations, and the evaluation of the Heisenberg time- evolution operators through real-time propagation.

26. NSF Career Award CHE#0345984 ACS PRF#37789-G6 NSF Nanoscale Exploratory Research (NER) Award ECS#0404191 Research Corporation, Innovation Award#RI0702 Hellman Family Fellowship Anderson Fellowship Yale University, Start-Up Package NERSC Allocation of Supercomputer Time ACS Meeting Organizing Committee (Prof. Hammes-Schiffer, Prof. Jensen) Thank you ! Acknowledgments

27. Electron Tunneling in Multidimensional Systems

28. 2-dimensional (Model I)

32. 2-dimensional (model I)

33. 5-dimensional (model I)

40. 10-dimensional (model I)

41. Electron Tunneling in Multidimensional Systems Model II

42. (2-dimension Model II)

43. 2-dimensional (model II)

45. 2-dimensional (Model II)

46. 20-dimensional (Model II)

47. 20-dimensional (model II) Benchmark calculation:

48. TS/SC-IVR Approach

49. The (TS) implementation avoids most of the difficulties of the standard SC-IVR, since the propagator is applied only for short time-slices while the semiclassical approximation is still accurate and efficient. However, the method introduces a new challenge: the reinitialization of the time-evolved wavefunction after each propagation time-slice. In order to optimize the efficiency of the re-expansion procedure, the time- evolved wavefunction is represented (“compressed”) at the end of each propagation time-slice according to a matching-pursuit coherent-state expansion.

50. TSHK QM HK 2-dimensional tunneling

51. 157 nm TS/SC-IVR Approach

52. 2.42 fs 3.63 fs 31 40 Instantaneous Time-Dependent Wavepackets

53. Survivial Amplitudes

54. Total Photodissociation Cross Sections

55. 31 Partial Photodissociation Cross Sections

58. Conclusions We have introduced the MP/SOFT method for time-sliced simulations of quantum processes in systems with many degrees of freedom. The MP/SOFT method generalizes the grid-based SOFT approach to non-orthogonal and dynamically adaptive coherent-state representations generated according to the matching-pursuit algorithm. The accuracy and efficiency of the resulting method were demonstrated in simulations of deep-tunneling quantum dynamics for systems with up to 20 coupled degrees of freedom. Work in progress involves simulations of excited-state intramolecular proton transfer in 2,2’-hydroxyphenyl-oxazole as well as calculations of the equilibrium density matrix (equilibrium properties of quantum systems). We have also introduced the TS/SC-IVR approach, a method that concatenates finite-time propagators and computes real-time path integrals based on the HK SC-IVR. We have shown that the approach significantly improves not only the accuracy of simulations of deep-tunneling quantum dynamics based on the HK SC-IVR but also the accuracy of computations of photo-dissociation cross sections of vibrationally hot molecules (sensitive to subtle interference effects).

59. Acknowledgments NSF Career Award CHE-0345984 NSF Nanoscale Exploratory Research (NER) Award ECS-0404191 ACS PRF 37789-G6 Research Corporation, Innovation Award Hellman Family Fellowship Anderson Fellowship Yale University, Start-Up Package NERSC Allocation of Supercomputer Time CNLS Workshop Organizing Committee at LANL Thank you !

60. Reaction Coordinates in HPO r 1 : H-stretching

61. Reaction Coordinates in HPO r 2 : internal bending