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. Multidimensional Quantum Dynamics: Methods and Applications Tuesday, September 28th, 2004 - Physical Chemistry Seminar 11:00 a.m., Room 1315 Chemistry Building Department of Chemistry, University of Wisconsin-Madison

2. 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)

3. Computation of Observables Time Dependent Reactant Population: Absorption Spectrum: Time Dependent Survival Amplitude

4. 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

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

6. Reaction Coordinates in HPO r 2 : internal bending

7. CASSCF Reaction Surface Potential V 0 (r 1,r 2 )

8. Time-Sliced Simulations of Quantum Processes

9. 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

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

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

15. Douhal et.al. JPC 100, 19789 (1997), HPMO in n-hexane S1S1 S0S0 Comparison with experimental data

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

17. 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)

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

19. Comparison with experimental data Femtosecond fluorescent transient at 420nm for HPMO in 3-methylpentane JPC 102,1657 (1998) Zewail and co-workers Time dependent reactant (enol) population

20. 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)

21. Development of new methodologies for studies of Decoherence and Coherent-Control

22. Contour plot of the percentage product yield for bichromatic coherent-control at 100 fs after photoexcitation of the system, as a function of the laser controllable parameters. Coherent-Control of the keto-enolic isomerization in HPO

23. Electron Tunneling in Multidimensional Systems Wu,Y.; Batista, V.S. J. Chem. Phys. 121, 1676 (2004)

24. 2-dimensional (Model I)

28. 2-dimensional (model I)

29. 5-dimensional (model I)

36. 10-dimensional (model I)

37. Electron Tunneling in Multidimensional Systems Model II

38. (2-dimension Model II)

39. 2-dimensional (model II)

41. 2-dimensional (Model II)

42. 20-dimensional (Model II)

43. 20-dimensional (model II) Benchmark calculation:

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

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

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

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

50. Position-Position Correlation Function

51. Time-Dependent Position Ensemble Average

52. 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, as well as in simulations of deep-tunneling quantum dynamics for systems with up to 20 coupled degrees of freedom. 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.

53. 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 Department of Chemistry, University of Wisconsin Madison Thank you ! Acknowledgments