Yinghua Wu* Xin Chen, Yinghua Wu and Victor S. Batista Department of Chemistry, Yale University, New Haven, CT 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

Time-Sliced Simulations of Quantum Processes

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

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, (2002) Batista, V.S.; Brumer, P. Phys. Rev. Lett. 89, (2002)

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

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

Computation of Observables Time dependent reactant population: Absorption Spectrum:

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

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

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

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

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)

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

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

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

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

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

Position-Position Correlation Function

Time-Dependent Position Ensemble Average

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.

NSF Career Award CHE# ACS PRF#37789-G6 NSF Nanoscale Exploratory Research (NER) Award ECS# 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

Electron Tunneling in Multidimensional Systems

2-dimensional (Model I)

2-dimensional (model I)

5-dimensional (model I)

10-dimensional (model I)

Electron Tunneling in Multidimensional Systems Model II

(2-dimension Model II)

2-dimensional (model II)

2-dimensional (Model II)

20-dimensional (Model II)

20-dimensional (model II) Benchmark calculation:

TS/SC-IVR Approach

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.

TSHK QM HK 2-dimensional tunneling

157 nm TS/SC-IVR Approach

2.42 fs 3.63 fs Instantaneous Time-Dependent Wavepackets

Survivial Amplitudes

Total Photodissociation Cross Sections

31 Partial Photodissociation Cross Sections

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).

Acknowledgments NSF Career Award CHE NSF Nanoscale Exploratory Research (NER) Award ECS ACS PRF 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 !

Reaction Coordinates in HPO r 1 : H-stretching

Reaction Coordinates in HPO r 2 : internal bending