Yinghua Wu

Matching-pursuit for simulations of quantum processes

The matching-pursuit algorithm is implemented to develop an extension of the split-operator Fourier transform method to a nonorthogonal, nonuniform and dynamically adaptive coherent-state representation. The accuracy and efficiency of the computational approach are demonstrated in simulations of deep tunneling and long time dynamics by comparing our simulation results with the corresponding benchmark calculations.

Quantum tunneling dynamics in multidimensional systems: A matching-pursuit description

Rigorous simulations of quantum tunneling dynamics in model systems with up to 20 coupled degrees of freedom are reported. The simulations implement an extension of the recently developed matching-pursuit/split-operator Fourier-transform method to complex-valued coherent-state representations. The resulting method recursively applies the time-evolution operator, as defined by the Trotter expansion to second order accuracy, in dynamically adaptive coherent-state representations generated by an approach that combines the matching-pursuit algorithm with a gradient-based optimization method.

Nonadiabatic surface hopping Herman-Kluk semiclassical initial value representation method revisited: Applications to Tully’s three model systems

The nonadiabatic surface hopping Herman-Kluk (HK) semiclassical initial value representation (SC-IVR) method for nonadiabatic problems is reformulated. The method has the same spirit as Tullys surface hopping technique [J. Chem. Phys. 93, 1061 (1990)] and almost keeps the same structure as the original single-surface HK SC-IVR method except that trajectories can hop to other surfaces according to the hopping probabilities and phases, which can be easily integrated along the paths. The method is based on a rather general nonadiabatic semiclassical surface hopping theory developed by Herman [J. Chem. Phys. 103, 8081 (1995)], which has been shown to be accurate to the first order in h and through all the orders of the nonadiabatic coupling amplitude. Our simulation studies on the three model systems suggested by Tully demonstrate that this method is practical and capable of describing nonadiabatic quantum dynamics for various coupling situations in very good agreement with benchmark calculations.

On the properties of a primitive semiclassical surface hopping propagator for nonadiabatic quantum dynamics

A previously developed nonadiabatic semiclassical surface hopping propagator [M. F. Herman J. Chem. Phys. 103, 8081 (1995)] is further studied. The propagator has been shown to satisfy the time-dependent Schrodinger equation (TDSE) through order h, and the O(h2) terms are treated as small errors, consistent with standard semiclassical analysis. Energy is conserved at each hopping point and the change in momentum accompanying each hop is parallel to the direction of the nonadiabatic coupling vector resulting in both transmission and reflection types of hops. Quantum mechanical analysis and numerical calculations presented in this paper show that the h2 terms involving the interstate coupling functions have significant effects on the quantum transition probabilities. Motivated by these data, the h2 terms are analyzed for the nonadiabatic semiclassical propagator. It is shown that the propagator can satisfy the TDSE for multidimensional systems by including another type of nonclassical trajectories that reflect on the same surfaces. This h2 analysis gives three conditions for these three types of trajectories so that their coefficients are uniquely determined. Besides the nonadiabatic semiclassical propagator, a numerically useful quantum propagator in the adiabatic representation is developed to describe nonadiabatic transitions.

A justification for a nonadiabatic surface hopping Herman-Kluk semiclassical initial value representation of the time evolution operator

A justification is given for the validity of a nonadiabatic surface hopping Herman-Kluk (HK) semiclassical initial value representation (SC-IVR) method. The method is based on a propagator that combines the single surface HK SC-IVR method [J. Chem. Phys. 84, 326 (1986)] and Hermans nonadiabatic semiclassical surface hopping theory [J. Chem. Phys. 103, 8081 (1995)], which was originally developed using the primitive semiclassical Van Vleck propagator. We show that the nonadiabatic HK SC-IVR propagator satisfies the time-dependent Schrodinger equation to the first order of variant Plancks over 2pi and the error is O(variant Plancks over 2pi(2)). As a required lemma, we show that the stationary phase approximation, under current assumptions, has an error term variant Plancks over 2pi(1) order higher than the leading term. Our derivation suggests some changes to the previous development, and it is shown that the numerical accuracy in applications to Tullys three model systems in low energies is improved.

Matching-pursuit∕split-operator Fourier-transform simulations of nonadiabatic quantum dynamics

A rigorous and practical approach for simulations of nonadiabatic quantum dynamics is introduced. The algorithm involves a natural extension of the matching-pursuitsplit-operator Fourier-transform (MPSOFT) method [Y. Wu and V. S. Batista, J. Chem. Phys. 121, 1676 (2004)] recently developed for simulations of adiabatic quantum dynamics in multidimensional systems. The MPSOFT propagation scheme, extended to nonadiabatic dynamics, recursively applies the time-evolution operator as defined by the standard perturbation expansion to first-, or second-order, accuracy. The expansion is implemented in dynamically adaptive coherent-state representations, generated by an approach that combines the matching-pursuit algorithm with a gradient-based optimization method. The accuracy and efficiency of the resulting propagation method are demonstrated as applied to the canonical model systems introduced by Tully for testing simulations of dual curve-crossing nonadiabatic dynamics.

Matching-pursuit/split-operator-Fourier-transform computations of thermal correlation functions.

A rigorous and practical methodology for evaluating thermal-equilibrium density matrices, finite-temperature time-dependent expectation values, and time-correlation functions is described. The method involves an extension of the matching-pursuit/split-operator-Fourier-transform method to the solution of the Bloch equation via imaginary-time propagation of the density matrix and the evaluation of Heisenberg time-evolution operators through real-time propagation in dynamically adaptive coherent-state representations.

Quantum Dynamics of the Excited State Intramolecular Proton Transfer in 2-(2'-Hydroxyphenyl)-Benzothiazole

The excited-state intramolecular proton-transfer dynamics and pho- toabsorption associated with the ketoenolic tautomerization reaction in 2-(2¢-hydr oxyphenyl)benzothiazole are simulated according to a numerically exact quantum- dynamics propagation method and a full-dimensional excited-state potential energy surface based on an ab initio reaction surface Hamiltonian. The simulations involve the propagation of 69-dimensional wave packets according to the matching-pursuit/ split-operator Fourier transform (MP/SOFT) method (Wu, Y.; Batista, V.S. J.�Chem.� Phys. 2004, 121, 1676-1686). The underlying propagation scheme recursively ap- plies the time-evolution operator as defined by the Trotter expansion to second-or - der accuracy in dynamically adaptive coherent-state expansions. Computations of time-dependent survival amplitudes, the time-dependent product population, and photoabsorption linewidths are compared to experimental data. The reported results provide fundamental insight on the nature of the excited-state reaction dynamics and demonstrate the capabilities of the MP/SOFT method as a powerful computational tool to study ultrafast reaction dynamics in polyatomic systems.