Matching-pursuit split-operator Fourier-transform simulations of excited-state intramolecular proton transfer in 2-(2′-hydroxyphenyl)-oxazole

Steered quantum dynamics for energy minimization

We introduce a quantum optimal control algorithm for energy minimization that combines the diffeomorphic modulation under observable response preserving homotopy (D-MORPH) gradient and the Broyden Fletcher Goldfarb Shanno (BFGS) iterative scheme for nonlinear optimization. An extended set of controls defining the time-dependent mass, dipole moment, and external perturbational field are optimized to find an effective Hamiltonian that steers the dynamics of the system into the global minimum without getting trapped into local minima. The algorithm is illustrated as applied to energy minimization on rugged surfaces and golf potentials comparable to those previously explored for testing quantum annealing methodologies.

Description of bound reactive dynamics within the approximate quantum trajectory framework

The quantum trajectory framework incorporates quantum effects on dynamics through the quantum potential acting on a trajectory ensemble in addition to the classical potential. A global quadratic approximation to the quantum potential makes the method practical in many dimensions and captures dominant quantum effects in semiclassical systems. In this paper the approach is further developed to describe the "double well" dynamicsa prototype of the proton transfer reactionswhich exhibits the "hard" quantum effect of tunneling. Accurate description is achieved by combining the approximate quantum trajectory dynamics with the population amplitudes in the reactant and product wells. The quantum trajectory dynamics is defined by the asymptotic classical potentials. The population amplitudes represented in a small basis describe transfer between the wells. The method is exact if the reactant/product potentials are quadratic and the basis size is sufficiently large. In the semiclassical regime the trajectory dynamics is approximate and the basis size can be as small as two functions. The approach is fully compatible with the trajectory description of multidimensional systems capturing quantum tunneling along the reactive coordinate and zero-point energy flow among all degrees of freedom.

Matching-pursuit/split-operator-Fourier-transform simulations of excited-state nonadiabatic quantum dynamics in pyrazine

A simple approach for numerically exact simulations of nonadiabatic quantum dynamics in multidimensional systems is introduced and applied to the description of the photoabsorption spectroscopy of pyrazine. The propagation scheme generalizes the recently developed matching-pursuit/split-operator-Fourier-transform (MP/SOFT) method [Y. Wu and V. S. Batista, J. Chem. Phys. 121, 1676 (2004)] to simulations of nonadiabatic quantum dynamics. The time-evolution operator is applied, as defined by the Trotter expansion to second order accuracy, in dynamically adaptive coherent-state expansions. These representations are obtained by combining the matching-pursuit algorithm with a gradient-based optimization method. The accuracy and efficiency of the resulting computational approach are demonstrated in calculations of time-dependent survival amplitudes and photoabsorption cross sections, using a model Hamiltonian that allows for direct comparisons with benchmark calculations. Simulations in full-dimensional potential energy surfaces involve the propagation of a 24-dimensional wave packet to describe the S(1)S(2) interconversion of pyrazine after S(0)-->S(2) photoexcitation. The reported results show that the generalized MP/SOFT method is a practical and accurate approach to model nonadiabatic reaction dynamics in polyatomic systems.