Arnaldo Donoso

Semiclassical multistate Liouville dynamics in the adiabatic representation

In this paper, we describe implementation of the semiclassical Liouville method for simulating molecular dynamics on coupled electronic surfaces in the electronic adiabatic representation. We cast the formalism in terms of semiclassical motion on Born–Oppenheimer potential energy surfaces with nonadiabatic coupling arising from the coordinate dependence of the adiabatic electronic eigenstates. Using perturbation theory and asymptotic evaluation of the resulting time integrals, we derive an expression for the probability of transition between adiabatic states which agrees with the result given previously by Miller and George [W. H. Miller and T. F. George, J. Chem. Phys. 56, 5637 (1972)]. We also demonstrate numerically the equivalence of semiclassical trajectory-based calculations in the adiabatic and diabatic representations by performing molecular dynamics simulations on a model two-state system and comparing with exact quantum mechanical results. Excellent agreement between the exact and semiclassical ...

Simulation of quantum processes using entangled trajectory molecular dynamics

In this paper, we describe a new method for simulating quantum processes using classical-like molecular dynamics. The approach is based on solving the quantum Liouville equation in the Wigner representation using ensembles of classical trajectories in phase space. The nonlocality of quantum mechanics is incorporated in the trajectory representation as nonclassical interactions between the members of the ensemble, leading to an entanglement of their evolution. The statistical independence of the individual trajectories making up an ensemble in the classical limit is lost when quantum effects are included, and the entire state of the system must be propagated as a unified whole. We develop the formalism and its numerical implementation, and illustrate its application on two model problems of quantum mechanical tunneling: escape from a metastable well and wave packet penetration of the Eckhart barrier.

Simulation of nonadiabatic wave packet interferometry using classical trajectories

In this paper, we describe the application of our recently developed multistate semiclassical Liouville equation method for modeling molecular dynamics on multiple coupled electronic states [C. C. Martens and J.-Y. Fang, J. Chem. Phys. 106, 4918 (1997); A. Donoso and C. C. Martens, J. Phys. Chem. 102, 4291 (1998)] to problems where electronic coherence effects play a dominant role. We consider a model problem involving the simultaneous evolution of wave packets on two coupled electronic states. We analyze the problem qualitatively from both quantum and semiclassical perspectives using perturbation theory, and identify the roles played by coupling strength and relative phase of the initial wave packets. We then perform trajectory-based simulations on a two-state one-dimensional model problem and compare the results with those of exact quantum calculations. In marked contrast with most current methods for modeling nonadiabatic dynamics with classical trajectories, the semiclassical Liouville method is found...

A shock-capturing SPH scheme based on adaptive kernel estimation

Here we report a method that converts standard smoothed particle hydrodynamics (SPH) into a working shock-capturing scheme without relying on solutions to the Riemann problem. Unlike existing adaptive SPH simulations, the present scheme is based on an adaptive kernel estimation of the density, which combines intrinsic features of both the kernel and nearest neighbor approaches in a way that the amount of smoothing required in low-density regions is effectively controlled. Symmetrized SPH representations of the gas dynamic equations along with the usual kernel summation for the density are used to guarantee variational consistency. Implementation of the adaptive kernel estimation involves a very simple procedure and allows for a unique scheme that handles strong shocks and rarefactions the same way. Since it represents a general improvement of the integral interpolation on scattered data, it is also applicable to other fluid-dynamic models. When the method is applied to supersonic compressible flows with sharp discontinuities, as in the classical one-dimensional shock-tube problem and its variants, the accuracy of the results is comparable, and in most cases superior, to that obtained from high quality Godunov-type methods and SPH formulations based on Riemann solutions. The extension of the method to two- and three-space dimensions is straightforward. In particular, for the two-dimensional cylindrical Nohs shock implosion and Sedov point explosion problems the present scheme produces much better results than those obtained with conventional SPH codes.

Solution of phase space diffusion equations using interacting trajectory ensembles

In this paper, we present a new method for simulating the evolution of the phase space distribution function describing a system coupled to a Markovian thermal bath. The approach is based on the propagation of ensembles of trajectories. Instead of incorporating environmental perturbations as stochastic forces, however, the present method includes these effects by additional deterministic interactions between the ensemble members. The general formalism is developed and tested on model systems describing one-dimensional diffusion, relaxation of a coherently excited harmonic oscillator coupled to a thermal bath, and activated barrier crossing in a bistable potential. Excellent agreement with exact results or approximate theories is obtained in all cases. The method provides an entirely deterministic trajectory-based approach to the solution of condensed phase dynamics and chemical reactions.

Entangled trajectory dynamics in the Husimi representation

We solve quantum dynamical equations of simple systems by propagating ensembles of interacting trajectories. A scheme is proposed which uses adaptive kernel density estimation for representing probability distribution functions and their derivatives. The formulation is carried on in the Husimi representation to ensure the positiveness of the distribution functions. By comparing to previous work, the effect of changing representations is studied as well as the advantage of using adaptive kernels for the estimation of probability distributions. We found significant improvement in the accuracy of the results.

Theory and simulation of condensed-phase ultrafast dynamics

In this paper, we describe a new approach to simulating many-body molecular dynamics on coupled electronic surfaces. The method is based on a semiclassical limit of the quantum Louisville equation, which yields equations of motion for classical-like distribution functions describing both nuclear probability densities on the coupled surfaces and the coherences between the electronic states. The Hamiltonian dynamics underlying the evolution of these distributions is augmented by nonclassical source and sink terms, which allow the flow of probability between the coupled surfaces and the corresponding formation and decay of electronic coherences. We show that this approach reproduces the familiar Landau-Zehnder transition probability in the limit of weak electronic coupling. In addition, we describe a trajectory-based implementation in the context of a conventional molecular dynamics simulation.