arXiv subjects

Sandy Yang

Publications and source records attributed to Sandy Yang.

2 recordsLinked to original sources

arXiv2008

Multiple Spawning with Optimal Basis Set Expansion

The Full Multiple Spawning (FMS) method is designed to simulate quantum dynamics in the multi-state electronic problem. The FMS nuclear wavefunction is represented in a basis of coupled, frozen Gaussians, and the spawning procedure prescribes a means of adaptively increasing the size of the basis in order to capture population transfer between electronic states. Parent trajectories create children when passing through regions of significant nonadiabatic coupling. In order to converge branching ratios without allowing the basis to reach an impractical size, population transfer at individual spawning events should be made as effective as possible. Herein we detail a new algorithm for specifying the initial conditions of freshly spawned basis functions, one that minimizes the number of spawns needed for convergence by maximizing the efficiency of individual spawning events. Optimization is achieved by maximizing the coupling between parent and child trajectories, as a function of child position and momentum, at the point of spawning. The method is tested with a two-state, one-mode avoided crossing model and a two-state, two-mode conical intersection model.

physics.chem-ph↗

arXiv2005

Path-integral virial estimator for reaction rate calculation based on the quantum instanton approximation

The quantum instanton approximation is a type of quantum transition state theory that calculates the chemical reaction rate using the reactive flux correlation function and its low order derivatives at time zero. Here we present several path-integral estimators for the latter quantities, which characterize the initial decay profile of the flux correlation function. As with the internal energy or heat capacity calculation, different estimators yield different variances (and therefore different convergence properties) in a Monte Carlo calculation. Here we obtain a virial-type estimator by using a coordinate scaling procedure rather than integration by parts, which allows more computational benefits. We also consider two different methods for treating the flux operator, i.e., local-path and global-path approaches, in which the latter achieves a smaller variance at the cost of using second-order potential derivatives. Numerical tests are performed for a one-dimensional Eckart barrier and a model proton transfer reaction in a polar solvent, which illustrates the reduced variance of the virial estimator over the corresponding thermodynamic estimator.

physics.chem-ph↗