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

Journal Article · Sat Jul 28 04:00:00 EDT 2007 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.2756532· OSTI ID:20991299

Wu, Yinghua; Herman, Michael F ^[1]

---

1. Department of Chemistry, Tulane University, New Orleans, Louisiana 70118 (United States)

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 Schroedinger equation (TDSE) through order ({Dirac_h}/2{pi}), and the O(({Dirac_h}/2{pi}){sup 2}) 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 ({Dirac_h}/2{pi}){sup 2} terms involving the interstate coupling functions have significant effects on the quantum transition probabilities. Motivated by these data, the ({Dirac_h}/2{pi}){sup 2} 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 ({Dirac_h}/2{pi}){sup 2} 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.

• OSTI ID: 20991299
• Journal Information: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 4 Vol. 127; ISSN JCPSA6; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COUPLING
PROPAGATOR
QUANTUM MECHANICS
REFLECTION
SCHROEDINGER EQUATION
SEMICLASSICAL APPROXIMATION
SURFACES
TIME DEPENDENCE
TRAJECTORIES
TRANSMISSION
VECTORS