Uniform semiclassical IVR treatment of the S-matrix

Abstract

A new, uniform, semiclassical, initial value representation expression is obtained for the S-matrix in the case of collinear collisions. The derivation is based on an asymptotic analysis ͑for large inter-fragment distances͒ of a uniform semiclassical integral expression for the time independent scattering wave function. Although this derivation specifically treats the case of the collision of an atom with a harmonic diatom, the final expression is generalized to arbitrary collinear collisions. The various properties of the expression and its relation to existing semiclassical methods are discussed. Numerical tests are performed for the well-known Secrest-Johnson system. Among other important advantages, the present treatment is a well-defined, uniform, semiclassical approximation that is capable of good accuracy and high computational efficiency, requiring a relatively small number of classical trajectories to obtain converged S-matrix elements for a given energy and initial state.

The three-dimensional nonadiabatic dynamics calculation of DH2+ and HD2+ systems by using the trajectory surface hopping method based on the Zhu–Nakamura theory

“…3,4 For the goal of establishing a practical mixed-quantumclassical approximation, sorts of semiclassical methods have been developed to deal with high dimensional nonadiabatic dynamics, in which various quantum effects should be taken into account. Quantum mechanics can afford useful physical and chemical insights in the molecular scale, 1 but rigorous quantum mechanical calculations become unfeasible as the number of dimension increases.…”

Semiclassical initial value theory of rotationally inelastic scattering: Some remarks on the phase index in the interaction picture

“…Amazingly accurate SCIVR calculations have been performed by Elran and Kay. 52 To date, however, their approach has only been applied to collinear processes, and its applicability to three-dimensional collisions is an open issue. 52 Moreover, the mathematical form of their S-matrix elements is much more complex than the one of Eqs.…”

“…In an illuminating analysis, McCurdy and Miller 66 showed within a planar model of atom-diatom inelastic collision that the semiclassical theory of molecular collision [42][43][44][45][46][47][48][49][50][51][52][53][54][55] not only reproduces the previous interference features, but also provides deep insight into their physical origin. The primary reason for this success is that, as previously stated, semiclassical methods assign probability amplitudes and phases to classical trajectories and make them interfere, respecting thereby the quantum principle of superposition.…”

Initial-value representation of the semiclassical zeta function

“…IVR treatments have previously been developed for the time-dependent propagator [15][16][17], the time-independent wave function [18,20], the S matrix [21,22], the Green's function [19], and its trace [12]. Recently, and most relevant to the present work, a particular kind of IVR approximation was also proposed for the zeta function [23].…”