Erratum: "Semiclassical initial value representation: From Møller to Miller" [J. Chem. Phys. 153, 174102 (2020)]

Semiclassical initial value representation: From Møller to Miller. II

As shown by W. H. Miller in a seminal article [J. Chem. Phys. 53, 3578 (1970)], the most convenient and accurate semiclassical (SC) theory of molecular scattering in action-angle coordinates is based on the initial value representation (IVR) and the use of shifted angles, which are different from the natural angles usually used in the quantum and classical treatments. Here, we show for an inelastic molecular collision that the initial and final shifted angles define three-segment classical paths that are exactly those involved in the classical-limit of Tannor-Weeks quantum scattering theory [J. Chem. Phys. 98, 3884 (1993)], provided that the translational wave packets |g₊⟩ and |g_-⟩ into play in this theory are both taken at |0⟩. Assuming this to be the case, using van Vleck propagators, and applying the stationary phase approximation, Miller's SCIVR expression of S-matrix elements is found, with an additional cut-off factor canceling the energetically forbidden transition probabilities. This factor, however, is close to unity in most practical cases. Furthermore, these developments show that the Møller operators underlie Miller's formulation, thus confirming, for molecular collisions, the results recently established in the simpler case of light-induced rotational transitions [L. Bonnet, J. Chem. Phys. 153, 174102 (2020)]. Last but not least, we show, based on the previous results, that for processes involving long-range anisotropic forces, implementing the Skinner-Miller method [Chem. Phys. Lett. 300, 20 (1999)] in shifted coordinates makes its predictions both easier and more accurate than in natural coordinates.

Semiclassical descriptions of rotational transitions in natural and shifted angles: Analysis of unexpected results

In the semiclassical theory of rotational transitions, S-matrix elements are expressed as integrals over initial and final angles of probability amplitudes calculated along the classical paths joining these angles, before final passage to an initial value representation [W. H. Miller, J. Phys. Chem. A 105, 2942 (2001)]. These angles can be either natural angles fixing the orientation of the rotor or angles shifted with respect to the previous ones so as to vary only within the interaction region causing the transitions. The two approaches, however, were recently shown to lead to different predictions. While the theory in natural angles lacks precision and exhibits unphysical behavior, the theory in shifted angles is much more accurate and physically well behaved [L. Bonnet, J. Chem. Phys. 153, 174102 (2020)]. The present work is devoted to the analysis of this unexpected finding.