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.