By Stuart A. Rice

Advances in Chemical Physics is the single sequence of references to be had that explores the innovative of analysis in chemical physics. This sequence presents the chemical physics box with a discussion board for serious, authoritative reviews of advances in each quarter of the self-discipline.

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As discussed later, the topological obstruction in the case of LiCN is a finite ‘‘fold’’ between the interpenetrating eigenvalues of LiCN and those of LiNC [9]. However, there is no such finite region in the case of HCN, and therefore no quantum monodromy [10]. The mathematical discussion centers on the connectivity of classical invariant tori [24–26], which are the analogs of quantum mechanical wavefunctions, as one moves over the energy and angular momentum plane. Each point in the plane has an associated two-dimensional torus in a fourdimensional phase space, which is characterized by two classical actions, H Iv (or quantum numbers), determined by topologically distinct loop integrals, p dq; by a time period, T, for one of the degrees of freedom; and by the angle change, Áy (or twist [10] over the surface of the torus), in the second degree of freedom.

Section III describes the quantum monodromy in highly excited states of HCP (as modeled by a spherical pendulum) and LiCN, and explains why the effect does not occur for HCN. It will be seen that the reorganization of the quantum level structure around the HPC conformation of HCP mimics that around the barrier to linearity in H2O because both are dictated by the same type of isolated critical point of the classical mechanics. In LiCN, on the other hand, the role of the critical point is replaced by that of a finite folded part of the quantum spectrum, over which bending states of LiCN interleave with those of LiNC—finite in the sense that there are no bound states of LiNC for sufficiently high vibrational angular momentum.

Gray In Eq. (44), gel ðTÞ is the ratio of transition state and reactant electronic partition functions [31] and the rotational degeneracy factor gj1 ;j2 ¼ ð2j1 þ 1Þð2j2 þ 1Þ for heteronuclear diatomics, and will also include nuclear spin considerations in the case of homonuclear diatomics. The rigorous evaluation of the above quantities involves calculations that include the Coriolis coupling between all of the K states that contribute to a given value of total angular momentum J. We present a method for doing these rigorous Coriolis-coupled calculations in Section IV [32].