A classical mechanical analysis of molecular motions. Resonances in transition-state spectra of FH−2, FDH−, and FD−2

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Abstract
A classical method of analysis is used to assign the various peaks in the transition‐state spectra of FH−2, FDH−, and FD−2 to two series of resonances. Each series is ‘‘assigned’’ to a different periodic orbit whose motion is that of the nuclei in the resonances. The assignment is based on the parallels between periodic orbit properties and the experimental spectra upon isotope substitution. Relative to previous periodic orbit analysis and exact calculations, not only are new resonances found but it is shown that their role in the dynamics was not fully appreciated for one series and somewhat different than previously believed for the other series. Classical mechanics is here used, not to compute cross sections or spectra but to locate the effective potentials that, when quantized, yield the observed quantum states. Variants of the analysis method are discussed for systems other than FH−2 where the simplest version of the method is adequate.