FUNDAMENTAL FREQUENCIES INCREASING WITH REDUCED MASSES - AN INVERSE QUANTUM ISOTOPE EFFECT IN MOLECULES WITH SHALLOW DOUBLE-WELL POTENTIALS, EG-SEMIBULLVALENES

We predict an inverse quantum isotope effect for molecules that may isomerize in a shallow double-well potential. Here the corresponding fundamental vibrational transition may excite a delocalized state with energy just above the potential barrier. In this case, increasing molecular masses is predicted to yield increasing fundamental frequencies, in marked contrast to the familiar opposite trend in other molecules. The novel effect is illustrated for simple models representing symmetric semibullvalenes, consistent with experimental values for the relevant masses, bond lengths, and NMR and UV spectra. The effect is explained in terms of illuminating approximations, i.e., harmonic oscillators for the potential wells and a square well for the domain of the potential barrier. Turning the table, we predict that observations of the novel effect indicate shallow double-well potentials with barrier heights slightly below the level which is excited by the fundamental transition.