Mixed-valence (MV) systems are referred to here as MV-2 and MV-3 depending on whether two or three consecutive valence states are involved. MV-3 systems range from systems with Hubbard U>>0, corresponding to a single stable, intermediate valence state, and U<<0, corresponding to stable alternating valences differing by two units. Experiments using inelastic neutron scattering or inelastic X-ray scattering show softening of breathing phonon modes in MV systems compared with related systems with a single valence. It is hypothesized that softening is due to coupling between potential energy surfaces, corresponding to differing localizations of the electron. As predicted, softening is larger in the delocalized case. A mechanism for superconductivity is suggested.
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