We show how the coupling between the phonons and electrons in a strongly
correlated metal can result in phonon frequencies which have a non-monotonic
temperature dependence. Dynamical mean-field theory is used to study the
Hubbard-Holstein model that describes the \kappa-(BEDT-TTF)_2 X family of
superconducting molecular crystals. The crossover with increasing temperature
from a Fermi liquid to a bad metal produces phonon anomalies that are
consistent with recent Raman scattering and acoustic experiments.Comment: 6 pages, 3 eps figure
