  We provide a prescription for constructing Hamiltonians representing the low
energy physics of correlated electron materials with dynamically screened
Coulomb interactions. The key feature is a renormalization of the hopping and
hybridization parameters by the processes that lead to the dynamical screening.
The renormalization is shown to be non-negligible for various classes of
correlated electron materials. The bandwidth reduction effect is necessary for
connecting models to materials behavior and for making quantitative predictions
for low-energy properties of solids.
