The lattice vibrations are determined in the quasi‐harmonic approximation for elemental Au and Cu to twice their normal density by first‐principles electronic band‐structure calculations. It is found for these materials that the important moments of the phonon density of states can be obtained to high accuracy from short‐ranged force constant models. We discuss the implications for the Gru¨neisen parameters on the basis of calculated phonon moments and their approximations by using bulk moduli and Debye‐Waller factors. © 2004 American Institute of Physics