Energy and pressure versus volume: Equations of state motivated by the stabilized jellium model

Explicit functions are widely used to interpolate, extrapolate, and differentiate theoretical or experimental data on the equation of state (EOS) of a solid. We present two EOS functions which are theoretically motivated. The simplest realistic model for a simple metal, the stabilized jellium (SJ) or structureless pseudopotential model, is the paradigm for our SJEOS. A simple metal with exponentially overlapped ion cores is the paradigm for an augmented version (ASJEOS) of the SJEOS. For the three solids tested (Al, Li, Mo), the ASJEOS matches all-electron calculations better than prior equations of state. Like most of the prior EOS's, the ASJEOS predicts pressure P as a function of compressed volume v from only a few equilibrium inputs: the volume v(o), the bulk modulus B-o, and its pressure derivative B-1. Under expansion, the cohesive energy serves as another input. A further advantage of the new equation of state is that these equilibrium properties other than vo may be found by linear fitting methods. The SJEOS can be used to correct B-o and the EOS found from an approximate density functional, if the corresponding error in v(o) is known. We also (a) estimate the typically small contribution of phonon zero-point vibration to the EOS, ib) find that the physical hardness By does not maximize at equilibrium, and (c) show that the "ideal metal'' of Shore and Rose is the zero-valence limit of stabilized jellium.