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

Abstract

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 v0, the bulk modulus B0, and its pressure derivative B1. 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 v0 may be found by linear fitting methods. The SJEOS can be used to correct B0 and the EOS found from an approximate density functional, if the corresponding error in v0 is known. We also (a) estimate the typically small contribution of phonon zero-point vibration to the EOS, (b) find that the physical hardness Bv does not maximize at equilibrium, and (c) show that the “ideal metal” of Shore and Rose is the zero-valence limit of stabilized jellium