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 ${v}_{0},$ the bulk modulus ${B}_{0},$ 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 ${v}_{0}$ may be found by linear fitting methods. The SJEOS can be used to correct ${B}_{0}$ and the EOS found from an approximate density functional, if the corresponding error in ${v}_{0}$ is known. We also (a) estimate the typically small contribution of phonon zero-point vibration to the EOS, (b) find that the physical hardness $\mathrm{Bv}$ does not maximize at equilibrium, and (c) show that the ``ideal metal'' of Shore and Rose is the zero-valence limit of stabilized jellium.