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 ͑EOS͒ of a solid. We present two EOS functions which are theoretically motivated. The simplest realistic model for a simple metal, the stabilized jellium ͑SJ͒ 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 ͑ASJEOS͒ of the SJEOS. For the three solids tested ͑Al, Li, Mo͒, 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 ͑a͒ estimate the typically small contribution of phonon zero-point vibration to the EOS, ͑b͒ find that the physical hardness Bv does not maximize at equilibrium, and ͑c͒ show that the ''ideal metal'' of Shore and Rose is the zero-valence limit of stabilized jellium.

Elastic properties of rhombohedral, cubic, and monoclinic phases of LaNiO 3 by first principles calculations

“…corrections for the experimental data. On one hand, the ZPAE corrections are straightforwardly applicable only for the cubic systems [42]. On the other hand, ZPAE can expand the equilibrium lattice constant by 1% for light atoms like Li and much less for heavy atoms [43], thus it should not have a noticeable influence on material like LaNiO 3 .…”

Self-consistent meta-generalized gradient approximation within the projector-augmented-wave method

“…In the rest of this work, we will compute lattice constants by minimizing the total energy (fitted to an equation of state [47][48][49] ) with respect to the lattice constant. We will use selfconsistent densities, although the effect of using say the LSDA density instead of the selfconsistent one would be small 58 .…”

“…The atomization energies for the AE6 molecules were calculated at an energy cutoff of 1000 eV. We determined the equilibrium lattice constants a 0 and bulk moduli B 0 by calculating the total energy per unit cell at 7-12 points in the range V 0 ± 7% (where V 0 is the equilibrium unit cell volume for each exchange-correlation functional), fitting the data to the stabilized jellium equation of state (SJEOS) [47][48][49] . The cohesive energy, defined as the energy per atom needed to atomize the crystal, is calculated for each functional from the energies of the crystal at its equilibrium volume and the spinpolarized symmetry-broken solutions of the constituent atoms (no fractional occupancies) 50 .…”

“…Full phononspectrum estimates for about 60 solids will be available soon 59 . The experimental cohesive energies were corrected for the zero-point vibration energy 38,47 .…”

Generalized-gradient-approximation noninteracting free-energy functionals for orbital-free density functional calculations

“…As is evident from that figure, the widely used ftSGA and ftTF functionals, as well as the ftTW functional, do not predict energy minima, at least in the range of densities treated. The lower part of Table I shows OF-DFT results for the equilibrium lattice constant and bulk moduli obtained by fitting the calculated total energies per cell to the stabilized jellium model equation of state (SJEOS) 36 . Two functionals, ftGGA(KST2) and ft(VWTF), predict quite similar results: the lattice constant is underestimated by three percent, but the bulk modulus is overestimated by about 40%.…”