Equation of State
An equation of state for a solid relates energy or pressure to volume, and fitting one to computed or measured data yields the equilibrium volume, cohesive energy and bulk modulus. Many analytical forms exist (Murnaghan, Birch-Murnaghan, Vinet, Poirier-Tarantola, stabilized jellium and others), and the choice among them affects the extracted properties. See also Uncertainty quantification.
Equations of state as a test of interatomic potentials (2016)
Boes and coworkers used PBE energy-volume curves of fcc, simple cubic, diamond, bcc and hcp gold, fit with a third-order inverse polynomial, as a benchmark for a neural network potential and a ReaxFF potential. The network matched DFT closely (fcc: 17.99 versus 17.97 ų minimum volume, 145 versus 147 GPa bulk modulus; diamond 57 versus 56 GPa), while ReaxFF gave similar minimum energies but bulk moduli about 20 GPa or more too low (fcc 122 GPa) and large errors far from the minimum because of a convex region in its bond-energy term. The authors attribute the ReaxFF bulk modulus error to differences in curvature near the minimum (Boes et al. 2016). These Au energy-volume data were later reused in zhan2022a. Summary: boes2016.
Uncertainty in equation of state properties (2022)
Using DFT energy-volume data for fcc Pd and Au, Zhan and Kitchin fitted seven analytical EOS forms and found small fit errors but bulk moduli spread over about 15 GPa for Pd and 20 GPa for Au, with the third-order polynomial the outlier and the chosen data window shifting results by several GPa (Zhan 2022). They compared delta method, Bayesian regression and derivative-aware Gaussian process uncertainties, showing that only the GP spans the model-selection uncertainty. Summary: zhan2022a.