Equations of state and thermodynamics of solids using empirical corrections in the quasiharmonic approximation

Current state-of-the-art thermodynamic calculations using approximate density functionals in the quasiharmonic approximation (QHA) suffer from systematic errors in the prediction of the equation of state and thermodynamic properties of a solid. In this paper, we propose three simple and theoretically sound empirical corrections to the static energy that use one, or at most two, easily accessible experimental parameters: the room-temperature volume and bulk modulus. Coupled with an appropriate numerical fitting technique, we show that experimental results for three model systems (MgO, fcc Al, and diamond) can be reproduced to a very high accuracy in wide ranges of pressure and temperature. In the best available combination of functional and empirical correction, the predictive power of the DFT + QHA approach is restored. The calculation of the volume-dependent phonon density of states required by QHA can be too expensive, and we have explored simplified thermal models in several phases of Fe. The empirical correction works as expected, but the approximate nature of the simplified thermal model limits significantly the range of validity of the results.