A simple and accurate extension to the quasiharmonic approximation for the calculation of thermodynamic properties of solids.*

The quasiharmonic approximation (QHA) is the main computational method for the prediction of structural and thermodynamic properties of periodic solids, including their phase stability, at arbitrary temperatures and pressures. In a QHA calculation, the static energy and the harmonic phonon density of states are calculated on a volume grid spanning the region of interest. QHA has had great success in the prediction of material properties which are difficult to measure or inaccessible to experiment. The most important drawback of QHA is that, at temperatures higher than a material- and pressure-dependent validity limit, there is a complete breakdown of the theory with spurious thermodynamic predictions across the board. This is caused by the incorrect description of anharmonicity by QHA via the volume dependence of the harmonic vibrational frequencies. In the past, computationally intensive approaches such as ab initio molecular dynamics (AIMD) have been used to calculate thermodynamic properties beyond the QHA limit. To circumvent the use of complex methods like AIMD, we present in this work a simple and efficient way of extending the validity range of QHA. Our method is based on the combination of three ingredients: i) the calculation of force constants to nth order and the subsequent calculation of effective temperature-dependent second-order force constants using the hiphive method (Eriksson et al., Adv. Theory Simul. 2 (2019) 1800184), ii) Allen's quasiparticle theory (Phys. Rev. B 92 (2015) 064106) that posits the calculation of the anharmonic entropy from temperature-dependent frequencies, and iii) a simple fitting method based on the Debye model to obtain the system's free energy as well as the rest of the thermodynamic properties. The proposed method is conceptually and computationally very simple, with a cost similar to that of plain QHA, and reproduces the QHA results below its validity limit by construction. Therefore, our method retains the accuracy of QHA at low temperature while providing a physically grounded and accurate extension to QHA in the high-temperature limit. The implementation of our new method in the gibbs2 program is described, as well as illustrative examples.