Thermodynamics of solids including anharmonicity through quasiparticle theory

Abstract

The quasiharmonic approximation (QHA) in combination with density-functional theory is the main computational method used to calculate thermodynamic properties under arbitrary temperature and pressure conditions. QHA can predict thermodynamic phase diagrams, elastic properties and temperature- and pressure-dependent equilibrium geometries, all of which are important in various fields of knowledge. The main drawbacks of QHA are that it makes spurious predictions for the volume and other properties in the high temperature limit due to its approximate treatment of anharmonicity, and that it is unable to model dynamically stabilized structures. In this work, we propose an extension to QHA that fixes these problems. Our approach is based on four ingredients: (i) the calculation of the n-th order force constants using randomly displaced configurations and regularized regression, (ii) the calculation of temperature-dependent effective harmonic frequencies ω(V, T) within the self-consistent harmonic approximation (SCHA), (iii) Allen’s quasiparticle (QP) theory, which allows the calculation of the anharmonic entropy from the effective frequencies, and (iv) a simple Debye-like numerical model that enables the calculation of all other thermodynamic properties from the QP entropies. The proposed method is conceptually simple, with a computational complexity similar to QHA but requiring more supercell calculations. It allows incorporating anharmonic effects to any order. The predictions of the new method coincide with QHA in the low-temperature limit and eliminate the QHA blowout at high temperature, recovering the experimentally observed behavior of all thermodynamic properties tested. The performance of the new method is demonstrated by calculating the thermodynamic properties of geologically relevant minerals MgO and CaO. In addition, using cubic SrTiO₃ as an example, we show that, unlike QHA, our method can also predict thermodynamic properties of dynamically stabilized phases. We expect this new method to be an important tool in geochemistry and materials discovery.