pgm: A Python package for anharmonic free energy calculations

The quasiharmonic approximation (QHA) is a powerful method for computing the free energy and thermodynamic properties of materials at high pressures (P) and temperatures (T). However, anharmonicity, electronic excitations in metals, or both, introduce an intrinsic T-dependence on the phonon frequencies, making the QHA inadequate. Here we present a Python package, pgm, for free energy and thermodynamic property calculations. It is based on the concept of phonon quasiparticles and the phonon gas model (PGM). The free energy is obtained by integrating the entropy, which can be readily calculated for a system of phonon quasiparticles. This method is useful for computing the free energy in anharmonic insulators and harmonic or anharmonic metals. The current implementation offers properties in a continuum P,T range. The necessary inputs are ab-initio T_el-dependent static energies and T-dependent phonon quasiparticle frequencies, both at several discrete volumes, and the user-specified P- and T- range. To accelerate the numerical computation, we employ techniques like just-in-time (JIT) compiling and parallel computing. We demonstrate successful applications of pgm to hcp-iron (ε-Fe) at extreme conditions [1] and cubic CaSiO₃-perovskite [2], a strongly anharmonic system.