pgm: A Python package for free energy calculation

The quasi-harmonic approximation (QHA) is a powerful method for computing 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, which makes 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 getting free energy in anharmonic insulators and harmonic or anharmonic metals. The current implementation offers properties in a continuum range of states, bypassing the intensive VDoS calculations required by the traditional QHA method at each optimized structure. The necessary inputs are the volume-dependent ab-initio static energies and phonon frequencies for several discrete temperatures and the user-specified P- and T- range of the calculation. 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 (-Fe) at extreme conditions [1] and cubic CaSiO3-perovskite [2], a strongly anharmonic system. [1] Zhuang, J., Wang, H., Zhang, Q., & Wentzcovitch, R. M. (2021). Thermodynamic properties -Fe with thermal electronic excitation effects on vibrational spectra. Phys. Rev. B, 103(14), 144102. [2] Zhang, Z., & Wentzcovitch, R. M. (2021). Ab initio anharmonic thermodynamic properties of cubic CaSiO3 perovskite. Phys. Rev. B, 103(10), 104108. * Research supported by DOE grant DE-SC0019759