Quasiharmonic approximation via irreducible derivatives: low symmetry crystals

The quasiharmonic approximation is a standard approach to include anharmonicity when evaluating temperature-dependent vibrational observables, yet computing arbitrary observables is nontrivial. Here we execute the irreducible derivative approach to the quasiharmonic approximation, greatly reducing the computational cost and facilitating the study of lower symmetry crystals. Specifically, we study PbTiO$_3$ using density functional theory within various exchange-correlation functionals, computing the thermal expansion and the full elastic constant tensor as a function of temperature. The Born-Oppenheimer potential and the irreducible components of the dynamical matrix are parametrized by a Taylor series expansion in symmetrized strain, allowing for the systematic study of successively higher order truncations of the quasiharmonic potential. Additionally, we explore the validity of the quasiharmonic approximation in metals, including ZrN. Results are compared to existing experimental measurements.