The quasiharmonic approximation via space group irreducible derivatives*

The quasiharmonic approximation (QHA) is the simplest nontrivial approximation for interacting phonons under constant pressure, bringing the effects of anharmonicity into temperature dependent observables.  Nonetheless, the most general version of the QHA is often implemented with additional approximations due to the complexity of computing phonons under arbitrary strains.  Here we circumvent the aforementioned complexity by employing irreducible second order displacement derivatives of the Born-Oppenheimer potential and their strain dependence, which are efficiently and precisely computed using the lone irreducible derivative approach.  We execute two complementary strain parametrizations: a discretized strain grid interpolation and a Taylor series expansion in symmetrized strain.  We illustrate our approach by evaluating the thermal expansion and temperature dependence of the elastic constant tensor in thoria and lead titanate using density functional theory, and compare to experimental measurements.  Our irreducible derivative approach to the QHA will facilitate reproducible, high throughput applications.