Temperature-dependent phonons from ab initio molecular dynamics and density functional perturbation theory.

Phonons play an important role in understanding properties of materials. Quasiharmonic approximation (QHA) introduces an implicit dependence of phonon frequencies on temperature via volume, allowing reasonable prediction of thermal expansion coefficient and free energy of materials. On the other hand, QHA is insufficient in capturing anharmonic effects that occur in the absence of thermal expansion, and breaks down in dynamically unstable materials where the harmonic phonons are negative. Here we develop a method for computing temperature-dependent phonons by fitting interatomic force constants (FCs) to ab-initio molecular dynamics (AIMD) forces. While our method is equivalent to that of [1] and [2], it differs in two ways: the 0K FCs are from density functional perturbation theory rather than finite-difference in supercell, and they are decomposed on symmetrized orthogonal basis, which are the parameters that are minimized during the fitting. Thus, we use highly efficient reciprocal-space representation in order to minimize the number of degrees of freedom. We demonstrate the effectiveness of this technique by computing temperature-dependent phonon shift in fcc Aluminum, where the QHA also works, and temperature renormalized phonons in bcc Titanium, where QHA fails.