Effect of Parameter Choice in Density Functional Perturbation Theory Calculations of Phonons and Related Properties

In atomic matter, phonon modes and frequencies determine material properties such as thermal and electrical conductivity. Allowed vibrational frequencies are found by solving a characteristic equation for the dynamical matrix constructed through the second derivatives of energy with respect to displacements of the atoms. One method for effecting quantum mechanical solutions in this context is density functional perturbation theory (DFPT). In this method, the electron density is calculated by solving a mean-field Hamiltonian self-consistently for the its energy and wave functions, keeping the atoms at their relaxed positions. Then, the perturbation in energy with respect to perturbations of the atoms is calculated for every unique atomic displacement combination. DFPT has multiple parameters to control for to produce realistic simulations. We investigate the effects of varying these parameters on the resulting phonon frequencies in terms of the relative and absolute error from a highly convergent phonon frequency using several electronically distinctive solid-state systems. We take the same approach to compare calculated with experimentally determined phonon frequencies, aiming to provide advice in choosing parameters for accurate DFPT calculations.