Lattice dynamics and electron-phonon coupling calculations using nondiagonal supercells

Abstract

We study the direct calculation of total energy derivatives for lattice dynamics and electron-phonon coupling calculations using supercell matrices with nonzero off-diagonal elements. We show that it is possible to determine the response of a periodic system to a perturbation characterized by a wave vector with reduced fractional coordinates $({m}_{1}/{n}_{1},{m}_{2}/{n}_{2},{m}_{3}/{n}_{3})$ using a supercell containing a number of primitive cells equal to the least common multiple of ${n}_{1},\phantom{\rule{0.16em}{0ex}}{n}_{2}$, and ${n}_{3}$. If only diagonal supercell matrices are used, a supercell containing ${n}_{1}{n}_{2}{n}_{3}$ primitive cells is required. We demonstrate that the use of nondiagonal supercells significantly reduces the computational cost of obtaining converged zero-point energies and phonon dispersions for diamond and graphite. We also perform electron-phonon coupling calculations using the direct method to sample the vibrational Brillouin zone with grids of unprecedented size, which enables us to investigate the convergence of the zero-point renormalization to the thermal and optical band gaps of diamond.