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 (m1/n1,m2/n2,m3/n3) using a supercell containing a number of primitive cells equal to the least common multiple of n1,n2, and n3. If only diagonal supercell matrices are used, a supercell containing n1n2n3 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.