Rapid convergence of crystalline energy bands by use of a plane-wave-gaussian mixed basis set

Abstract

All of the crystalline electron wave functions are expanded in an analytic mixed LCAO-PW basis. The LCAO'S, expressed as contracted sets of non-overlapping even-tempered Gaussians, describe the short wave length part of the electron wave functions, while the plane waves describe the long wave length part. One LCAO is obtained from each isolated atom electron state (neglecting electron spin) for each atom in the unit cell. About 65 plane waves give valence and low conduction band convergence to 0.2 eV for both C and zincblende ' ZnO, whereas over a thousand terms would be required for comparable OPW convergence. The analytic mixed basis set should be applicable to the calculation of electron energy bands in a wide variety of crystalline compounds.

Polarization calculations for ferroelectric sodium nitrite

“…The energy bands for ferroelectric sodium nitrite were calculated using the PWG program originally written by Euwema [9] and later modified by Ivey [lo]. The program was written for an X r exchange and utilizes a mixed basis of plane waves and nonoverlapping Guassians.…”

Local density exchange approximations versus hartree-fock for ground-state calculations

“…The Bloch sum is of the form where p refers to the quantum labels of the electron states and the plane wave term is of the form with R being the volume of the primitive unit cell and N the number of unit cells. All the matrix elements of the Hamiltonian and of the overlap matrix have been expressed in closed form in [6]. In previous PWG work [6,7] the Cholewski decomposition [ 8 ] of the overlap matrix was used to reduce it to the form U = L Lt, where L is a lower triangular matrix.…”

“…All the matrix elements of the Hamiltonian and of the overlap matrix have been expressed in closed form in [6]. In previous PWG work [6,7] the Cholewski decomposition [ 8 ] of the overlap matrix was used to reduce it to the form U = L Lt, where L is a lower triangular matrix. The transformed matrix equation…”