Dual-space approach for density-functional calculations of two- and three-dimensional crystals using Gaussian basis functions

We reformulate theories for electronic structure calculations of periodic systems in a way suitable for large scale calculations using Gaussian basis functions. An accurate grid is introduced for efficient calculation of matrix elements. A dual-space approach is used to calculate the Coulomb potential with computational cost that scales linearly with the size of basis set. A preconditioned generalized conjugate gradients approach is introduced for rapidly converging wave functions expressed in terms of Gaussian basis functions. This method is applied to a variety of crystals (including diamond, GaN, AlN, CdTe, and ${\mathrm{C}}_{60}$) and surfaces [including GaAs (110) and BN (110)] with excellent results.