Self-consistent first-principles technique with linear scaling

An algorithm for first-principles electronic-structure calculations having a computational cost that scales linearly with the system size is presented. Our method exploits the real-space localization of the density matrix, and in this respect it is related to the technique of Li, Nunes, and Vanderbilt. The density matrix is expressed in terms of localized support functions, and a matrix of variational parameters ${\mathit{L}}_{\mathrm{\alpha }\mathrm{\beta }}$ having a finite spatial range. The total energy is minimized with respect to both the support functions and the ${\mathit{L}}_{\mathrm{\alpha }\mathrm{\beta }}$ parameters. The method is variational and becomes exact as the ranges of the support functions and the L matrix are increased. We have tested the method on crystalline silicon systems containing up to 216 atoms, and we discuss some of these results.