New approach for solving the density-functional self-consistent-field problem

Abstract

A new approach for obtaining the minimum of the density-functional total energy is developed by the application of the variational method to the effective potential rather than to wave functions. The resulting conditions on the effective potential are shown to reduce to a system of simultaneous nonlinear equations. This system can then be solved easily with the use of modern ideas from optimization theory. This also gives a unified description of most self-consistency convergence accelerators and enables us to design a superior procedure. The new approach has been implemented in a completely general band-structure method. A special construction of the potential and mixed basis set enables us to calculate efficiently the band structure of materials with both complex unit cells and interacting $d$ states. The method is demonstrated on crystalline Si and ZnS and is used to obtain the first ab initio band structure for CuIn${\mathrm{Se}}_2$ (8 atoms per unit and 292 electrons per unit cell).