Highly efficient method for Kohn-Sham density functional calculations of 500-10000 atom systems

A method for the solution of the self-consistent Kohn-Sham equations using Gaussian-type orbitals is presented. Accurate relative energies and forces are demonstrated to be achievable at a fraction of the computational expense for large systems. With this approach calculations involving around 1000 atoms can easily be performed with a serial desktop computer and ∼10000 atom systems are within reach of relatively modest parallel computational resources. The method is applicable to arbitrary systems including metals. The approach generates a minimal basis on the fly while retaining the accuracy of the large underpinning basis set. Convergence of energies and forces are given for clusters as well as cubic cells of silicon and aluminum, for which the formation energies of defects are calculated in systems up to 8000 and 4000 atoms, respectively. For these systems the method exhibits linear scaling with the number of atoms in the presently important size range of ∼500-3000 atoms. © 2009 The American Physical Society