Recent developments of fast algorithms for Kohn-Sham density functional theory
Lin Lin, Lawrence Berkeley Lab

Abstract:
Kohn-Sham density functional theory (KSDFT) is the most widely used electronic structure theory for condensed matter systems. The standard method for solving KSDFT requires solving N eigenvectors for an O(N) * O(N) Kohn-Sham  Hamiltonian matrix, with N being the number of electrons in the system.  The computational cost for such procedure is expensive and scales as O(N³).  We have developed pole expansion plus selected inversion (PEpSI) method, in which KSDFT is solved by evaluating the selected elements of the inverse of a series of sparse symmetric matrices, and the overall algorithm scales at most O(N²) for all materials including metallic and insulating systems.  Recently we generalize the new method to nonorthogonalbasis set, with the electron density, total energy, Helmholtz free energy and atomic force calculated simultaneously and accurately.  Combined with atomic orbital basis functions, the new method can be applied to study the electronic structure of boron nitride nanotube and carbon nanotube with more than 10,000 atoms on a single processor.