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(N^{3}). 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(N^{2}) 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.