  We describe a scheme for efficient large-scale electronic-structure
calculations based on the combination of the pole expansion and selected
inversion (PEXSI) technique with the SIESTA method, which uses numerical atomic
orbitals within the Kohn-Sham density functional theory (KSDFT) framework. The
PEXSI technique can efficiently utilize the sparsity pattern of the Hamiltonian
and overlap matrices generated in SIESTA, and for large systems has a much
lower computational complexity than that associated with the matrix
diagonalization procedure. The PEXSI technique can be used to evaluate the
electron density, free energy, atomic forces, density of states and local
density of states without computing any eigenvalue or eigenvector of the
Kohn-Sham Hamiltonian. It can achieve accuracy fully comparable to that
obtained from a matrix diagonalization procedure for general systems, including
metallic systems at low temperature. The PEXSI method is also highly scalable.
With the recently developed massively parallel PEXSI technique, we can make
efficient use of more than $10,000$ processors on high performance machines. We
demonstrate the performance and accuracy of the SIESTA-PEXSI method using
several examples of large scale electronic structure calculations, including
1D, 2D and bulk problems with insulating, semi-metallic, and metallic
character.
