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 it 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.

This work was partially supported by the Laboratory Directed Research and Development Program of Lawrence Berkeley National Laboratory under the US Department of Energy contract number DE-AC02-05CH11231, by Scientific Discovery through Advanced Computing (SciDAC) program funded by the US Department of Energy, Office of Science, Advanced Scientific Computing Research and Basic Energy Sciences, by the Center for Applied Mathematics for Energy Research Applications (CAMERA), which is a partnership between Basic Energy Sciences and Advanced Scientific Computing Research at the US Department of Energy (LL and CY), by the European Community’s Seventh Framework Programme [FP7/2007-2013] under the PRACE Project grant agreement number 283493 (G. H.), by the Spanish MINECO through grants FIS2009-12721-C04-03, FIS2012-37549-C05-05 and CSD2007-00050 and by Generalitat de Catalunya (2014 SGR 301) (AG).

Peer Reviewed