Non-orthogonal orbitals for localized electrons

Gérald Bignonneau, Alain Fritsch, Laurent Ducasse

Andrew Williamson, Fernando Agustín Reboredo, Giulia Galli

James P. Finley, Kimihiko Hirao

Fernando Agustín Reboredo, Andrew Williamson

We derive an automatic procedure for generating a set of highly localized, non-orthogonal orbitals for linear scaling quantum Monte Carlo calculations. We demonstrate the advantage of these orbitals in calculations of the total energy of both semiconducting and metallic systems by studying bulk silicon and the homogeneous electron gas. For silicon, the improved localization of these orbitals reduces the computational time by a factor five and the memory by a factor of six compared to localized, orthogonal orbitals. For jellium, we demonstrate that the total energy is converged for orbitals truncated within spheres with radii 7-8 $r_s$, opening the possibility of linear scaling QMC calculations for realistic metallic systems.

John Avery, Roy Mcweeny

Steven K. Burger, Weitao Yang

An absolute energy minimum variational principle is used for carrying out linear scaling calculations with non-orthogonal localized orbitals. Compared with results based on orthogonal localized molecular orbitals, the method is shown to give significantly more accurate results when the localized molecular orbitals are allowed to be non-orthogonal. This is made possible by introducing a second minimization for approximating the inverse overlap matrix. We also show how an exact line search may be used efficiently with the conjugate gradient method for minimizing the energy functional.