Linear-scaling quantum calculations using non-orthogonal localized molecular orbitals

An absolute energy minimum variational principle is used for carrying out linear-scaling calculations with non-orthogonal localized orbitals. Comparing 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