By Fenglong Gu
South China Normal University

The elongation method was proposed in the early 1990’s as an effective method to achieving linear scaling for large system calculations. The elongation method works in the orthogonal localized molecular orbital (OLMO) basis. The key point of the elongation method is to neglect the contributions from frozen orbitals but the tailing of OLMOs makes it difficult. The non-orthogonal localized molecular orbital (NOLMO) is the most localized representation of electronic degrees of freedom. As such, NOLMOs are thus potentially the most efficient for linear scaling calculations of electronic structures for large systems. In this talk, direct ab initio calculations with NOLMO will be presented by solving its slow convergence in the optimization of NOLMO. An effective preconditioning approach by taking into account the diagonal elements of the second order derivatives has been proposed and it is shown that the convergence of the energy optimization is very much significantly improved. For the studies on nonlinear optical properties, we have derived the corresponding CPHF equations based on NOLMOs up to the third order, which are significantly different from those of a conventional CPHF method because of the release of the orthogonal restrictions on MOs. This work represents the first step towards efficient calculations of molecular response and excitation properties with NOLMOs. Quantum chemical methods based on NOLMOs are potentially ideal for investigating large systems, not only for energies but also for other properties.