Progress in Linear Scaling Non-orthogonal Localized Molecular orbitals method

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. However, direct ab initio calculations with NOLMO have not been fully implemented and widely used, partly because of the slow convergence issue in the optimization of NOLMO. We developed an effective preconditioning approach using the diagonal part of the second order derivatives and show that the convergence of the energy optimization is significantly improved. The speed of convergence of the energy and density matrix are comparable with that of the conventional SCF approach, tests on water chain shown the NOLMO method could achieve in linear scaling. Furthermore, our recent work shows that divide the large molecular to apart, and optimize the NOLMOs part by part, then construct the NOLMOs of the whole molecular by the optimized NOLMOs of the parts could decrease the total CPU time significantly. Our group have also applied the NOLMOs to CPHF method successfully, thus paving the way for application of NOLMO to post-HF methods.