Regularized Localized Molecular Orbitals in a Divide-and-Conquer Approach for Linear Scaling Calculations

Non-orthogonal localized molecular orbitals (NOLMOs) have been employed as building blocks for the divide-and-conquer (DC) linear scaling method. The NOLMOs are calculated from subsystems and used for constructing the density matrix (DM) of the entire system, instead of the subsystem DM in the original DC approach. Also, unlike the original DC method, the inverse electronic temperature parameter β is not needed anymore. Furthermore, a new regularized localization approach for NOLMOs has been developed, in which the localization cost function is a sum of the spatial spread function, as in the Boys method, and the kinetic energy, as a regularization measure to limit the oscillation of the NOLMOs. The optimal weight of the kinetic energy can be determined by optimization with analytical gradients. The resulting regularized NOLMOs have enhanced smoothness and better transferability because of reduced kinetic energies. Compared with the original DC, while NOLMO-DC has a similar computational linear scaling cost, the accuracy of NOLMO-DC is better by several orders of magnitude for large conjugated systems and by about 1 order of magnitude for other systems. The NOLMO-DC method is thus a promising development of the DC approach for linear scaling calculations.