An efficient method for constructing nonorthogonal localized molecular orbitals.

A new method for constructing nonorthogonal localized molecular orbitals (NOLMOs) is presented. The set of highly localized NOLMOs is obtained by minimization of the spread functional starting from an initial set of canonical orthogonal molecular orbitals. To enhance the stability and efficiency, the centroids of the NOLMOs are constrained to be those of the corresponding orthogonal localized molecular orbitals (OLMOs), which are obtained with the Boys criterion in advance. In particular, these centroid constraints make the optimization for each NOLMO independent of the others, which is an attractive feature for application to large systems. The minimization with the constraints incorporated through the multiplier-penalty function method is stable and efficient in convergence. While exhibiting the classical bonding pattern in chemistry and sharing a spatial distribution similar to that of the corresponding OLMOs, the obtained NOLMOs are more compact than the corresponding OLMOs with about 10%-28% reduction in the value of the spread functional and devoid of the troublesome "orthogonalization tails."