Localized basis orbitals: minimization of 2-electron integrals array and orthonormality of basis set

A new scheme for deriving localized basis orbitals (LBOs) and for obtaining integral transformations from the basis orbitals (BOs) to the LBOs has been introduced. The scheme was tested at the ab initio Hartree-Fock level using the STO-3G basis set. It has been revealed that it provides results that are close to the conventional ab initio approximations for various physical-chemical properties. At the same time, both the number of differential overlaps and the number of electron repulsion integrals (ERIs) grow with the system size notably slower than those calculated for the usual BOs. The power exponent for ERI/LBO is typically smaller by 0.3-0.6 than that for ERI/BO. The exponent reaches the value of 1.69 even for triglycine (24 atoms only), which represents a relatively small molecular model. Thus, the localization of the BOs (using LBOs) may result in additional improvements in efficiency even for electronically delocalized systems. It was shown that ERI/LBO is particularly efficient for systems with complex spatial structures (including conjugated species). The obtained results indicate that the proposed scheme could be included in computational methods targeted at calculating large molecular systems (which achieve linear scaling for more distant interactions). Neglecting ERI/LBO does not depend on the delocalization of the localized MO using ERI/LBO. The orthogonality and locality of the LBOs should make them useful in methods based on dividing the system into orthogonal subsystems.