Alternative approach to calculate two-center overlap matrix through deformed exponential function

In this work, we propose an alternative approach to evaluate two-center overlap integrals. It is computationally more efficient than the standard procedure and is based on the deformed exponential function. In the new procedure, the CPU time to calculate each element of the overlap matrix (Sμ,ν) is constant and independent of the number of Gaussian primitives (NG), whereas in the usual procedure this time increases, formally, with NG2. To evaluate the accuracy of the proposed methodology, we computed different molecular properties such as dipole moments, hardness values, atomic charges, multicenter bond indices, group indices, and some thermodynamic properties. In this work, all calculations were performed using a minimal STO-6G basis set and WTBS and the double-ζ Pople split-valence 6-31G basis set on the Hartree–Fock (HF) and post-HF approximations. The integrals were parametrized for the atoms of the first two rows of the periodic table. All calculations were performed in the general ab initio quantum chemistry package GAMESS, where the integrals were implemented.