Absolute and relative energies from polarized atomic orbital self-consistent field calculations and a second order correction. Convergence with size and composition of the secondary basis

Polarized atomic orbitals (PAO's) are molecule-adapted minimal basis functions that are variationally obtained as an atom-blocked transformation from a conventional extended basis set, as a Hartree-Fock calculation is performed in the PAO basis. This approximation yields a higher energy than a HF calculation performed in the extended basis, although the two results converge to the same limit as the extended basis approaches completeness on each atom. To test the rate of convergence, PAO-HF calculations were performed using cc-pVXZ and aug-cc-pVXZ basis sets for the water monomer and dimer, and six substituted ethylenes. The results show that the quality of PAO calculations converges smoothly with X. The use of augmented functions is recommended. To correct a PAO-HF calculation for residual deficiencies, a noniterative second order correction is introduced. This correction corresponds to an energy-weighted steepest descent step, and substantially improves the quality of PAO energies.