Ab initio calculations on valence-shell molecular orbitals

Abstract

The following method is proposed for calculating valence electron wave functions and energies in the SCFMO scheme without including inner shells in the basis. (1) The valence orbital bases are Slater functions orthogonalized by the Schmidt procedure to core orbitals. (2) All one-centre integrals are calculated exactly in this basis. The nuclear attraction integrals are multiplied by an effective nuclear charge Z_eff which is determined from an atomic calculation to give atomic orbital energies identical to those from an all-electron calculation. (3) All multi-centre two-electron integrals are taken to be equal to the values appropriate to the non-orthogonalized valence basis. (4) Two and three-centre one-electron integrals are calculated from the orthogonalized basis, with the effective nuclear charges equal to the total nuclear charge less the number of core electrons in that atom.

This procedure can fit readily into standard SCFMO programs as the core potential is Coulombic for all two and three centre integrals.

Calculations on H₂O, H₂S, CH₄ and SiH₄ show agreement to within 0.01 a.u. (0.5 eV) of the all-electron calculation for occupied molecular orbital energies. The equilibrium bond angle and bond length for H₂O obtained by this model are also in good agreement with those obtained in the all-electron calculation. Calculations on N₂, at its equilibrium bond length and greater, show good agreement with the all-electron results but at shorter bond lengths an incorrect ordering of the molecular orbitals is obtained and the total energy is poor.