Ab initio calculation of natural hybrid orbitals

The natural hybrid orbital (NHO) procedure is tested at the ab initio level by use of the density matrix in a Löwdin orthogonalized atomic orbital basis. The direct NHO calculation based on the whole density matrix also includes the hybridization of the inner atomic orbitals, and the NHO calculation employing the valence orbital part of the density matrix considers only the hybridization of the valence atomic orbitals. The numerical results obtained by using the NHO calculation based on the ab initio calculation with an STO-3G basis show that the components of the s atomic orbitals in the NHOs obtained from the two kinds of NHO calculations are very close to each other, and that the two kinds of NHOs have excellent correlations with the nuclear spin-spin coupling constants.