Substantiation of the basis set orthogonality assumption for saturated molecules and crystals on account of their common topological structure

Abstract

The overlap matrices of saturated (tetrahedral) systems in the basis of sp 3 hybrid AOs have been presented as a single matrix ( S) consisting of zero-order and first-order terms. The common expression for the respective Löwdin's orthogonalization matrix ( S − 1 2 ) has been obtained in the form of a power series and the structure of the orthogonalized basis orbitals has been analyzed. The relevant common hamiltonian matrix ( H) has been transformed into the basis of the orthogonalized orbitals and the resulting matrix H ̃ has been compared with the initial one. The similarity between the most essential qualitative peculiarities of the matrices H and H ̃ has been established: the presence of the zero-order terms of similar structure and first-order terms, the local nature of the relation between the hamiltonian matrix elements and the structure of the system, and the transferability of the elements associated with the similar atoms and bonds, are inherent to both H and H ̃ . These results follow from the common topological structure of saturated molecules and crystals and serve to support the basis set orthogonality assumption extensively used in qualitative quantum chemistry.