Interpretation of ab initio total energy results in a chemical language:: I.: Formalism and implementation into a mixed-basis pseudopotential code

A new variant of the recently developed energy-partitioning scheme is introduced, which allows us to give an interpretation of ab initio total energy results in a chemical language. In this scheme the energy of the bonds between atom-localized orbitals is represented by the covalent bond energy, which is invariant with respect to a constant shift of the effective crystal potential. This feature is a precondition for a comparison of the bond energies for various crystal structures within the framework of a band structure calculation. The implementation in a mixed-basis pseudopotential code is described, which requires the projection of the crystal pseudowavefunctions onto a minimal set of atom-localized non-orthogonal basis functions.