On Rudenberg's integral approximations and their unrestricted and combined use in crystal orbital theories of Hartree-Fock type

Abstract

The analysis based on Rudenberg's well-known letter of 1951, which has been outlined for molecules in a preceding contribution, now will be transfered to translational periodic systems in one, two, or three dimensions. Again, when applied unrestrictedly to "Linear Combination of Atomic Orbitals" representations (LCAO) of both "Unrestricted" and "Restricted Hartree-Fock" pictures (UHF and RHF), Rudenberg's integral approximations of Mulliken type lead to a thorough interpretation of "Extended Huckel" crystal orbital theories (EHT). Moreover, Rudenberg's ideas provide us with "Unrestricted and Combined" extensions (U&C) of the widely-used approximation schemes "Zero Differential Overlap" (ZDO) and "Neglect of Diatomic Differential Overlap" (NDDO). An improved variant of EHT is also presented. Corresponding "Restricted and Combined" concepts (R&C), which overcome some shortcomings inherent in Rudenberg's original recipes, will be sketched.