On R�denberg's integral approximations and their unrestricted and combined use in molecular orbital theories of Hartree-Fock type

Autor: Wolfhard Koch
Rok vydání: 2000
Předmět:
Zdroj: International Journal of Quantum Chemistry. 76:148-160
ISSN: 1097-461X
0020-7608
DOI: 10.1002/(sici)1097-461x(2000)76:2<148::aid-qua5>3.0.co;2-r
Popis: Ruedenberg's well-known letter of 1951 contains two implications which still have been employed so far in numerical computations: (1) Whenever all types of attraction and repulsion integrals are subject to the Ruedenberg approximations in its simplest form partially known already from Mulliken, the attractive, the Coulomb, as well as the exchange part of the restricted Hartree-Fock-Roothaan equation can be led back to the calculation of corresponding diagonal elements, only. Using Ruedenberg's more elaborate concepts, which are invariant with respect to the rotation of local coordinate axes, the complete Fock-matrix representation can be constructed equivalently from only its own diagonal blocks, each belonging to one atom. Similar formulas are valid for the unrestricted Hartree-Fock theory of Pople and Nesbet. (2) If, however, one prefers to calculate all types of one- and two-center integrals exactly as suggested in Ruedenberg's headline, the original simplicity of both representations is lost. Instead, one is led to more complicated expressions, which arise from the fact that Ruedenberg's integral formulas, when applied to certain kinds of three-center repulsion integrals, imply considerable oversimplifications. In spite of this critical result, Ruedenberg's ideas offer an extension together with an interpretation of the semiempirical Wolfsberg and Helmholz recipe (better known frommore » Hoffmann's extended Hueckel theory), on the one hand, and of the neglect of differential overlap schemes ZDO and NDDO, on the other, from a common point of view.« less
Databáze: OpenAIRE
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