Hamiltonian equation derivative Hartree-Fock theory

As in the Hartree-Fock theory, the OEL equations for a given orbital functional E are equivalent to the conditions (a Q i) = 0, / < TV < u, assuming orthonormal orbitals, where Q is the effective Hamiltonian defined by orbital functional derivatives. Equivalently, (8< /< ,) = 0, i N. If a local potential vxc(r)... 

Abstract Some previous results of the present author are combined in order to develop a Hermitian version of the Chemical Hamiltonian Approach. In this framework the second quantized Bom-Oppenheimer Hamiltonian is decomposed into one- and two-center components, if some finite basis corrections are omitted. (No changes are introduced into the one- and two-center integrals, while projective expansions are used for the three- and four-center ones, which become exact only in the limit of complete basis sets.) The total molecular energy calculated with this Hamiltonian can then presented as a sum of the intraatomic and diatomic energy terms which were introduced in our previous chemical energy component analysis scheme. The corresponding modified Hartree-Fock-Roothaan equations are also derived they do not contain any three- and four-center integrals, while the non-empirical character of the theory is conserved. This scheme may be useful also as a layer in approaches like ONIOM. 

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