Hamiltonian with electrons identified

A basic tenet of the Hiickel jr-electron theory is that the orbital energies add to give the TT-electron energy. Yet 1 demonstrated earlier that HF orbital energies do not add in this way, so the Hiickel Hamiltonian cannot be strictly identified with the HF Hamiltonian. 

The accepted wisdom is that the Hiickel Hamiltonian matrix should be identified with the matrix (h where G is the electron repulsion matrix of Chapter 6. The basis for this belief is that that the matrix (h has eigenvalues that do sum correctly to the electronic energy. 

H(r,Q) is the Hamiltonian of the interacting electrons and nuclei. The configuration variables of ne electrons, r=(r1,...,rnc), and nN nuclei, Q=(Qi,...,QnN) are defined with respect to a coordinate frame fixed in the laboratory. The nuclei are identified by their nuclear charges, Z=(eZ,...,eZ N), where e is the electron charge, and the mass vector (or block diagonal 3nNx3nN matrix) M=(m,.m ). 

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