Reactivity Indices in Many-Electron Theory

Most of these developments may be applied most directly within the framework of the isolated molecule method, in which the reactivity indices are the charges and self-polarizabilities of the unperturbed ground state of a given molecule calculations based on the localization model (e.g. Nesbet, 1962) have made less progress, and will not be considered. It is therefore natural to enquire whether indices similar to and tt,, in Hiickel theory can still be defined, and calculated more precisely, in self-consistent field theory. The obvious questions are 

It would be out of place to give a detailed review of the approximate SCF theory, as developed for 7r-electron systems, at this point. It is, however, necessary to explain the basic equations, and convenient to use a form in which only the charges and bond orders appear (McWeeny, 1956, 1964). The total 7r-electron energy E may then be written 

When all MO s are doubly occupied, the stationary conditions yield the familiar secular equations 

With suitable approximations it turns out that h is linked (through G ) to the charge density and the basic parameters by 

Here Zg is the number of tt electrons provided by atom is essentially an ionization potential for an electron extracted from in the presence of the part of the framework associated with atom r alone (a somewhat hypothetical quantity), is a framework resonance integral, and is the coulomb interaction between electrons in orbitals , and ( ,. The essential parameters, in the semi-empirical form of the theory, are cug, and and from their definition these quantities are expected to be characteristic of atom r or bond r—s, not of the particular molecule in which they occur (for a discussion see McWeeny, 1964). In the SCF calculation, solution of (95) leads to MO s from which charges and bond orders are calculated using (97) these are used in setting up a revised Hamiltonian according to (98) and (99) and this is put back into (95) which is solved again to get new MO s, the process being continued until self-consistency is achieved. It is now clear that prediction of the variation of the self-consistent E with respect to the parameters is a matter of considerable difficulty. 

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C. Some Related Topics Reactivity Indices in Many-Electron Theory... 

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