Electron Calculations and the Analysis of Experimental Data

Treatment of Unsaturated Molecules in Pure -Electron Theories 

If one considers only hydrocarbons, and more especially the so-called alternant hydrocarbons, i.e. first of all the conjugated polyenes and the aromatic hydrocarbons of the benzene series, the greater part of their physical properties, ionization potentials, lower electronic transitions etc., can be interpreted qualitatively and often quantitatively in terms of the electronic structure of the n system alone. As the number of n electrons is small with respect to the total number of electrons of the molecule, a considerable simplification of the quantum-mechanical problem is obtained. However, it must be noted immediately that the assumptions of a complete a—n separation and of a rigid a frame are not sufficient to eliminate the a electrons completely from the theory because the n electrons of an unsaturated molecule are not attracted by bare nuclei, but are subject to an effective potential containing Coulomb and exchange contributions from the a electrons. 

The basic GMS assumption lies in the form of the Hamiltonian H of the 7i electron system  

In order to give an explicit form to the potentials Up, Goeppert-Mayer and Sklar assumed that the a electron distribution around each atom is the same as in a molecule with infinitely large intemuclear distances the potential Up is then given by the Hartree-Fock potential for the atom P in the appropriate valence state 4 for instance, in the case of the carbon atom in the valence state (V4, s pxpypz) 

As has been mentioned in Chapter 3, the total wave function of the yr-electron system is constructed from atomic orbitals that are antisymmetric with respect to the principal plane of the molecule. We shall confine ourselves to bases formed by the it valence orbitals of the unsaturated atoms of a molecule, e.g. the 2px orbitals of doubly linked 

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