Electronic Indices from Greens Functions

This means that the poles of the Green s function, i.e., the molecular orbital energies, are obtained as eigenvalues of a negative definite matrix with elements -Kr Srs + Srs)Ks. The molecular orbital coeflficients can straightforwardly be inferred from the residues at the poles of this spectral representation. 

In spite of the very simple assumptions leading to this model, it leads to quite acceptable approximate values for electron binding energies for molecular species when compared with some other approximate approaches. This model has been applied under the name Energy Weighted Maximum Overlap (EWMO) to a number of problems involving photoelectron spectra and to a number of problems in the interpretation of spin resonance experiments. 

The electron propagator can be used to calculate the charge distribution and other electronic indices that are relevant for a discussion of ground state properties of molecules. We will examine in detail the Mulliken population analysis, which attempts to relate charge distributions to a partial occupation of atomic orbitals and valence shells. 

The number operator for electrons in a limited basis is obtained from Eq. (10.6) as 

The gross atomic population, which gives a measure of the formal charge of an atom in a molecule, is defined as the sum over all N(r) for r a spin orbital on the atom under consideration. 

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