Molecular properties An introduction

So far we have considered only the internal properties of an isolated system— how the electrons and their spins may be described, and how their distribution determines the total electronic energy. Many important properties, however, relate to the response of a system when we do something to it to the way it changes when we change its Hamiltonian from H = Ho to H = Ho+H by interacting with it in some way. For 

Let us suppose that the density functions p and n for the isolated molecule with Hamiltonian Hq have been determined variationally so that the energy 

This is precisely equivalent to saying that the wavefunction W has been optimized by adjustment of all the parameters it contains. Then we suppose the interaction switched on this is a change that affects every electron in the same way, h(i)- h(i)-F 6h(/), but does not affect the mutual repulsion between electrons, g i, j). The densities p and n will change, and the energy change will be, to first order 

But the original densities, by assumption, possessed the stationary property expressed by (5.7.2), and therefore only one term remains  

This is just the expectation or average value of the interaction operator, 6h, taken over the electron density function of the isolated molecule, as would have been anticipated from perturbation theory. This is a simple, powerful and extremely general result, which provides a basis for discussion of all atomic and molecular properties that involve a first-order response, and is applicable even when we do not possess exact wavefunc-tions it is usually referred to as a generalized Hellmann-Feynman 

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