Perturbation Theory—Orbital Mixing Rules

The basic concept of perturbation theory is to begin with a Hamiltonian for a system, and then consider any new interactions as a perturbation to that Hamiltonian. Precise solutions to problems of this type are available, but our goal is to summarize the salient results of these treatments. The important point is that you need not actually know the correct wave-functions for the unperturbed Hamiltonian in order to appreciate the effects of a perturbation on the wavefunctions and their energies. 

We will be concerned with combining the orbitals of two fragments or molecules. When mixing orbitals, three factors must be considered  

Symmetry Only orbitals of like symmetry can interact. 

Overlap Orbitals must overlap in order to interact the greater the overlap, the stronger the interaction. The symmetry restriction is a special case of the overlap rule. 

3- Relative energy The closer in energy the interacting fragment orbitals, the stronger the interaction. 

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