The natural Lewis structure perturbative model

Equation (5.3) suggests a general perturbation theoretic approach to analyzing the quantum mechanical Schrodinger equation  

Given the model Lewis-type Schrodinger equation (5.5) as a starting point, we now introduce the difference operator and energy 5 such that the system 

In this formulation, the model Schrodinger equation (5.5) describes the model chemistry of an idealized resonance-free world, whereas describes the energetic 

Equations (5.3), (5.7), and (5.8) form the starting point for a systematic perturbation theory analysis, whose deeper details need not concern us here (see V B, p. 16ff). In this approach, the NLS model //op is regarded as the unperturbed Hamiltonian, with known eigenfunction and energy eigenvalue eP that are assumed to be well understood. The resonance-type corrections to energy (EP ), density (pnl), or other properties can then be expressed (analyzed or evaluated) in orderly fashion from the known properties of the model Lewis system. The NBO 

In the resonance-free world of hop the donor and acceptor NBOs have no interaction (due to their mutual orthogonality), i.e.. 

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