Principles of Perturbation Theory

The expression for the first-order perturbed wave function is often useful in organic chemistry (especially ir-orbitals) to predict which excited states may affect the ground state the most in a reaction. 

We can see two effects in the expression for the perturbed orbital. First, the effect will be greatest when is small in the denominator as for the HOMO-LUMO energy difference. Effects 

We need to be able to write a correct Hamiltonian operator, H, which includes all 

What does that mean Well it means that we can guess whatever we want (intelligently) for c[) and 

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Grimme s third major methodological development is the notion of double hybrid density functionals. This development came when he recognized that the principle of perturbation theory, expressed through MP2, could be appfied to DFT. He characterizes this realization as not a big step. ... 

The Sanchez-Lacombe model [48-50] is a lattice fluid model in which each component is divided into parts that are placed in a lattice. The different parts are allowed to interact with a mean-field intermolecular potential. By introducing an appropriate number of vacant sites (holes) in the lattice, the correct solution density can be obtained. SAFT [51-53] is based on the perturbation theory. The principle of perturbation theory is that first a model is derived for some idealized fluid with accurately known properties, called the reference fluid . Subsequently, the properties of this model are related to those of a real dense fluid. By expanding this reference fluid into power series over a specified parameter, the power terms can be regarded as corrections or "perturbations for the reference fluid as compared to reality. Obviously, the more the reference model approaches reality, the smaller the corrections are. Therefore, the key issue for applying perturbation theory is deriving the most suitable reference fluid. 

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