Hartree-Fock theory fluctuation potential

In the second, response theory, approach, the response of the Hartree-Fock ground state is calculated by perturbation theory. First-order perturbation theory in the fluctuation potential gives a method known as the random phase approximation (REA). The RPA linear response gives the dynamic polarizability, the quadratic response gives the first hyperpolarizability etc. One can obtain expressions for the response functions as sums over states formulae, but they are not calculated as such, rather they are calculated from coupled linear equations. RPA is equivalent to TDCPHF. 

The zero-order states are the Hartree-Fock determinant and the determinants excited with respect to this state. The resulting theory is known as M0ller-Plessetperturbation theory (MPPT) [5], For systems with small static correlation contributions, the Hartree-Fock wave function provides an adequate zero-order approximation to the FCI wave function. In such situations, the Mpller-PIesset partitioning of the Hamiltonian is both appealing and well motivated the averaged electron-electron interactions are incorporated in the zero-order operator and the perturbation operator (the fluctuation potential) represents the difference between the averaged and instantaneous interactions. 

The Hartree-Fock energy may be viewed as the sum of the orbital energies corrected to first order in perturbation theory with the fluctuation potential as the perturbation operator. Going to higher orders in perturbation theory, we obtain cmrections to the Hartree-Fock energy which take into account the effects of electron correlation see Section 5.8 and, for a full discussion. Chapter 14. 

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