Formalism

  Thus far expressions for and have been derived through infinite order without having said anything about the particular nature of , , or their associated solutions. The RSPT equations derived in the last section have been applied to everything from optics to special relativity. In quantum chemistry the electronic structure of an atom or molecule is typically the system of interest. Thus for an N electron system we know the form of .
 
Although there are a variety of ways to partition this operator a very intuitive partition leads to Møller-Plesset PT (MPPT), a particular formulation of the more general Many-Body PT (MBPT). It is rather appealing to use a Hartree-Fock wavefunction as a first approximation to the exact solutions to (those which recover all electron correlation). The electron correlation is then treated perturbatively. Thus the unperturbed Hamiltonian is merely the sum of one electron Fock operators.
 
The perturbation is readily obtained via the difference between and . Subtracting Eqn 49 from Eqn 48 we have
 

A basis must also be chosen to complete the MPPT approach. It is convenient to expand the perturbed wavefuntions as a linear combination of excited determinants. For the ground state we have
 
The extra index of the expansion coefficients has been dropped since it is assumed we are dealing with the ground state .

Note that due to the nature of the electronic Hamiltonian and the basis set several simplifications immediately arise.

• for all due to intermediate normalization
• Two-particle nature of and truncates expansion
• Brillouin's theorem must hold which further simplifies expressions
• RSPT equations from earlier are directly applicable to UHF and closed shell RHF reference wavefunctions.