in Eqn 51 (or Eqn
55) can couple with
the ground state reference wavefunction 
through 
.
Ground State
of Eqn 51 must be zero due to
intermediate normalization.
Single Excitations
Single exitations also do not couple with the ground state reference
determinant (i.e. 
).
Double Excitations
Thus double excitations can couple with the reference wavefunction.
Higher Order Excitations
Due to the two particle nature of , higher order excitations are
unable to couple with the reference.
By summing over all possible double excitations
Eqn 60 can be simplified.
Thus the MP2 energy is
So far our treatment has been solely in terms of spin orbitals. However, if
we consider only closed shell systems with a RHF wavefunction the second
order MPPT energy correction is greatly simplified. For an N electron
system
Here a, b, r, s, are indices for spatial orbitals. Notation will
revert to that for spin orbitals in the following derivations of the higher
order MPPT energy corrections.