3rd Order MP Energy

  Algebraic derivation of the MP3 energies is similar to that just done for MP2. However, the derivation is drastically more tedious, and the expression is far more complicated. Alternate diagramatic techniques have been developed to simplify the derivation (See Section 6.2 of Ref [4]. We state the results without proof. First we redefine .

Thus from Eqn 45 we have

Here the sum runs over all possible double excited determinants (i and j are just dummy indices). And of course this gives rise to the MP3 energy.

Note that the epressions for the MP3 energy still only involve doubly excited determinants.