Plesset Perturbation Theory for Energy

A very common choice of the potential V used to define as in Eq. (3.13) is the HF potential 

With the above choice of H now made, the perturbation U becomes 

These choices of and U, when used in RSPT, give rise to what is commonly called (Pople et a/., 1977) Miller-Plesset perturbation theory (MPPT) and the expression for reduces to the familiar form 

The RSPT expression for / can also be expressed in terms of orbital energies and two-electron integrals. The kets k ) appearing in Eq. (3.22) for 

To obtain more insight into the structure of the size-consistent and -inconsistent terms, we derive an explicit expression for the quantity A appearing in Eq. (3.29) within MPPT. Realizing that only the doubly excited determinants k contribute in Eq. (3.29) because of the BT, we obtain 

---