Size Extensivity of the Coupled Cluster Energy

Consider the structure of the Cl Schrodinger equation (assuming intermediate normalization as well as normal-ordered and C operators), beginning from the linear ansatz of Eq. [32]  

Left-projection of this equation by the reference determinant, 3 o leads to the energy equation. 

If canonical Hartree-Fock orbitals are chosen, the first term is zero by Bril-louin s theorem. 

The Cl coefficient equations are obtained by left-projection of Eq. [186] by excited determinants. For example, the equation from full Cl is 

The coupled cluster energy, on the other hand, does not suffer from this lack of size extensivity for two reasons (1) the amplitude equations in Eq. [50] are independent of the coupled cluster energy and (2) the Hausdorff expansion of the similarity-transformed Hamiltonian in Eq. [106], for example, guarantees that the only nonzero terms are those in which the Hamiltonian is con- 

---