Perturbation Theory Energies from the Coupled Cluster Hamiltonian

Perturbation Theory Energies from the Coupled Cluster Hamiltonian 

The partitioning of the electronic Hamiltonian and the corresponding breakdown of the cluster operators leads to an expansion of the coupled cluster effective Hamiltonian, H, in orders of perturbation theory through the Haus-dorff expansion given in Eq. [122]  

Since the zeroth-order component of H consists of just the Fock operator in Moller-Plesset theory, the first-order components of H may be written as 

Each of these expressions is constructed by simply assigning the appropriate perturbational orders to each operator in Eq. [122] and retaining only the terms that correspond to the desired order, n. Using H as an approximate Hamiltonian, one may construct th-order Schrodinger equations of the form 

One computes the energy in the th order of MBPT via a zeroth-order expectation value, namely. 

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