An Eigenvalue Approach to Coupled Cluster Theory

The coupled cluster Schrodinger equation, which leads to the energy and amplitude expressions given in Eqs. [50] and [51], may be written as 

Like Eq. [60], this equation represents an eigenvalue problem ° in which the similarity-transformed Hamiltonian, H = is used in place of the bare 

As a result of the asymmetry of H, the right-hand eigenvalue problem given in Eq. [61] is different from the left-hand eigenvalue problem. 

The computed energy, E, however, is the same for both equations. In Eq. [65], the left eigenvector, (5 l, may be written in terms of a cluster operator, X, acting on the reference from the right, namely, 

The operator may be defined in analogy to the cluster operator, T, as a sum of of cluster operators. 

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