Hermitian formulation of the coupled-cluster approach

Abstract

A Hermitian formulation of the coupled-cluster approach (CCA) is developed, based on the Jorgensen condition, P Omega Dagger Omega P=P, Omega being the wave operator and P the projection operator for the model space. This leads to a formalism where the exact as well as the model functions are orthonormal, and the effective Hamiltonian has the manifestly Hermitian form Heff=P Omega Dagger H Omega P. It is shown that the Jorgensen condition is compatible with the connectivity criteria (connected cluster operator and effective Hamiltonian) for a general, incomplete model space. Even with an effective Hamiltonian of this form, however, nonHermiticity may be introduced when the cluster expansion is truncated. This can be remedied by a reformulation of the coupled-cluster equations, where additional terms, which cancel in the complete expansion, preserve Hermiticity at each truncation. The new equations also lead to additional terms in the cluster operator itself, which make it possible, for instance, to include important effects in the pair approach that otherwise would require the evaluation of three- and four-body clusters.