Aspects of linked cluster expansion in general model space many‐body perturbation and coupled‐cluster theory

Abstract In this paper, a method of generating separable forms of the wave‐operator for incomplete model spaces is discussed. With a time‐dependent access to the many‐body perturbation and coupled‐cluster theories, it is shown how one can extract the regular part of the wave‐operator which consists of linked cluster‐operators only in the adiabatic limit. The procedure naturally suggests a hierarchy of lower valence model spaces P ( k ) . once a particular m ‐valence incomplete model space P ( m ) is specified. The wave‐operator Ω and the effective Hamiltonian H eff are linked in this development and are valence‐universal in the sense of being valid for all P ( k ) ' s. 0 ⩽ k ⩽ m . We have derived two distinct forms for Ω: (i) Ω = {exp( S )}, with { } as normal order with respect to suitable vacuum, where S are open operators inducing transitions from P ( m ) to outside it; (ii) Ω N = {exp( S + X )}, where X are additional closed operators which are introduced to maintain isometry of Ω N : P ( k ) Ω N + Ω N P ( k ) = P ( k ) . In neither of these choices do we have intermediate normalization. It is also possible to develop an alternative strategy with the complete model spaces, such that an effective valence‐universal operator H may be found which generates roots, only a subset of which are equal to the eigenvalues of H . These subsets are the ones that H eff would have furnished. This may thus be viewed as a Fock‐space realization of the intermediate Hamiltonian approach.