A general method for constructing bases for operator manifolds for any propagator, which satisfy ‘‘vacuum annihilation conditions’’ (VAC’s) is developed. This approach is based on the observation that if the transformation of the unperturbed ground state to the correlated ground state is represented as a rotation in the Fock space, the corresponding rotation induced in the basis of the concerned operator space would generate a basis which satisfies VAC’s on the correlated ground state. The associated requirements for the Hermiticity of superoperator Hamiltonian would also be met in this new basis. The proposed method is noniterative in that, once the form of the ground-state function is specified, the expansion of the operator manifold satisfying VAC’s on the ground state does not require any iterative readjustment. The resultant propagators in this approach are fully linked. It is shown that this theory is equivalent to a propagator formalism in terms of hole- and particle-creation and/or annihilation operators with a modified effective Hamiltonian. The self-consistent electron and polarization propagators are considered as examples, and their underlying perturbative structures are analyzed. The role of density shift operators and higher-rank operators are discussed.

Vibrational excited state energies have been calculated using vibrational coupled cluster linear response theory (CCLRT). The method has been implemented on formaldehyde and water molecule. Convergence studies have been shown with varying the cluster operator from S4 to S6 as well as the excitation operator from four bosons to six bosons. A good agreement with full configuration interaction results has been observed with S6 truncation at coupled-cluster method level and six bosonic excitations at CCLRT level.

The time‐dependent coupled cluster method is developed to provide a formally exact theory of quantum‐mechanical motion of a vacuum state on multidimensional anharmonic surfaces with a view to calculate the molecular absorption spectra. The exact time evolution operator is represented as an exponential of creation operators. Since the separability requirments of many‐particle systems are built into such an ansatz, it is possible to develop approximations which can take into account any number of modes with much less computational effort than in a calculation by basis‐set expansion. The method gives a closed set of equations for harmonic surfaces and finite ordered equations for anharmonic surfaces when truncated at some finite rank.