Variational and Coupled Cluster Method for Many-Particle Systems

The use of canonical transformations in both quantum chemistry and physics in the construction of effective Hamiltonians has long been a useful tool in the hands of theoreticians. Here we wish to revisit the basic tenets of the Coupled Cluster Method, wherein the exponentials appearing in the transformed Hamiltonian $e^{-S}He^{S}$ are expanded out. These terms are then recombined to form the basis states of a recently developed variational scheme. Here the operator $S=\sum_{n}\lambda_{n}s_{n}$ represents the excitations of the system. We then apply this new method to a number of Hamiltonian systems.