Abstract
The different approximate versions of a coupled-cluster approach (CCA) are discussed and applied for the correlation-energy calculations of small closed-shell molecular systems. The CCA results reproduce the corresponding configuration-interaction correlation energies with very high accuracy. The CCA construction of Nesbet's hierarchy of Bethe-Goldstone equations and the Newton-Raphson method to accelerate the iterative solution of CCA systems of coupled nonlinear equations are presented.