On the coupled-cluster equations. Stability analysis and nonstandard correction schemes

i) The coupled-cluster equations being nonlinear, they have to be solved iteratively. An insight into the convergence properties of this iteration can be obtained by analysing the stability of the converged solutions as fixed points. (ii) The usual form of coupled-cluster equations represents an example to the method of moments, with the number of unknown amplitudes being equal to the number of equations. The method of moments generates nonsymmetric equations loosing the variational character of the coupled-cluster method, but enabling efficient evaluation of the matrix elements. Taking higher moments into account, one may obtain more equations than parameters, thus the latter must be determined by minimizing the sum-of-squares of all moments. This leads to additional effort but improved coupled-cluster wave functions and/or energies. (iii) Another way of improving the coupled-cluster method is perturbation theory, which needs special formulations due to the nonsymmetric nature of the formalism. An efficient way to do this is offered by multi-configuration perturbation theory.