If the Hamiltonian is non-relativistic, see, e.g., Eqs. ( 1.1 )–( 1.3 ), then it is spin-independent. Consequently, the total spin of the electrons is preserved and one can search for common eigenvectors of the operators \(\hat {\mathsf {H}},\hat {\mathsf {S}}^2,\hat {\mathsf {S}}_z\) , where \(\hat {\mathsf {S}}^2\) and \(\hat {\mathsf {S}}_z\) designate the square and the projection on the z-axis of the total spin operator. Thus, in addition to the permutational symmetry, we include the spin symmetry as well. This naturally begs the question how to use these two symmetries to simplify the approximate calculation. Further, we show how the system of quadratic equations for the cluster amplitudes can be solved by the iterative Newton-Raphson method. We illustrate all these points by applying the cc method to the Hubbard model of benzene.Further, we show how to include monexcitations exactly and triexcitations perturbatively in a cc calculation. We conclude this chapter by showing how one can apply the cc method to the one-electron open-shell systems.