Spin adapted restricted Hartree–Fock reference coupled cluster theory for open shell systems

The coupled clusters (CC) method for effective calculations of open shell systems with the single restricted Hartree–Fock (ROHF) reference determinants is formulated. We apply the spin adaptation described in our previous work, aimed at removing the spin contamination in both coupled cluster (CC) amplitudes and CC energy, both for the linear and nonlinear versions of the single and double excitation coupled cluster (CCSD) method. We give a comparison of results with adapted and nonadapted methods. Together with the elimination of the spin contamination, our spin adaptation yields CC equations, which reduce the number of CC amplitudes and the number of arithmetical operations, which results in computational time comparable with analogous closed shell calculations. The complication in the full spin adapted CC method is that individual spin states require specific spin adapted excitations, so that for every spin state, a different implementation is needed. It is possible to define a very effective approximation to the full spin adapted model that is common to all half-spin states. The method is less complicated in implementation, while the computational requirements increase in comparison with the full spin adapted method only slightly. We also suggest how to introduce spin adaptation in a very simple way to existing ROHF CCSD programs.