Third-order Douglas-Kroll relativistic coupled-cluster theory through connected single, double, triple, and quadruple substitutions: Applications to diatomic and triatomic hydrides

The coupled-cluster methods including through and up to the connected single, double, triple and quadruple substitutions were derived. The method was used in the conjunction with a one-component third-order Douglas-Kroll approximation for relativistic corrections. The experimental singlet-triplet separations within 0.02 eV for five triatomic hydrides were predicted. The spin-orbit effects on dissociation energies were estimated from the measured spin-orbit coupling constants of atoms and diatomic molecules.