Orbital instabilities and spin-symmetry breaking in coupled-cluster calculations of indirect nuclear spin-spin coupling constants

The effect of orbital instabilities is investigated for spin-symmetry breaking perturbations, namely the Fermi-contact (FC) and spin-dipole (SD) contributions to the indirect nuclear spin-spin coupling constants. For the CO and N2 molecules the FC and SD contributions have been calculated and orbital-stability analyses for various interatomic distances have been carried out. This includes calculations at the Hartree-Fock self-consistent field (HF-SCF), coupled-cluster (CC) singles and doubles (CCSD), CC3, CCSD(T), CCSDT-4, CC singles, doubles, and triples (CCSDT) levels, and for the first time also at the CC singles, doubles, triples, and quadruples (CCSDTQ) level of theory. For calculations with relaxation of the reference orbitals in the presence of the perturbation, unphysical results are obtained over a wide range of the potential curve. This is due to a triplet instability of the Hartree-Fock reference determinant which leads to a pronounced pole in the FC and SD contributions. The effect of orbital instabilities in the relaxed methods is most dramatic for perturbative approaches like CCSD(T), while it is less pronounced for methods of the classical CC hierarchy. CC calculations without relaxation of the orbitals, i.e., so-called “unrelaxed” calculations, do not show any of these effects.