Spin–spin coupling constants and triplet instabilities in Kohn–Sham theory

Abstract

Indirect nuclear spin–spin coupling constants calculated using restricted Hartree–Fock theory are unreliable since the usually dominant Fermi-contact (FC) contribution arises from a triplet perturbation of the electronic system, poorly described in the Hartree–Fock theory – in particular, at geometries close to the onset of triplet instabilities. These problems are usually but not invariably overcome in Kohn–Sham theory, which typically provides good spin–spin coupling constants. We here examine the sensitivity of spin–spin coupling constants to triplet instabilities in Kohn–Sham and Hartree–Fock theories by correlating the quality of the spin–spin coupling constants and the quality of the lowest triplet excitation energy for a number of small molecules. In general, the FC contributions are most stable in the local density approximation (LDA) and slightly less stable in the generalised gradient approximation (GGA); on the other hand, GGA coupling constants are usually more accurate than LDA constants. Importantly, although hybrid theory often gives better results than the GGA theory, it is also more susceptible to triplet instabilities (inheriting some of the problems of the Hartree–Fock theory) and therefore less reliable than the GGA theory for spin–spin coupling constants. For calculations of spin–spin coupling constants, we recommend the Perdew–Burke–Ernzerhof GGA exchange-correlation functional, which provides a good compromise of accuracy and robustness.