A Lanczos-based algorithm for the analysis of NMR spin–spin coupling constants in terms of pairs of occupied and virtual orbitals: The Fermi-contact term at the RPA level of theory

The analysis of indirect nuclear spin-spin coupling constants in terms of contributions from localized molecular orbitals is a commonly used approach for gaining a deeper understanding of experimentally observed trends in these couplings. In the vast majority of these studies, contributions from pairs of one occupied and one virtual orbital are calculated and analyzed. Analyses in terms of two pairs of an occupied and a virtual orbital, which would allow for the study of coupling pathways, are much more seldom, as they require calculating the coupling constants as a sum over all excited states. Previous studies have shown that, for the often dominating Fermi-contact contribution to the coupling constants, more or less all excited states have to be calculated when employing a Davidson algorithm, because the most high-lying excited states can also make a significant contribution to the Fermi-contact term. In this study, we investigated therefore, whether by employing a Lanczos algorithm, one can obtain converged values of the Fermi-contact contribution to the indirect nuclear spin-spin coupling constants already with a significantly smaller percentage of the total number of excited states included in the sum-over-states expression. To this purpose, we have extended the recent implementation of a Lanczos algorithm in the Dalton program. The new procedure was tested on 17 molecules containing first, second, and third row atoms. We find that, for most coupling constants, less than 50% of the excited pseudo states are necessary for converging the Fermi-contact term with an error of <0.5 Hz. For the few exceptions, typically for molecules with third-row atoms, around 60% were necessary.