✍ Scribed by Mark A. Watson; Paweł Sałek; Peter Macak; Michał Jaszuński; Trygve Helgaker
No coin nor oath required. For personal study only.
We present calculations of indirect nuclear spin–spin coupling constants in large molecular systems, performed using density functional theory. Such calculations, which have become possible because of the use of linear‐scaling techniques in the evaluation of the Coulomb and exchange‐correlation contributions to the electronic energy, allow us to study indirect spin–spin couplings in molecules of biological interest, without having to construct artificial model systems. In addition to presenting a statistical analysis of the large number of short‐range coupling constants in large molecular systems, we analyse the asymptotic dependence of the indirect nuclear spin–spin coupling constants on the internuclear separation. In particular, we demonstrate that, in a sufficiently large one‐electron basis set, the indirect spin–spin coupling constants become proportional to the inverse cube of the internuclear separation, even though the diamagnetic and paramagnetic spin‐orbit contributions to the spin–spin coupling constants separately decay as the inverse square of this separation. By contrast, the triplet Fermi contact and spin‐dipole contributions to the indirect spin–spin coupling constants decay exponentially and as the inverse cube of the internuclear separation, respectively. Thus, whereas short‐range indirect spin–spin coupling constants are usually dominated by the Fermi contact contribution, long‐range coupling constants are always dominated by the negative diamagnetic spin‐orbit contribution and by the positive paramagnetic spin‐orbit contribution, with small spin‐dipole and negligible Fermi contact contributions.
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