Theoretical Details To The Calculation Of Nuclear Spin-Rotation Constants
Interactions between the nuclear spin and the rotation of a molecule cause additional splittings in the rotational spectra. The corresponding molecular parameters are the so-called nuclear spin-rotation constants which are given as the second derivative of the molecular energy with respect to nuclear spin of the n-th nucleus and rotational angular momentum
The quantum chemical calculation of suffers from a slow basis-set convergence and an (unphysical) origin dependence concerning the electronic angular momentum (though an appropriate choice might be the corresponding nucleus). These problems can be overcome by using perturbation-dependent basis functions (often refered to as rotational London orbitals)
In addition, it should be noted that a close relationship between the shielding tensor and the nuclear spin-rotaztion tensor . This relationship is usually stated as
with the paramagnetic part of the shielding computed with the corresponding nucleus as gauge origin, denoting the nuclear contribution to and as the gyromagnetic ratio. When using perturbation-dependent basis functions (rotational London orbitals), this expression has to be modified to
with the diamagnetic contribution to calculated in the usual manner with as gauge origin.
J. Gauss, K. Ruud, and T. Helgaker, J. Chem. Phys. 105, 2804 (1996)