Low-field theory of nuclear spin relaxation in paramagnetic low-symmetry complexes for electron spin systems of S = 1, 3/2., 2, 5/2, 3 and 7/2

A low-field theory of nuclear spin relaxation in paramagnetic systems is developed, resulting in closed analytical expressions. We use the same approach as Westlund, who derived the low-field expression in the case of S = 1 for a rhombic static zero-field splitting (ZFS). In the present paper we extend the derivation to include S = 3/2, 2, 5/2, 3 and 7/2 for the case of an axial static ZFS, whereas only S = 3/2 is considered for a rhombic static ZFS. The slow-motion theory of nuclear spin relaxation in paramagnetic systems was recently generalized to account for arbitrary electron spin S and the calculations showed some unexpected features. Thus, one objective of the derivation of closed analytical low-field expressions is to provide a framework for physical explanation of slow-motion calculations. We find that the results of the low-field theory are, indeed, in good agreement with the slow-motion calculations in the case of slowly rotating complexes (e.g. metalloproteins). It is evident that the static ZFS influences the electron spin relaxation more markedly for higher spin systems than for S = 1. In fact, systems of S = 2 and S = 3 show more similarities in the electron spin-lattice relaxation properties to half-integer spin systems than to S = 1 in the case of an axially symmetric static ZFS. These findings show the shortcomings of using Bloembergen-Morgan theory for the description of electron spin relaxation in the low-field limit and provide improved tools for the interpretation of experimental variable-field relaxation data.