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 de veloped, resulting in closed analytical expressions. We use the same approa ch as Westlund, who derived the low-field expression in the case of S = 1 f or a rhombic static zero-field splitting (ZFS). In the present paper we ext end 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 syst ems was recently generalized to account for arbitrary electron spin S and t he calculations showed some unexpected features. Thus, one objective of the derivation of closed analytical low-field expressions is to provide a fram ework for physical explanation of slow-motion calculations. We find that th e results of the low-field theory are, indeed, in good agreement with the s low-motion calculations in the case of slowly rotating complexes (e.g. meta lloproteins). It is evident that the static ZFS influences the electron spi n 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-lat tice relaxation properties to half-integer spin systems than to S = 1 in th e case of an axially symmetric static ZFS. These findings show the shortcom ings of using Bloembergen-Morgan theory for the description of electron spi n relaxation in the low-field limit and provide improved tools for the inte rpretation of experimental variable-field relaxation data.