Paramagnetic proton nuclear spin relaxation theory of low-symmetry complexes for electron spin quantum number S = 52

A generalization of the modified Solomon-Bloembergen-Morgan (MSBM) equations has been derived in order to describe paramagnetic relaxation enhancement (PRE) of paramagnetic complexes characterized by both a transient (DeltaZFSt) and a static (DeltaZFSs) zero-field splitting (ZFS) interaction. The new theory includes the effects of static ZFS, hyperfine coupling, and angular dependence and is presented for the case of electron spin quantum number S = 52, for example, Mn(II) and Fe(III) complexes. The model gives the difference from MSBM theory in terms of a correction term delta which is given in closed analytical form. The theory may be important in analyzing the PRE of proton spin-lattice relaxation dispersion measurements (NMRD profiles) of low-symmetry aqua-metal complexes which are likely to be formed upon transition metal ions associated with charged molecular surfaces of biomacromolecules. The theory has been implemented with a computer program which calculates solvent water proton T1 NMRD profiles using both MSBM and the new theory.