A novel derivation of the Solomon-Bloemberpa-Morgan equations: Application to solvent relaxation by Mn²⁺-Protein complexes

Abstract

We present a novel derivation of the equations that are used to describe the spin-lattice (longitudinal) magnetic relaxation of nuclear spin moments caused by magnetic dipolar interactions with neighboring paramagnetic ions, the Solomon-Bloembergen-Morgan equations. The derivation, which depends on a physical view of the relaxation processes opposite to that usually considered, has the advantage that it can be readily generalized to include effects due both to ligand-field splitting of the levels of the ions, and to delocalization of the ion spin moment. Application of the generalized equations to some controversial and ambiguous results obtained from the magnetic-field dependence of the relaxation rate of solvent protons in solutions of several Mn2+-protein complexes re-enforces earlier arguments that the apparent strength of the dipolar interaction is a factor of 5 larger than expected in at least one, and possibly all three, cases investigated by us. The results, possibly due to delocalization of the magnetic moment of the Mn2+ ions, show that, for at least three proteins, it is not possible to use solvent proton relaxation measurements alone to determine the number of exchanging water molecule ligands of complexed Mn2+ ions. © 1978.