Approximate solutions of the Bloch-McConnell equations for two-site chemical exchange

Abstract

Approximate formulas for the transverse-relaxation rate constant and resonance frequency have been derived for nuclear spins subject to two-site chemical exchange. The new results are more accurate than previous approximations when chemical exchange does not approach the fast-exchange limit or when site populations are not highly asymmetric. Results are derived from an effective average evolution operator that contains contributions from both exact eigenvalues of the Bloch-McConnell equations. These expressions are useful for interpretation of chemical exchange processes in NMR spectroscopy.