Approximate Solutions of the Bloch–McConnell Equations for Two‐Site Chemical Exchange

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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.