R1rho relaxation outside of the fast-exchange limit

Chemical-exchange effects in NMR spectroscopy enable kinetic processes to be characterized at equilibrium in solution. Beginning with the Bloch-McConnell equations, new expressions are derived for the spin relaxation rate constant in the rotating frame, R1rho, for chemical exchange between two sites that have distinct magnetic environments and Larmor frequencies. The results are accurate provided that the spin relaxation decay is dominated by a single exponential damping constant and are applicable to a wider range of conditions than existing theoretical descriptions. The new expressions for R1rho will be particularly useful in analyzing experimental data when exchange is not fast and site populations are unequal.