An R(1ρ) expression for a spin in chemical exchange between two sites with unequal transverse relaxation rates.

An analytical expression is derived for the rotating frame relaxation rate, R(1ρ), of a spin exchanging between two sites with different transverse relaxation times. A number of limiting cases are examined, with the equation reducing to formulae derived previously under the assumption of equivalent relaxation rates at each site. The measurement of a pair off-resonance R(1ρ) values, with the carrier displaced equally on either side of the observed correlation, forms the basis of one of the approaches for obtaining signs of chemical shift differences, Δω, of exchanging nuclei. The results presented here establish that this method is relatively insensitive to differential transverse relaxation rates between the exchaning states, greatly simplifying the calculation of optimal parameters in R(1ρ) based experiments that are used for measurement of signs of Δω.