“…(2) T 1e is short compared with translational diffusion correlation times. The first case is relevant to nitroxide centers and some metal centers that have been used most often in the past; ,,,,− ,,− the second is important to the present discussion where we use dioxygen as the paramagnetic relaxation agent. ,,, The paramagnetic contribution to the k th proton in solution originating from a dipolar coupling to the oxygen center is given by Freed 16
where
[ C ] is the concentration of the paramagnetic molecule, while S is the electron spin, 1 in this case, ω is the Larmor frequency for the nuclear spin, I , or the electron spin, S , P is a factor discussed below that equals 1 for a hydrogen atom, b is the distance of closest approach between the electron and nuclear spin, D is the relative diffusion constant, and 〈 r 2 〉 is the mean-square jump length of the small solute. In the present case, the motion of the protein is slow so that the effective diffusion constant becomes that for the paramagnet, oxygen.…”