The Dipolar Relaxation Pathway

The NOE arises through the dipolar interaction of spins, which is an interaction that occurs between two spin-y2 nuclei through space. The dipolar interaction is tensorial in nature, meaning simply that it depends on the relative orientation of the two dipoles in space. It is a through-space effect and not a through-bond effect like 1-coupling. 

The dipolar interaction does, however, often play a role in the relaxation of spins. Even though the net effect of dipolar interactions 

For a two spin system, Wq is the rate constant for the zero quantum spin flip, Wi is the rate constant for the single quantum spin flip, and W2 is the rate constant for the double quantum spin flip. For short correlation times, the ratio ofWjWyWo is 1Ve. 

Zero quantum spin flip rate constant, Wq. The kinetic rate constant controlling the simultaneous change in both spin states fora two-spin system where one of the spin-lk spins goes from the a to the p state while the other spin-lk spin goes from the P to the a state. 

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