Single quantum spin flip rate

Single quantum spin flip rate constant, W,. The kinetic rate constant controiiing the change in the spin state of a singie spin- /2 spin from either the a to the p state or from the a to the p state. 

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. 

The dipolar relaxation mechanism is unique because the dipolar coupling interaction contains two spin terms involving mutual spin flips - zero quantum t J. J. t and double quantum J J < j j transitions. All other relaxation processes are limited to single spin interchange. While the decoupler is on, the spin population differences between the levels irradiated are equalized as the rate of energy input from the decoupler greatly exceeds the outflow by relaxation. In dipolar coupled systems, the availability of double and zero quantum relaxation pathways (cross-relaxation) produces non-Boltzmann spin populations in the energy levels of the observed nucleus. These perturbed populations are measured as the nuclear Overhauser effect (nOe) effect rj). The relationship is... 

The triplet carbene, with its two nonbonding electrons of the same spin, must produce an intermediate that cannot close to a cyclopropane until a spin is somehow changed. Such spin flips are not impossible, but they are usually slow on the time scale of molecular processes. In particular, they are slow compared with the very rapid rotations about carbon-carbon single bonds. Therefore the stereochemistry of the original alkene need not be maintained in the eventual product of the reaction, the cyclopropane (Fig. 10.48). If rotation about the carbon-carbon bond is faster than the rate at which the spin quantum number of one electron changes (spin flip), it will not matter whether cis or trans alkene is used in the reaction with triplet methylene. The product will be a mixture of cis and trans 1,2-dialkylcyclopropanes in either case. 

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