Vector, internuclear, time-averaged

Here T2 is the order of time in which the nucleus resides in a given spin state. If there are no restrictions on the directions available to the internuclear vector, then the time average can be replaced by a space average, with the result that... 

Figure 2. The time-averaged result randomly oriented internuclear vector, tional axis, R.

The angle 6 defines the angle between the IS internuclear vector and the static magnetic field (Fig. 10.51a) and is time-dependent, the brackets indicating the time average over all molecular orientations as the molecule tumbles. The term bis is the dipole-dipole coupling constant... 

In a nuclear magnetic resonance measurement in solution, the direct dipolar interaction Xo actually disappears because, due to rapid molecular motion, the interspin (internuclear) vectors are rapidly space-averaged within the time-scale of a measurement. Hence, the terms Xs and Xj are detectable as sharp lines or splittings in a high-resolution spectrum of H or and they can be related to detailed molecular structure or conformation of the substance investigated. In a solid, on the contrary, the directions of the internuclear vectors are stationary even if they are distributed randomly in space. Then, X gives a very wide linewidth to the zeroth-order absorption line and completely masks all lines due to Xs and Xj. 

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