What is a typical dipolar coupling constant in a solid?

Abstract

Some statistical properties of the distributions of dipolar coupling constants and their products are discussed in the context of nuclear magnetic resonance (NMR) of solids. Transformations of the distributions (absolute values and their logarithms) reveal new statistical properties. The ‘‘relative fluctuations’’ of the absolute value distributions, i.e., (second absolute central moment)1/2/(first absolute moment) are shown to scale as N+1/2, where N is the number of spins. The ratio (first absolute moment)/(most probable value) is shown to diverge as N+3/2. Products of the absolute values of dipolar coupling constants follow lognormal distributions in large spin networks. The relative fluctuations of these products also scale with N+1/2. Numerical studies of spin systems, with 10≤N≤105, in one-, two-, and three-dimensional crystalline lattices support several of these results. Some implications for multiple quantum NMR spectroscopy are presented.