Molecular ordering
is important for physical and electrical properties of materials such as
polymers and liquid crystals. For these non-crystalline/amorphous materials,
multiple-quantum (MQ) spin-counting solid-state NMR[1] is a powerful tool
for structural analysis as it permits to get insight into the spatial
distribution of spins in such disordered solid yet the quantitative analysis of
size and shape of spin clusters by the density matrix approach remains very
difficult. Here we presents a novel stochastic approach for analyzing MQ spin
dynamics. The statistical
approach is based on the percolation theory with Monte Carlo methods and is
examined by applying it to the experimental results of three solid samples
having unique hydrogen arrangement for 1–3 dimensions: the *n*-alkane–d-urea inclusion complex as a one-dimensional
(1D) system, whose ^{1}H nuclei align approximately in 1D, and
magnesium hydroxide and adamantane as a two-dimensional (2D) and a
three-dimensional (3D) system, respectively. Four lattice models, linear,
honeycomb, square and cubic, are used to represent the ^{1}H
arrangement of the three samples. It is shown that the MQ dynamics in
adamantane is consistent with that calculated using the cubic lattice and that
in Mg(OH)_{2} with that calculated using the honeycomb and the square
lattices. For *n*-C_{20}H_{42}–d-urea, these
4 lattice models fail to express its result. It is shown that a more realistic
model representing the ^{1}H arrangement of *n*-C_{20}H_{42}–d-urea
can describe the result.[2] The approach is then applied to investigate ^{1}H
distribution in various inorganic materials, for example, tobermorite
and appetite. Application to MQ among
spins other than ^{1}H will also be presented.

[1] As for a review; M. Munowitz and A. Pines, Adv. Chem. Phys., 66 (1987) 1-152.

[2] Y. Mogami, Y. Noda, H. Ishikawa and K. Takegoshi, Phys. Chem. Chem. Phys. 15 (2013) 7403-7410.