# MCMC paper finished

*Abstract:*

Many nuclei probed by NMR are relatively insensitive to detection, requiring methods such as the Carr-Purcell Meiboom-Gill (CPMG) pulse sequence. Experiments which follow this general approach are composed of pulse trains, giving rise to characteristic spikelet patterns in the frequency domain. In the presence of multiple underlying chemical sites, each spikelet intensity is a sum of some unknown proportion of contributions from each site. This work outlines a modeling approach based around Markov Chain Monte Carlo (MCMC), which negates the need for intensive simulations using density matrix formalism. In support of this technique, a spikelet pattern is produced using the density matrix formalism for an ensemble of spin 1/2 nuclei, and the underlying chemical shifts and intensities reproduced using the method outlined. Finally, MCMC is used to model the CPMG spectrum of a (3,3,3-trifluoropropyl)dimethylchlorosilane (TFS) treated aluminosilicate, providing evidence in support of a particular model of silanol group surface attachment to the bulk.