However, some resonances were characterized by large standard deviations in the HMCMCpredicted chemical shift. A large standard deviation in the predicted chemical shifts occurs when peaks in the trial spectrum could not be fit to the experimental spectrum, either because the compound does not exist in the reaction mixture, or because the initial trial shifts were very poorly predicted by DFT. To address this issue, in the second HMCMC iteration, the standard deviation of the Gaussian distributions used for the chemical shifts was set to three standard deviations of the DFT error (0.3 ppm), and the HMCMC procedure was repeated. After this iteration, compound 3g was determined to be absent, and only 3a, 3d, and 3e remained. The standard deviations in the chemical shift predictions for 3a, 3d, and 3e were small, and a final application of the deconvolution procedure was performed to improve the fit. As shown in Fig. , the procedure yielded a prediction accuracy of 100% and an MAE of 9% in the concentrations of components, demonstrating that our approach can deconvolute NMR spectra that contain extensive overlapping of the resonances. Finally, we considered a complex mixture simulating the nonselective oxidation of the C-H bonds in heptane to form alcohol, ketone, aldehyde, and carboxylic acid products. This example simulates an experimentally-obtained spectrum by mixing commercially available compounds. This example poses a stringent test of the procedure because the spectra of many of the compounds are similar to each other. Thus, most of the peaks in the spectrum of the mixture overlap.