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On Application of Directed Graphs to NMR Spectroscopy

Here the directed graphs are used to estimate a quality of various theoretical methodologies to calculate chemical shifts. We propose that when comparing theoretical with experimental results, one should not only look how precisely the results agree for individual atoms but rather how theoretical predictions behave on the set of atoms. Some models will statistically significantly overestimate experimental results and other will underestimate them. The statistics used here is t-test for independent samples (matched pairs). This statistical analysis defines the partial order on the set of theoretical predictors which can be graphically represented by directed graphs, a novel object to study NMR shifts. By inspecting these directed graphs, one is able to tell which among many theoretical methods have to be chosen in order to have with great confidence (in statistical sense) lower and uper bounds for experimental data.

directed graphs; NMR spectroscopy; statistical analysis

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