Bayesian Inference for Model Analyses of Supramolecular Complexes: A Case Study with Nanocarbon Hosts.

A 126 π-electron nanobowl molecule, phenine tridehydrosumanene, was synthesized in 12 steps through the development of a polygon cyclization strategy that assembled the polygonal precursors by Ni-mediated macrocyclization. The bowl-shaped structure accommodated C as a guest at the concave site, and the ball-in-bowl structure was determined by X-ray crystallography. The host-guest equilibrium in solution was studied with titration experiments using isothermal calorimetry, which provided an interesting test case for studying the host-guest stoichiometry. Bayesian inference was introduced for stoichiometric analyses of the equilibrium, and a procedure to estimate the volume of prior probability in the parameter space was developed. The Bayesian procedure functioned as Occam's razor and provided quantitative support for a specific stoichiometry. The method was examined with five host-guest examples comprising nanocarbon hosts, which suggested the versatility of Bayesian inference for studies of supramolecular complexes.