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

Abstract

A 126π‐electron nanobowl molecule, phenine tridehydrosumanene, was synthesized in 12 steps through the development of a polygon cyclization strategy that assembled the polygonal precursors via Ni‐mediated macrocyclization. The bowl‐shaped structure accommodated C70 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 protocol to estimate the volume of prior probability in the parameter space was developed. The Bayesian protocol 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.