Akaike's Information Criterion for Stoichiometry Inference of Supramolecular Complexes.

"How do we decide the stoichiometry of host-guest complexes?" This question has long been answered by the Job plot since its first report in 1928. However, as the Job plot was claimed to be misleading in 2016, the question became an open question again and called for renewed investigations. An information-theoretic approach, called Akaike's information criterion, is introduced in this study to select the best model of host-guest complexes, which can rank the models with weight of evidence. A few test cases with unique cylindrical hosts were examined to demonstrate the applicability of the information-theoretic method. Consequently, reasonable views over the thermodynamic behaviors of dumbbell-and-cylinder complexes were obtained. Akaike's information criterion can be a useful and superior alternative to statistical null hypothesis testing, which was proposed as a remedy in place of the Job plot.

Activation of Positive Cooperativity by Size-Mismatch Assembly via Inclination of Guests in a Single-Site Receptor.

A halogenated bowl-shaped guest, corannulene, was encapsulated in a cylindrical host, [4]cyclochrysenylene, to form a bowl-in-tube complex, which mimicked supramolecular complexes between bowl guests and carbon nanotubes. As was the case with carbon nanotubes, the cylindrical space of [4]cyclochrysenylene trapped multiple corannulene molecules in an array, and 1 : 2 complexes were commonly obtained with the corannulene guests with various halogen substituents (F, Cl, Br and I). Careful statistical analyses of isothermal titration calorimetry data succeeded in revealing the stoichiometry, and the molecular structures of the 1 : 2 complexes were further clarified by X-ray crystallographic analyses. Two fluorinated corannulene guests were stacked perpendicular to the cylinder axis, while two chlorinated guests were stacked with inclined orientations. The structural difference resulted in a large difference in the cooperativity of the two-stage association in solution: fluorinated corannulene guests showed negative cooperativity for the 1 : 2 complexation, and the other, larger halogenated corannulene guests showed positive cooperativity.