The Frozen Cage Model: A Computationally Low-Cost Tool for Predicting the Exohedral Regioselectivity of Cycloaddition Reactions Involving Endohedral Metallofullerenes

Functionalization of endohedral metallofullerenes (EMFs) is an active line of research that is important for obtaining nanomaterials with unique properties that might be used in a variety of fields, ranging from molecular electronics to biomedical applications. Such functionalization is commonly achieved by means of cycloaddition reactions. The scarcity of both experimental and theoretical studies analyzing the exohedral regioselectivity of cycloaddition reactions involving EMFs translates into a poor understanding of the EMF reactivity. From a theoretical point of view, the main obstacle is the high computational cost associated with this kind of studies. To alleviate the situation, we propose an approach named the frozen cage model (FCM) based on single point energy calculations at the optimized geometries of the empty cage products. The FCM represents a fast and computationally inexpensive way to perform accurate qualitative predictions of the exohedral regioselectivity of cycloaddition reactions in EMFs. Analysis of the Dimroth approximation, the activation strain or distortion/interaction model, and the noncluster energies in the Diels-Alder cycloaddition of s-cis-1,3-butadiene to X@D-3h-C-78 (X = Ti2C2, Sc3N, and Y3N) EMFs provides a justification of the method.