An orifice-size index for open-cage fullerenes

In the field of open-cage fullerenes, there was a lack of a universal standard that could correlate and quantify the orifice size of open-cage fullerenes. One cannot compare the relative orifice size by simple comparison of the number of atoms that composes the orifice. We present a general term for easy estimation of relative orifice size by defining an index for open-cage fullerenes. We estimated the corresponding effective areas A(area) for orifices of open-cage fullerenes by matching calculated activation energies Ea(calcd) for hydrogen release from open-cage fullerenes (B3LYP/6-31G**//B3LYP/3-21G) to the computed energies required for a hydrogen molecule passing through a cyclo[n]carbon ring. Then we define an index K(orifice) based on experimental hydrogen release rate, where K(orifice) = In k/k degrees (k is rate constant of hydrogen-release rate of any open-cage fullerenes taken for comparison at 160 C; k is the hydrogen release rate from H-2@4a taken as the standard compound). We synthesized several opencage fullerenes and studied kinetics of a set of H-2-encapsulated open-cage fullerenes to evaluate their K values. A correlation of the index K(orifice) with the effective areas A(area) showed a good linear fit (r(2) = 0.972) that demonstrated a good interplay between experiment and theory. This allows one to estimate K(orifice) index and/or relative rate k of hydrogen release through computing activation energy Ea(calcd) for a designed open-cage fullerene.