Stability of Hydrocarbons of the Polyhedrane Family Containing Bridged CH Groups: A Case of Failure of the Colle-Salvetti Correlation Density Functionals

DFT-computed energies of polyhedric hydrocarbons, such as dodecahedrane C20H20, its smaller analogs C16H16 and C12H12, and the larger C24H24, estimated in comparison with corresponding isomeric hydrocarbons, vary widely with the choice of the density functional. In particular, large discrepancies were observed with the functionals that are based on the B88 (as well as G96, B86) exchange and the LYP (as well as OP) correlation parts. The problem is not related to the presence of the smaller cyclopropane rings in the C12H12 polyhedrane, for its hydrogenated products do show similar errors; moreover, the larger dodecahedrane that is free from the Bayer strain shows a similar trend. DFT-D corrections that are very useful in fixing long- and medium-range correlation issues with GGA DFT do not help in this case either. We show that these errors stem from the B88 (G96, B86) exchange functionals and are not compensated by Colle-Salvetti-based GGA correlation functionals such as LYP, OP, TCA, etc. However, they can be corrected by the PBE correlation functional based on the PW92 uniform electron gas (UEG) parametrization. Range-separated hybrids (Iikura and Hirao's LC-BOP, LC-BLYP) perform much better than the parent GGAs. Comparisons of polyhedranes with a well-studied system of similar size, the set of CnHn cyclophanes, reveal a completely different performance for the latter-for instance, RHF results are the poorest, and LC-type functionals do not give any improvement, but dispersion-corrected BLYP-D performs very well. We conclude that, while for polyhedranes medium-range delocalization errors from exchange dominate, for cyclophanes, the correlation/overlap-dispersion interactions are more important. The OPTX exchange functional shows significantly lower errors compared to B88 and G96; its combinations like OLYP and especially KT3 perform well for both test sets. The OPTX-based double hybrid, O2PLYP, also outperforms the corresponding B88-based B2PLYP functional for polyhedranes. Our computations also suggest that the (CH)16 and (CH)24 polyhedranes could be possible synthetic targets.