Delocalization errors in density functionals and implications for main-group thermochemistry.

The difficulty of approximate density functionals in describing the energetics of Diels-Alder reactions and dimerization of aluminum complexes is analyzed. Both of these reaction classes involve formation of cyclic or bicyclic products, which are found to be underbound by the majority of functionals considered. We present a consistent view of these results from the perspective of delocalization error. This error causes approximate functionals to give too low energy for delocalized densities or too high energy for localized densities, as in the cyclic and bicyclic reaction products. This interpretation allows us to understand better a wide range of errors in main-group thermochemistry obtained with popular density functionals. In general, functionals with minimal delocalization error should be used for theoretical studies of reactions where there is a loss of extended conjugation or formation of highly branched, cyclic, and cagelike molecules.