The failure of DFT in dealing with some seemingly straightforward reactions (as discussed in these previous blog posts: A, B, C, D, E, F) has become a bit clearer. Brittain and co-workers have identified the culprit.1 They examined twelve different reactions, involving neutral, radical, cations and anions:

R-Me + Me-H → R-H +Me-Me
R-Me + Me. → R. + Me-Me
R-Me + Me- → R- + Me-Me
R-Me + Me+ → R+ + Me-Me

where R is ethyl, i-propyl and t-butyl. They used a variety of different functionals, and benchmarked the energies against those found at CCSD(T)/cc-pVTZ. By systematically using different densities and different exchange and correlation components, DFT exchange is responsible for the poor performance – and it can be very poor: the error for the cation reaction with R=t-butyl is 12 kcal mol-1 with B3LYP and 18 kcal mol-1 with PBE. It should be noted that the maximum error with G3(MP2) and MP2 is 1.5 and 2.5 kcal mol-1, respectively. These authors make three important conclusions: (a) that traditional ab initio methods are preferred, (b) that development of new functionals should target the exchange component, and (c) Truhlar’s highly parameterized functional MO5-2X works quite well (maximum error is 2.6 kcal mol-1 – again for the cation t-butyl case) but the reason for its success is unknown.

References

(1) Brittain, D. R. B.; Lin, C. Y.; Gilbert, A. T. B.; Izgorodina, E. I.; Gill, P. M. W.; Coote, M. L., "The role of exchange in systematic DFT errors for some organic reactions," Phys. Chem. Chem. Phys. 2009, DOI: 10.1039/b818412g.