Assessment of density functionals for π systems: Energy differences between cumulenes and poly-ynes; proton affinities, bond length alternation, and torsional potentials of conjugated polyenes; and proton affinities of conjugated shiff bases

Woodcock et al. [J. Phys. Chem. A 2002, 106, 11923] pointed out that no density functional was able to obtain the correct sign of the relative energies of the allene and propyne isomers of C₃H₄ and that density functional theory (DFT) predicts that poly-ynes are insufficiently stabilized over cumulenes for higher homologues. In the present work, we show that the recent M05 density functional predicts the correct ordering of allene and propyne and gives a mean unsigned error (MUE) of only 1.8 kcal/mol for the relative energies of the two isomers of C₃H₄, C ₅H₄, and C₇H₄. Two other recent functionals, M05-2X and PWB6K, also give reasonably low MUEs, 2.7 and 3.0 kcal/mol, respectively, as compared to 6.2 kcal/mol for the popular B3LYP functional. Another challenging problem for density functionals has been a tendency to overpolarize conjugated π systems. We test this here by considering proton affinities of conjugated polyenes and conjugated Schiff bases. Again M05-2X performs quite well, with MUEs of 2.1 and 3.9 kcal/ mol, respectively, as compared to 5.8 and 5.9 kcal/mol for B3LYP. Averaged over the three problems, M05-2X has a MUE of 3.0 kcal/mol, the BMK functional of Boese et al. has an MUE of 3.2 kcal/mol, and M05 has an MUE of 5.1 kcal/mol. Twenty-two other tested functionals have MUEs of 5.2-8.1 kcal/mol averaged over the three test problems. Both M05 and M05-2X do quite well, compared to other density functionals, for torsion potentials in butadiene and styrene, and M05 does very well for bond length alternation in conjugated polyenes. Since the M05 functional has broad accuracy for main group and transition metal chemistry and M05-2X has broad accuracy for main group chemistry, we conclude that significant progress is being made in improving the performance of DFT across a wide range of problem types.