The much publicized failure of common DFT methods to accurately describe alkane isomer energy and bond separation reactions (which I have blogged about many times) has recently been attributed to long-range exchange¹ (see this post) or simply just DFT exchange² (see this post). Grimme now responds by emphatically claiming that it is a failure in accounting for medium-range electron correlation.³

First, Grimme notes that the bond separation energy for linear alkanes (as defined in
Reaction 1) is underestimated by HF, and slightly overestimated by MP2, but SCS-MP2 provides energy in nice agreement with CCSD(T)/CBS energies. Since MP2 adds in coulomb correlation to the HF energy (which treats exchange exactly within a one determinant wavefunction), the traditional wavefunction approach strongly suggests a correlation error.

CH₃(CH₂)_mCH₃ + mCH₄ → (m+1)CH₃CH₃        Reaction 1

Next, bond separation energies computed with PBE and BLYP (which lack exact exchange), PBE0 (which has 25% non-local exchange) and BHLYP (which has 50% non-local exchange) are all similar and systematically too small. So, exchange cannot be the culprit. It must be correlation.

He also makes two other interesting points. First, inclusion of a long-range correction – his recently proposed D3 method⁴ – significantly improves results, but the bond separation energies are still underestimated. It is only with the double-hybrid functional B2PLYP and B2GPPLYP that very good bond separation energies are obtained. And these methods do address the medium-range correlation issue. Lastly, Grimme notes that use of zero-point vibrational energy corrected values or enthalpies based on a single conformation are problematic, especially as the alkanes become large. Anharmonic corrections become critical as does inclusion of multiple conformations with increasing size of the molecules.

References

(1) Song, J.-W.; Tsuneda, T.; Sato, T.; Hirao, K., "Calculations of Alkane Energies Using Long-Range Corrected DFT Combined with Intramolecular van der Waals Correlation," Org. Lett., 2010, 12, 1440–1443, DOI: 10.1021/ol100082z

(2) 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.

(3) Grimme, S., "n-Alkane Isodesmic Reaction Energy Errors in Density Functional Theory Are Due to Electron Correlation Effects," Org. Lett. 2010, 12, 4670–4673, DOI: 10.1021/ol1016417

(4) Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H., "A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu," J. Chem. Phys., 2010, 132, 154104, DOI: 10.1063/1.3382344.