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.
Henry Rzepa responded on 14 Feb 2009 at 6:05 am #
Another advance on Jacob’s ladder (DOI: http://dx.doi.org/10.1063/1.1390175 ) is represented by the so called double-hybrid methods. These are characterised by both a high proportion of HF exchange AND a second component based on MP2 correlation. Martin (DOI: http://dx.doi.org/10.1021/jp710179r) suggests these new methods may be capable of yielding thermodynamic energies comparable to older (G3, W3) extrapolative methods, but at a fraction of the computational cost. The correlation component is handled using the `resolution of the identity” integral approximation applied to second- order many-body perturbation theory, or RI-MP2, which has the practical consequence that calculations for molecules specified by as many as 500+ basis functions (25 or so non hydrogen atoms) can now be attempted. It could be reasonably said that after some 20 years of increasingly widespread adoption, DFT methods are certainly coming of age. By the way, I can heartily recommend Orca for running such calculations (written by Frank Neese and colleagues).
Computational Organic Chemistry » Origin of DFT failures – part II responded on 25 May 2010 at 7:33 am #
[…] one more attempt to discern the failure of DFT to handle simple alkanes (see this earlier post for a previous attempt to answer this question). Tsuneda and co-workers1 have employed long-range […]
Computational Organic Chemistry » Origin of DFT failures – part III responded on 23 Sep 2013 at 11:53 am #
[…] 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 […]