Small Atomic Orbital Basis Set First-Principles Quantum Chemical Methods for Large Molecular and Periodic Systems: A Critical Analysis of Error Sources

Sure, R.; Brandenburg, J. G.; Grimme, S. ChemistryOpen, EarlyView, DOI: 10.1002/open.201500192 (CC by-nc-nd)
Contributed by Grant Hill

The use of density functional theory (DFT) calculations to produce insights into the chemistry unveiled by experiment is widespread due to its relative ease-of-use and ability to explain many chemical phenomena of interest. In particular, the B3LYP hybrid functional [1] and the Pople-type 6-31G* basis set [2] are incredibly popular, with some referring to this as Default Favourite Theory (a play on DFT).[3] A recent review by Grimme and co-workers sets out a case against using this B3LYP/6-31G* model chemistry by careful examination of errors.

The review contends that the use of small basis sets such as 6-31G* leads to relatively large errors due to both basis set superposition error (BSSE) and basis set incompleteness error (BSIE). It's not entirely clear how to separate these two terms and as a result the review mostly focuses on the BSSE element, with some emphasis on intramolecular BSSE in addition to the more familiar intermolecular BSSE. The question of why B3LYP/6-31G* still performs well in a number of cases is then examined in terms of a fortuitous cancellation of errors between BSSE and London forces (dispersion energy). It is demonstrated that this cancellation cannot be relied upon in all cases and a convincing case is made for choosing different basis sets and methods. While the review mostly focuses on intermolecular interactions, there is some generalisation to other problems of interest.

A number of alternative methods for including dispersion in DFT calculations are reviewed, and final recommendations are made that can easily be incorporated into the workflow of a non-specialist, without a significant increase in computational cost. This includes the use of the def2-SVP basis set of Weigend, Ahlrichs and co-workers.[4] This review should make for interesting reading for anyone routinely using DFT methods in conjunction with double-zeta basis sets.

References:
[1]a) Stephens, P. J.; Devlin, F. J.; Chablowski, C. F.; Frisch, M. J. J. Phys. Chem. 1994, 98, 11623. b) Becke, A. D. J. Chem. Phys. 1993, 98, 5648.
[2] Hehre, W. J.; Ditchfield, R.; Pople, J. A. J. Chem. Phys. 1972, 56, 2257.
[3] I first heard this at the Computational Molecular Science conference in 2008, but I can't recall the originator. The late Nick Handy responded by suggesting that DFT could instead be "Damn Fine Theory".
[4] See Weigend, F.; Ahlrichs, R. Phys. Chem. Chem. Phys. 2005, 7, 3297 and references therein. These basis sets are available to download from the EMSL basis set exchange in formats suitable for most electronic structure packages.