How should one add diffuse functions to the basis set? Diffuse functions are known to be critical in describing the electron distribution of anions (as discussed in my book), but they are also quite important in describing weak interactions, like hydrogen bonds, and can be critical in evaluating activation barriers and other properties.

The Truhlar group has been active in benchmarking the need of basis functions and their recent review^{1} summarizes their work. In particular, they recommend that for DFT computations a minimally augmented basis set is appropriate for examining barrier heights and weakly bound systems. A minimally augmented basis set would have s and p diffuse functions on heavy atoms for the Pople split-valence basis sets and the Dunning cc-pV*xZ basis sets.*

For wavefunction based computations, they recommend the use of the “jun-“ basis sets. The “jun” basis set is one of the so-called calendar basis set derived from the aug-cc-pV*x*Z, which includes diffuse functions of all types. So, for C in the aug-cc-pVTZ basis set, there are diffuse *s, p, d*, and *f* functions. The “jun-“ basis set omits the diffuse *f* functions along with all diffuse functions on H.

The great advantage of these trimmed basis sets is that they are smaller than the fully augmented sets, leading to faster computations. And since trimming off some diffuse functions leads to little loss in accuracy, one should seriously consider using these types of basis sets. As Truhlar notes, these trimmed basis sets might allow one to use a partially augmented but larger *zeta* basis set at the same cost of the smaller *zeta* basis that is fully augmented.

### References

(1) Papajak, E.; Zheng, J.; Xu, X.; Leverentz, H. R.; Truhlar, D. G., "Perspectives on Basis Sets Beautiful: Seasonal Plantings of Diffuse Basis Functions," *J. Chem. Theory Comput.*, **2011**,

*7*, 3027-3034, DOI: 10.1021/ct200106a

Qadir Timerghazin responded on 20 Dec 2011 at 1:10 pm

#It’s rather sad that antique basis set such as the venerable 6-31G* are still the most widely used basis sets around… Especially the 6-31G* itself that has the same d-exponent for all second-raw atoms. Pople’s basis sets played tremendous role in computational chemistry, but it is the time we start using better-constructed and better-optimized basis sets.

Also, aug-cc-pVxZ/cc-pVxZ basis sets are used quite a bit for DFT calculations, although they were developed and optimized for post-HF methods. For a while I thought that Jensen’s pc-family was the way to go for the DFT, but their sheer size and the general contraction scheme they use makes them not so practical. Karlsruhe def2- family seems promising, but lacks ‘official’ diffuse functions. Apparently, Truhlar group also developed minimalistic diffuse sets for def2-; it will be interesting to test these.

Holger Kruse responded on 21 Dec 2011 at 5:18 am

#“Karlsruhe def2- family seems promising, but lacks ‘official’ diffuse functions. ”

Not true anymore: Rappaport and Furche developed def2-SVPD, def2-TZVPD, etc. basis set for many elements. doi:10.1063/1.3484283 .

Truhlar seemed to have overlooked them…

Can be found in the EMSL. Although they are optimized for response they work very well in general and they, too, follow a minimalistic approach and thus using less diff functions than Dunnings “aug-” set.

Henry Rzepa responded on 21 Dec 2011 at 7:57 am

#Along with the functional zoo, we now have basis set zoos, constructed not just for optimal energies, but often for a myriad of other desired properties. Thus NMR shieldings and couplings often require “tuned” basis sets and I speak from experience with VCD spectroscopy that this requires a particularly tuned basis set. Semi-empirical theory went this way a few years ago, with parameter sets tuned to the project one wanted to do (Truhlar himself used to parametrise SE methods for a small section of a potential in order to do MD on it).

All this can cause problems. It is increasingly common to find geometries optimised at one level, and properties computed at another. One is constantly parameterising, calibrating, and finding suitable combinations for the various properties. Sadly, the “B3LYP” days, where a multitude of literature calibrations of this particular method were available are vanishing. And we are left with much uncertainty whether the results of any particular project may overly depend on poor calibration, wrong selection of functional or basis, unsuitable salvation method, etc. The chances of any two groups using the same combination are negligible, so one would rarely be able to compare two independent studies with proper balance.

Can we go on like this?

Steven Bachrach responded on 21 Dec 2011 at 8:30 am

#While Henry probably meant “unsuitable solvation method” perhaps we need a suitable “salvation” method.

The functional and basis set zoos are a truly complicating matter, especially for the beginner or less experienced user. Even for someone who has been doing this for a long time now, I often feel like I am choosing methods based more on hope than on some definitive logic.

The predominance of the old Pople basis sets even today is easy to understand. They are featured within Gaussian, and the code is optimized for their use – a 6-31G(d) computation is way faster than a cc-pVDZ computation.

Computational Organic Chemistry » Large water clusters and DFT performance responded on 25 Feb 2013 at 1:31 pm

#[...] the energies using 73 different density functionals with the jun-cc-pVTZ basis set (see this post for a definition of the ‘jun’ basis sets). Binding energies (relative to 16 isolated water molecules) were computed along with the 10 [...]