The Elephant in the Room of Density Functional Theory Calculations

Stig Rune Jensen, Santanu Saha, José A. Flores-Livas, William Huhn, Volker Blum, Stefan Goedecker, and Luca Frediani (2017) (Updated paywalled version)

Contributed by Jan Jensen

While basis set convergence sounds straightforward (though time-consuming) it is hard to rule out that underlying assumptions in  the design of the basis set influences the results.  However, converged basis set DFT results are needed to separate basis set errors from errors due to the functional. Multiwavelets, a systematic and adaptive multiresolution numerical solution of the one-electron problem, appear to be a way around this.

The paper presents PBE and PBE0 total energies, atomization energies, and dipoles moments for 211 molecules that are converged with respect to basis set to μHartree accuracy, and benchmarks Gaussian-type orbitals (GTOs), all-electron numeric atom-centered orbitals (NAOs) and full-potential augmented plane wave (APW) calculations. 

In the case of atomization energies, a quintuple GTO basis set (aug-cc-pV5Z) is needed to reach a 1 kcal/mol accuracy in both MAE and RMSE. For aug-cc-pVQZ the MAE is below 1 kcal/mol, but the RMSE is about 1.5 kcal/mol.  Perhaps more importantly, the maxAE goes from ca 10 to 2-5 kcal/mol on going from quadruple to pentuple basis set.  So even aug-cc-pV5Z cannot consistently reach the basis set limit for atomization energies!  It would have been very interesting to see whether extrapolated-CBS values are able to do this.

This dataset will be an important resource for developers of both DFT and basis sets.

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Simulation-Based Algorithm for Two-Dimensional Chemical Structure Diagram Generation of Complex Molecules and Ligand–Protein Interactions

Frączek, T. J. Chem. Inform. Model. 2016, 56, 2320-2335
Contributed by Steven Bacharach
Reposted from Computational Organic Chemistry with permission

Making a good drawing of a chemical structure can be a difficult task. One wants to prepare a drawing that provides a variety of different information in a clean and clear way. We tend to want equal bond lengths, angles that are representative of the atom’s hybridization, symmetrical rings, avoided bond crossings, and the absence of overlapping groups. These ideals may be difficult to manage. Sometimes we might also want to represent something about the actual 3-dimensional shape. So for example, the drawing on the left of Figure 1 properly represents the atom connectivity with no bond crossing, but the figure on the right is probably the image all organic chemists would want to see for cubans.

Figure 1. Two drawing of cubane

For another example, the drawing on the left of Figure 2 nicely captures the relative stereo relationships within D-glucose, but the drawing on the right adds in the fact that the cyclohexyl ring is in a chair conformation. Which drawing is better? Well, it likely is in the eye of the beholder, and the context of the chemistry at hand.

Figure 2. Two drawings of D-glucose.

Frączek has reported on an automated procedure for creating aesthetically pleasing 2-D drawings of chemical structures.¹ The method involves optimizing distances between atoms projected onto a 2-D plane, along with rules to try to keep atom lengths and angles similar, and symmetrical rings, and minimize overlapping bonds. He shows a number of nice examples, especially of natural products, where his automated procedure PSM (physical simulation method) provides some very nice drawings, often noticeably superior to those generated by previously proposed schemes for preparing drawings.

Using the web site he has developed (http://omnidepict.p.lodz.pl/), I recreated the structures of some of the molecules I have discussed in this blog. In Figure 3, these are shown side-by-side to my drawings. My drawings were generally done with MDL/Isis/Accelrys/Biovia Draw (available for free for academic users) with an eye towards representing what I think is a suitable view of the molecule based on what I am discussing in the blog post. For many molecules, PSM does a very nice job, sometimes better than what I have drawn, but in some cases PSM produces an inferior drawing. Nonetheless, creating nice chemical drawings can be tedious and PSM offers a rapid option, worthy of at least trying out. Ultimately, what we decide to draw and publish is often an aesthetic choice and each individual must decide on one’s own how best to present one’s work.

My Drawing	PSM

Figure 3. Comparison of my drawings vs. drawing made by PSM.

References

1) Frączek, T., "Simulation-Based Algorithm for Two-Dimensional Chemical Structure Diagram Generation of Complex Molecules and Ligand–Protein Interactions." J. Chem. Inform. Model. 2016, 56, 2320-2335, DOI: 10.1021/acs.jcim.6b00391.

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