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It is often said that general chemistry students tend to have trouble with the proper use of significant figures. However, it turns out that they are in good company–quantum chemists have been doing the same mistake for years (and yes, I’m one of them!).

This article discusses the problem:

Uncertainties in Scaling Factors for ab Initio Vibrational Frequencies
Karl K. Irikura, Russell D. Johnson III, and Raghu N. Kacker
J. Phys. Chem. A; 2005; 109 pp 8430 - 8437;

http://dx.doi.org/10.1021/jp052793n

As you may know (if you do quantum chemistry), the vibrational frequencies from ab initio calculations are systematically wrong, so they are often fudged by multiplying them by a “scaling factor". This factor is usually reported with four figures (something like 0.8982).

The authors of this article estimated the uncertainty of the scaling factor itself, and concluded:

The uncertainties presented in Table 1 reveal that the scaling factors are accurate to only two significant figures. The common practice of reporting four significant figures overstates the precision of vibrational scaling factors.

Figure 2 is especially revealing. It also shows that the basis set hardly affects the scaling factor, once the error bars are taken into consideration.

So, if this article is right, it turns out that generations of quantum chemists are sometimes no better than undergrads when it comes to reporting their results with “honest” precision!