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I don't see the STO-1G basis set in the available sets on the Gaussian website and the software (g16) throws an error if I try. I see how it seems possible to use a custom basis but I'm not entirely sure how to use that to run a HF/STO-1G. I was looking on the basissetexchange.org but there is no STO-1G available.

It seems to -e that such a simple set should be available (for technical analysis rather than accuracy, obviously) but I can't figure out how to use it.

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I don't believe there is a "STO-1G." Even if there were, it would exhibit poor performance.

The STO-nG basis sets were first published by Hehre, Stewart, and Pople in 1969: "Self-Consistent Molecular-Orbital Methods. I. Use of Gaussian Expansions of Slater-Type Atomic Orbitals"

Note that this was the first paper to use Gaussian approximations to Slater-type basis sets. There is no mention of an STO-1G.

We have obtained representations of Slater-type orbitals using 2-6 Gaussian functions by least-squares methods...

They conclude that STO-3G is an efficient minimal basis set:

The STO-3G set, in particular, is very economical to use and as a minimal (is, 2s, 2p) basis, can be applied to quite large organic molecules. Any further economy achieved by using an STO-2G set, however, is hardly worthwhile, since the calculation time is then dominated by the solution of the Roothaan equations, rather than integral evaluation.

While it is certainly possible to use one Gaussian to approximate the Slater atomic orbitals, the performance would be poor. Here's an example plot that I use in class.

comparison of Slater-type and Gaussian-type orbitals

Note that near the nucleus, the Gaussian-type function does a poor job of describing the wavefunction, and thus the electron density. Additionally, the single GTO is too high at medium range, and shows the wrong asymptotic behavior - it falls off too quickly at long range. (In other words, poor performance everywhere.)

Instead, if we use a best-fit to 3 Gaussian-type functions, we do a much better job at approximating the STO. Pretty much everywhere except very close to the nucleus has a good fit.

comparison of Slater-type to multiple Gaussians

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    $\begingroup$ Thanks for the answer. I understand that but from today's perspective, this 'sweet spot' argument doesn't really matter. STO-3G is terrible and shouldn't be used for actual calculations, just as much as 2G or 4G shouldn't be used. I need STO-1G for a 'conceptual' calculation rather than an interest in the result. I'd expect that somebody tried this out 'for the science of it' and fitted an STO-1G? $\endgroup$
    – ste
    May 6 at 16:18
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    $\begingroup$ STO-3G can sometimes be useful when you hit convergence issues, but yes I wouldn't recommend it otherwise. I did some searching and cannot find any reference to STO-1G, much less published parameters. It wouldn't be hard to do .. for element of interest, generate the relevant $s$ and $p$ STOs and do a best-fit for the Gaussian. $\endgroup$ May 6 at 16:21
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    $\begingroup$ Oh boy, okay, I never would've thought that I'll be fitting my own basis set. Thanks for the help! $\endgroup$
    – ste
    May 6 at 16:22
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    $\begingroup$ @ste - for something like STO-1G it would be fairly easy. Thus the example I use in class above. Maybe just pick something like water, in which you only need a few basis functions. :-) $\endgroup$ May 6 at 16:24

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