# Naming of quantum chemistry basis sets

For some DFT calculations I performed with localized (Gaussian) basis sets, I wonder how the basis sets I used are properly named. The names I could gather are:

• H, C and O: 6-311G(d,p)
• Al: 8-511G*
• Ga: 86-4111d41G

(They all come from this website.)

However, I am not sure that the above names are consistent. Specifically:

1. Shouldn't I write 6-311G** instead of 6-311G(d,p), for consistency with 8-511G*?

2. 86-4111d41G looks weird to me, but I don't know how it could otherwise be named. My knowledge of basis sets naming conventions didn't really cover anything beyond the third period of the periodic table!

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Regarding 6-311G**:

The * notation (one for polarization functions on the heavy atoms and ** for polarization functions on the heavy and hydrogen atoms) is an older notation belonging to the split-valence basis sets of John Pople. Many people still use this notation today but if you want to be more precise and more descriptive, the (d,p) notation is what you would want to use. In fact, we only ever use the explicit (d,p) type notation and never use the *'s in my lab.

X-YZg

Split-valence basis sets have the aforementioned structure for us to quickly and easily determine how that basis set was constructed. The X simply is the number of primitive Gaussians that describe the core electron shells of an atom. Most of the time you will be freezing core in your computations so you split the core and valence regions of your atoms and assign various basis functions to each one. The Y and Z components mean you have two sets of primitive Gaussian functions which describe your valence region. Because you have two sets here, you can denote this basis set as a double-zeta. In your case, a 6-311G** is in fact a triple-zeta quality basis set, which is better than a double-zeta.

For the sake of interest, a 6-31+G* includes a + symbol. This simply means that diffuse functions would be added to the heavy atoms. A ++ symbol would extend these diffuse functions to the hydrogen atoms. Of course we would never want to use the '*' notation so I should have written this as 6-31+G(d,p). Of course polarization functions can come in sets as well such as 6-31+G(2df,2pd), and other combinations exist.

Lastly, when using split-valence basis sets such as 6-311G*, you must be very careful to check the manual and see what function space the program is going to use by default. I will use Gaussian 09 as an example. By default, Gaussian 09 uses spherical harmonics as its default... EXCEPT FOR A FEW DIFFERENT TYPES OF BASIS SETS including the family of 6-31G* type basis sets which uses the CARTESIAN SPACE BY DEFAULT. This means that rather than the 5D, 7F stuff that you may be used to using on a regular basis, invoking the 6-31G* type basis set will automatically use the 6D, 10F function set which inevitably changes the size of your basis set which means that you may have data that is not readily comparable to other things. I always opt out for the 5D, 7F type functions.

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Okay, thanks, so I'll rather use “8-511G(d)” instead of “8-511G*”. What about 86-4111d41G, do you have any insight on that one? –  F'x Nov 2 '12 at 12:56
Metals is something we comp chemists try to avoid like the plague. Again this basis set takes on that split-valence form so I would assume that you have 86 primitive Gaussians available to describe your core (which makes sense because metals have a larger core than 2nd row atoms). It also looks like a quadrulple-zeta quality basis set but I am unsure as to what the d41 stands for thought I would imagine it relates to some optimized coefficients on some valence orbitals. I'll check around and post if I find out more. –  LordStryker Nov 2 '12 at 14:38
The Ga basis set (here) has 8 shells, respectively: s-type, 8 Gaussians; sp-type, 6 Gaussians; sp-type, 4 Gaussians; 3 more s shells with one Gaussian; one d shell with 4 Gaussians; 1 more d shell with 1 Gaussian. As such, maybe it should be noted 8-64111G(d,d)? –  F'x Nov 2 '12 at 14:46
The notation isn't really complete enough to suggest a fully informative label, I fear. What I've seen people do with lesser-known heavy element basis sets is, after the label provided, just say how many functions you started with of what types, and how many you contracted them to, so, for example, this is 8s13(sp)5d contracted to 1s5(sp)2d. –  Aesin Nov 3 '12 at 17:03