Why am I getting wrong information about basis functions on running gaussian calculation using the 6-31G basis set for the krypton atom?

Question

This is the information about basis functions which I am getting on doing Gaussian calculation. But according to the best of my knowledge Kr has six primitive Gaussians for 1s, 2s,2p, 3s, and 3p orbitals, and a split-valence pair of three and one primitives for valence orbitals, which are 4s, 4p, and 3d.

Here is the .com file for the calculation

%mem=90mw
%nprocs=23
%chk=Kr.chk
#HFS/6-31G output=wfn Pop =full
gfinput

title card

0 1
Kr     0.000000     0.000000     0.000000

Kr.wfn

These are the basis functions which I am getting.

 Standard basis: 6-31G (6D, 7F)
 AO basis set in the form of general basis input (Overlap normalization):
      1 0
 S   8 1.00       0.000000000000
      0.6057000000D+06  0.2196315394D-03
      0.9030000000D+05  0.1664833237D-02
      0.2092000000D+05  0.8639235302D-02
      0.5889000000D+04  0.3524208999D-01
      0.1950000000D+04  0.1121508530D+00
      0.7182000000D+03  0.2733050295D+00
      0.2854000000D+03  0.4336665192D+00
      0.1186000000D+03  0.2721971781D+00
 S   2 1.00       0.000000000000
      0.3816000000D+02  0.2786214677D+00
      0.1645000000D+02  0.7462366170D+00
 S   1 1.00       0.000000000000
      0.5211000000D+01  0.1000000000D+01
 S   1 1.00       0.000000000000
      0.2291000000D+01  0.1000000000D+01
 S   1 1.00       0.000000000000
      0.4837000000D+00  0.1000000000D+01
 S   1 1.00       0.000000000000
      0.1855000000D+00  0.1000000000D+01
 P   6 1.00       0.000000000000
      0.4678000000D+04  0.1377789341D-02
      0.1120000000D+04  0.1212089588D-01
      0.3571000000D+03  0.5975547326D-01
      0.1314000000D+03  0.2240843064D+00
      0.5286000000D+02  0.4076562538D+00
      0.2270000000D+02  0.4523828826D+00
 P   3 1.00       0.000000000000
      0.9547000000D+01  0.2904719606D+00
      0.4167000000D+01  0.5334844307D+00
      0.1811000000D+01  0.2708313155D+00
 P   1 1.00       0.000000000000
      0.5337000000D+00  0.1000000000D+01
 P   1 1.00       0.000000000000
      0.1654000000D+00  0.1000000000D+01
 D   5 1.00       0.000000000000
      0.1256000000D+03  0.1917698437D-01
      0.3531000000D+02  0.1258630876D+00
      0.1215000000D+02  0.3661649364D+00
      0.4350000000D+01  0.5030491390D+00
      0.1494000000D+01  0.2632849056D+00
 ****

Answer 1

This is a great question, and a bit of a rabbit hole

The simple (but unsatisfactory) answer is that the 6-31G keyword in Gaussian does not use a 6-31G style basis set for the atoms Ga-Kr.

Instead it uses a completely different basis set that doesn't conform to the Pople style naming convention. The basis set you are looking at is the contracted (14s11p5d) -> [6s4p1d] basis set by Binning and Curtiss, first published in 1990. In this naming convention, the first set of numbers (14s11p5d) correspond to the number of overall Gaussian primitives of each type, while the second set [6s4p1d] describe how these primitives are arranged (or contracted) into 11 overall basis functions. So for the S-type functions for example, there are 14 total Gaussian primitives in the set, contracted into 6 basis functions. You'll see both sets of numbers match the output printed by Gaussian. In their paper, the authors named their new basis set the "641 basis", but this name has no correlation to the Pople style naming convention.

You'll be glad to know you're not the first to be bamboozled by this unexpected behaviour. On the BSE, the family notes have this to say:

... Gaussian choses a different basis set for Ga-Kr. They have chosen the basis sets found in blaudeau1997a. This basis is not consistent with the typical terminology, and therefore moved to 6-31G(C), as recommended in rassolov2001a.

The blaudeau1997a reference is to yet another different basis set, suggesting that at one point Gaussian used a different (but still not 6-31G) basis for Ga-Kr, or else the author got their references mixed up.

Gaussian's inconsistent use of the 6-31G basis set has also been fairly thoroughly explored in this paper, where the authors describe the different calculation results for 6-31G between Gaussian and GAMESS. There are numerous differences in the basis set used from Na onwards.

The natural follow-up question is why does Gaussian do this.

Frustratingly, the Gaussian manual doesn't describe or explain this behaviour, but they do correctly cite the Binning and Curtiss paper in their references for 6-31G, so it certainly seems deliberate.

The first issue to consider is the natural ambiguity of applying the Pople basis set names to atoms beyond the third period. Up to Ar, it's obvious which shells are valence and what sub-shell types are contained in each. The first shell has 1s, the second shell has 2s, 2p, and the third shell has 3s and 3p. For the fourth period, things aren't so simple. At what point do we need to consider d-shells? Clearly for Sc onwards, but what about K and Ca? Is the 3d still valence for Ga-Kr, or can we consider it to be core now? Perhaps most importantly, do we need to use the same methodology for the s, p, and d block, or can we change to match the different behaviour of the elements in each?

Whether for these reasons and/or for others, the development of a 6-31G style basis for K onwards was delayed compared to the earlier periods. Rassolov et al. published a 6-31G and 6-31G* basis set for K - Kr in 2000, which I think is the first to adhere to the 6-31G structure although there may have been earlier attempts. They directly acknowledge some of these challenges:

Therefore, the 3d shell must be included into the valence space of calcium. This is contrary to our earlier version of an 6-31G basis set, where d-functions were included only for transition metals.

and

The d-functions are less important for potassium chemistry. However, for consistency we treat all of the third row in the uniform way.

This leaves a ~10 year gap between Binning/Curtiss and Rassolov. It seems likely that Gaussian adopted the earlier non-standard basis set before the Rassolov paper, and then for backwards compatibility chose not to update to the standard form later. The newer Rassolov basis might also have performed worse than the Binning/Curtiss set, it certainly didn't perform as well as the 'old' basis set for K and Ca:

The 6-31G and 6-31G∗ basis sets performs slightly worse than the old basis set by Blaudeau et al.

20 years later, it seems these decisions are too ingrained to be reversed, and we're now stuck with a weird mix of basis sets for what should be a simple keyword.