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I noticed when looking through the Basis set exchange website that the 6-311 Pople basis sets don't at all match their formulation once you go past the 2nd row of the periodic table. For example, oxygen's basis set looks like this (in Gaussian input format):

O     0 
S   6   1.00
8588.5000000              0.00189515       
1297.2300000              0.0143859        
299.2960000              0.0707320        
 87.3771000              0.2400010        
 25.6789000              0.5947970        
  3.7400400              0.2808020        
SP   3   1.00
 42.1175000              0.1138890              0.0365114        
  9.6283700              0.9208110              0.2371530        
  2.8533200             -0.00327447             0.8197020        
SP   1   1.00
  0.9056610              1.0000000              1.0000000        
SP   1   1.00
  0.2556110              1.0000000              1.0000000        

Where the core 's' orbital is formed from a contraction of 6 primitive gaussians and the valence 's' and 'p' orbitals are formed from a contracted set of 3 primitives and then two other sets of 1 primitive. Hence, 6-311.

Compare this to Sulfur:

S     0 
S   6   1.00
93413.4000000              0.0007430        
13961.7000000              0.0057930        
3169.9100000              0.0299540        
902.4560000              0.1190280        
297.1580000              0.3684320        
108.7020000              0.5772990        
S   3   1.00
108.7020000              0.1431860        
 43.1553000              0.6244650        
 18.1079000              0.2833660        
S   1   1.00
  5.5600900              1.0000000        
S   1   1.00
  2.1318300              1.0000000        
S   1   1.00
  0.4204030              1.0000000        
S   1   1.00
  0.1360450              1.0000000        
P   4   1.00
495.0400000              0.0083090        
117.2210000              0.0640240        
 37.7749000              0.2776140        
 14.0584000              0.7450760        
P   2   1.00
  5.5657400              0.6137120        
  2.2629700              0.4438180        
P   1   1.00
  0.8079940              1.0000000        
P   1   1.00
  0.2774600              1.0000000        
P   1   1.00
  0.0771410              1.0000000      

Why would this set of orbitals still get lumped together with the Pople basis sets when it doesn't resemble their formulation at all? And what is the meaning of this particular set of functions?

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From the Gaussian[1] webpage:

6-311G: Specifies the 6-311G basis for first-row atoms and the McLean-Chandler (12s,9p) → (621111,52111) basis sets for second-row atoms [McLean80, Raghavachari80b] (note that the basis sets for P, S, and Cl are those called negative ion basis sets by McLean and Chandler; these were deemed to give better results for neutral molecules as well).

I have no idea exactly why they still call it 6-311G: I suspect it is because this configuration provides a more accurate guess for a triple-zeta Pople basis set, and to create an entirely new basis set would be impractical.

What I do know is that when you use the '6-311G' basis set, you're not necessarily getting this configuration. What you're getting is a basis set which is roughly of this quality (computational effort, accuracy).

Whilst this explains the abnormality, it still doesn't explain the exact configuration: the original paper[2] suggests a (621111,52111) set whilst the set used is (621111,42111). I hope somebody can contribute to this and complete my answer as, whilst I recognise the abnormality, further investigation has led me to this confusion.

[1] http://gaussian.com,

[2] J. Chem. Phys. 72, 5639 (1980).

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