6-31G(2df,p) basis has two polarization functions on hydrogen

[paulsaxe]

https://www.basissetexchange.org/basis/6-31g(2df,p)/format/gaussian94/?version=0&elements=1

The downloadable basis for H looks like this

! Basis Set Exchange
! Version 0.10
! https://www.basissetexchange.org
!----------------------------------------------------------------------
!   Basis set: 6-31G(2df,p)
! Description: 6-31G(2df,p)
!        Role: orbital
!     Version: 0  (Data from the original Basis Set Exchange)
!----------------------------------------------------------------------


H     0
S    3   1.00
     18.7311370              0.03349460
      2.8253937              0.23472695
      0.6401217              0.81375733
S    1   1.00
      0.1612778              1.00000000
P    1   1.00
      1.5000000              1.0000000
P    1   1.00
      0.3750000              1.0000000
****

Gaussian claims it uses the following:

  1.87311370E+01  2.82539436E+00  6.40121692E-01  1.61277759E-01  1.10000000E+00
Contraction coefficients                   R   N=           5
  3.34946043E-02  2.34726953E-01  8.13757326E-01  1.00000000E+00  1.00000000E+00

which is the same for the valence (one extra decimal in the coefficient) but only 1 P function on H with exponent 1.1.

The notes for the basis set indicate that this was an error in the original BSE, which has not apparently been fixed:

   Original BSE Contributor: Edoardo Apra
            Original BSE PI: J.A. Pople
 Original BSE Last Modified: Mon, 11 Jul 2016 23:51:20 GMT
--------------------------------------------------------------------------------

In the original BSE, this basis set erroneaously uses 2p on H,He rather than a single p

[paulsaxe]

Note that the P exponents are not those in 6-31G(x,2p), which are 2.2 & 0.55

  1.87311370E+01  2.82539436E+00  6.40121692E-01  1.61277759E-01  2.20000000E+00
  5.50000000E-01
Contraction coefficients                   R   N=           6
  3.34946043E-02  2.34726953E-01  8.13757326E-01  1.00000000E+00  1.00000000E+00
  1.00000000E+00