How to calculate number of basis functions and primitive gaussians for some of Pople's split-valence basis sets?

Bartłomiej Gostyński @Bartlomiej-Gostynski-2

24 October 2017 4 6K Report

I was trying lately to calculate by hand the number of basis functions and primitive gaussians for CH4 using Pople's split-valence basis sets, namely 6-31G, 6-31G(d) and 6-31g(d,p) and compare my results to Gaussian09 output.

And when it comes to the two first basis - my calculations seem to be in prefect agreement with computer ones (6-31G: 17 basis functions, 38 primitive gaussians; 6-31G(d): 23 basis functions, 44 primitive gaussians) but for the 6-31G(d,p) basis according to my point of view thare's only 34 basis functions and 55 primitive gaussians. Gaussian output suggests however that it should be 35 basis functions and 56 primitve gaussians. Could someone find where I'm losing that additional function and which factors I'm not taking into account? I'm working with default (6d,7f) way of handling higher orbitals.

My way of thinking:

1s (core) - 1 contraction (6 prim. gauss) + 1 extra P-function ['contraction' of 1 prim. gauss.] [a bit far-fetched for me but because of (d,P)(?); the same for 2s]

2s (valence) - 1 contraction (3 prim. gauss) + 1 extra P-function ['contraction' of 1 prim. gauss.] , 1 'contraction' (1 prim. gauss) + 1 extra P-function ['contraction' of 1 prim. gauss.]

2px (valence) - 1 contraction (3 prim. gauss) + 1 extra D-function ['contraction' of 1 prim. gauss.], 1 'contraction' (1 prim. gauss) + 1 extra D-function ['contraction' of 1 prim. gauss.]

2py (valence) - 1 contraction (3 prim. gauss) + 1 extra D-function ['contraction' of 1 prim. gauss.], 1 'contraction' (1 prim. gauss) + 1 extra D-function ['contraction' of 1 prim. gauss.]

2pz (valence) - 1 contraction (3 prim. gauss) + 1 extra D-function ['contraction' of 1 prim. gauss.], 1 'contraction' (1 prim. gauss) + 1 extra D-function ['contraction' of 1 prim. gauss.]

TOTAL - 18 basis functions; 31 primitive gaussians

H(1):

1s (valence) - 1 contraction (3 prim. gauss) + 1 extra P-function ['contraction' of 1 prim. gauss.], 1 'contraction' (1 prim. gauss) + 1 extra P-function ['contraction' of 1 prim. gauss.]

H(2):

1s (valence) - 1 contraction (3 prim. gauss) + 1 extra P-function ['contraction' of 1 prim. gauss.], 1 'contraction' (1 prim. gauss) + 1 extra P-function ['contraction' of 1 prim. gauss.]

H(3):

1s (valence) - 1 contraction (3 prim. gauss) + 1 extra P-function ['contraction' of 1 prim. gauss.], 1 'contraction' (1 prim. gauss) + 1 extra P-function ['contraction' of 1 prim. gauss.]

H(4):

1s (valence) - 1 contraction (3 prim. gauss) + 1 extra P-function ['contraction' of 1 prim. gauss.], 1 'contraction' (1 prim. gauss) + 1 extra P-function ['contraction' of 1 prim. gauss.]

TOTAL - 16 basis functions; 24 primitive gaussians

Altogether - 34 basis functions; 55 primitive gaussians

Krishnendu Maity

6-31G(d,p) - the d polarization is added to the non hydrogen atoms and p polarization to the hydrogen ones.

I count the following way --

CH4

C-- 1s (6G), 2s (3G+1G), 2px, y, z ([3G+1G] three times) + 6G (d polarizations- dxx, dyy, dzz, dxy, dyz, dxz)----total 28 gaussians

H-- 1s (3G+1G) + 3G (p-polarizations--px, py, pz)--total 7 gaussians for one H

so, for CH4--- 28 + 7x4 = 56 gaussians

Basheer Al-Anesi

In case of 6-31G(d ). the d polarization is added to the heavy atoms (non- hydrogen)

example

for CH4 molecule

C: 1s 2s 2s´ 2Px 2Py 2Pz 2P´x 2P´y 2P´z d1 d2 d3 d4 d5 d6 =15

H: 1s 1s´=2

H: 4*2=8

CH4= 15+8=23 number of basis functions

Gaurav Jhaa

For : 3-21G

Primitive Gaussian counting:-

CH4

C à1s (3G), 2s (2G+1G), 2px, y, z ([2G+1G] three times) à total 15 primitive Gaussians

H à 1s (2G+1G) à total 3 primitive Gaussians for one H

so, for CH4 : 15 + 3x4 = 27 primitive Gaussians

For : 6-31G(d,p)

Primitive Gaussian counting:-

CH4

C à1s (6G), 2s (3G+1G), 2px, y, z ([3G+1G] three times) + 6G (d polarizations - dx2, dy2, dz2, dxy, dyz, dxz) à total 28 primitive Gaussians

H à 1s (3G+1G) + 3G (p-polarizations - px, py, pz) à total 7 primitive Gaussians for one H

so, for CH4 : 28 + 7x4 = 56 primitive Gaussians

For: 6-31G(d)

Primitive Gaussian counting:-

CH4

C à1s (6G), 2s (3G+1G), 2px, y, z ([3G+1G] three times) + 6G (d polarizations - dx2, dy2, dz2, dxy, dyz, dxz) à total 28 primitive Gaussians

H à 1s (3G+1G) à total 4 primitive Gaussians for one H

so, for CH4 : 28 + 4x4 = 44 primitive gaussian

https://gauravjhaa.blogspot.com/2023/02/basis-sets-in-theoretical-chemistry.html

Gaurav Jhaa

https://gauravjhaa.blogspot.com/2023/02/basis-sets-in-theoretical-chemistry.html

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