# Forming Basis Functions from 6-31G Basis Set for Carbon Atom

I am a computer science grad and I am working to write an electronic structure calculation program and I am stuck at forming basis functions using 6-31G Basis set for atoms having higher atomic numbers (p,d,f shells).

For example, consider a gaussian g as

g(alpha) = (2*alpha/pi)^(3/4) * exp(-alpha*r^2).


Looking at the Carbon (1s2 2s2 2p2) basis set data for 6-31G basis set

C     0
S   6   1.00
0.3047524880D+04       0.1834737132D-02
0.4573695180D+03       0.1403732281D-01
0.1039486850D+03       0.6884262226D-01
0.2921015530D+02       0.2321844432D+00
0.9286662960D+01       0.4679413484D+00
0.3163926960D+01       0.3623119853D+00
SP   3   1.00
0.7868272350D+01      -0.1193324198D+00       0.6899906659D-01
0.1881288540D+01      -0.1608541517D+00       0.3164239610D+00
0.5442492580D+00       0.1143456438D+01       0.7443082909D+00
SP   1   1.00
0.1687144782D+00       0.1000000000D+01       0.1000000000D+01


How many basis functions will carbon have in this case? I have been following a lecture series which does HF SCF calculation for a simple H2 molecule where each Hydrogen atom has two basis functions as per 6-31G basis set.

H     0
S   3   1.00
0.1873113696D+02       0.3349460434D-01
0.2825394365D+01       0.2347269535D+00
0.6401216923D+00       0.8137573261D+00
S   1   1.00
0.1612777588D+00       1.0000000


I can write the two basis functions in the form

b1= 0.0334*g(18.73) + 0.2347*g(2.825) + 0.8137*g(0.64);
b2= g(0.161);


In a similar manner, how would I go about writing the basis functions for Carbon atom. Any advise would be very helpful as I am stuck in this for couple of days and haven't been able to find any substantial resource for this.

I did stumble upon this previous post but having a hard time figuring out how did 9 basis functions come for Carbon.

• Did you see the PDF in the 2nd update of the linked question? To get 9 basis functions, the name 6-31 tells you how to set it up. Starting from the electron configuration from carbon, you write the core orbitals as contraction of 6 Gaussian functions. The 1s orbital is the only core one in this case, so it is represented by one basis function. Then, the -31 says you write the valence orbitals as two functions: one a contraction of 3 Gaussians and the other a single Gaussian. For carbon, this makes 8 more basis functions for a total of 9. – Tyberius Oct 19 at 19:23