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.