How to exploit STO-nG coefficients from basissetexchange (BSE)?

Question

I am trying to understand how to use the data of STO-6G basis from BSE in order to code my own DFT package. I started with a simple DFT code for H2. So the primitive gaussians are of the from : $$\left( \frac{2\alpha}{\pi} \right)^{\frac{3}{4}} e^{-\alpha x^2}$$

Let's take for example Neon in NWChem format:

#----------------------------------------------------------------------
# Basis Set Exchange
# Version v0.9.1
# https://www.basissetexchange.org
#----------------------------------------------------------------------
#   Basis set: STO-6G
# Description: STO-6G Minimal Basis (6 functions/AO)
#        Role: orbital
#     Version: 1  (Data from Gaussian09)
#----------------------------------------------------------------------


BASIS "ao basis" SPHERICAL PRINT
#BASIS SET: (12s,6p) -> [2s,1p]
Ne    S
      0.2146955475E+04       0.9163596281E-02
      0.3936419362E+03       0.4936149294E-01
      0.1101268283E+03       0.1685383049E+00
      0.3783153777E+02       0.3705627997E+00
      0.1469109318E+02       0.4164915298E+00
      0.6050603466E+01       0.1303340841E+00
Ne    SP
      0.8550442919E+02      -0.1325278809E-01       0.3759696623E-02
      0.1692355799E+02      -0.4699171014E-01       0.3767936984E-01
      0.5259829210E+01      -0.3378537151E-01       0.1738967435E+00
      0.2023645885E+01       0.2502417861E+00       0.4180364347E+00
      0.8788707870E+00       0.5951172526E+00       0.4258595477E+00
      0.4028507849E+00       0.2407061763E+00       0.1017082955E+00
END

Are the STO-nG coefficients the same for each of the p-orbitals ($p_x$, $p_y$ and $p_z$), d-orbitals, and higher angular momentum? If this is the case how can non-spherical effects be included?

Also what is the form of the primitive gaussian in case it must be changed from the Hydrogen/Helium case?

Answer 1

My first question is: why write your own package if you already have many open source ones upon which to build? NWChem, psi4, pyscf, …

Note: Ne does not have d-functions within STO-6G.

For the d-orbitals, have a look at the corresponding basis set for Kr, shown below with some comments added. For a clear explanation of what the functions and corresponding orbitals look like, read Szabo/Ostlund or Frank Jensen's "Introduction to computational chemistry". Or Google "split valence basis sets", and you will find e.g. David Sherill's lecture notes.

#----------------------------------------------------------------------
# Basis Set Exchange
# Version v0.9.1
# https://www.basissetexchange.org
#----------------------------------------------------------------------
#   Basis set: STO-6G
# Description: STO-6G Minimal Basis (6 functions/AO)
#        Role: orbital
#     Version: 1  (Data from Gaussian09)
#----------------------------------------------------------------------


BASIS "ao basis" SPHERICAL PRINT
#BASIS SET: (24s,18p,6d) -> [4s,3p,1d]
#MS: 1s orbitals 
Kr    S
      0.2885373644E+05       0.9163596281E-02
      0.5290300991E+04       0.4936149294E-01
      0.1480035573E+04       0.1685383049E+00
      0.5084321647E+03       0.3705627997E+00
      0.1974390878E+03       0.4164915298E+00
      0.8131631964E+02       0.1303340841E+00
#MS: 2s and 2p orbitals
Kr    SP
      0.2425796448E+04      -0.1325278809E-01       0.3759696623E-02
      0.4801284244E+03      -0.4699171014E-01       0.3767936984E-01
      0.1492235564E+03      -0.3378537151E-01       0.1738967435E+00
      0.5741168085E+02       0.2502417861E+00       0.4180364347E+00
      0.2493393212E+02       0.5951172526E+00       0.4258595477E+00
      0.1142904540E+02       0.2407061763E+00       0.1017082955E+00
#MS: 3s and 3p orbitals
Kr    SP
      0.1284965766E+03      -0.9737395526E-02      -0.8104943356E-02
      0.3700047197E+02      -0.7265876782E-01      -0.1715478915E-01
      0.1455321200E+02      -0.1716155198E+00       0.7369785762E-01
      0.6651312517E+01       0.1289776243E+00       0.3965149986E+00
      0.3310132155E+01       0.7288614510E+00       0.4978084880E+00
      0.1699958288E+01       0.3013317422E+00       0.1174825823E+00
#MS: 4s and 4p orbitals
Kr    SP
      0.8808666254E+01       0.3775056180E-02      -0.7052075733E-02
      0.2834325299E+01      -0.5585965266E-01      -0.5259505547E-01
      0.1211009836E+01      -0.3192946152E+00      -0.3773450392E-01
      0.6038871793E+00      -0.2764780132E-01       0.3874773403E+00
      0.3259517997E+00       0.9049199432E+00       0.5791672602E+00
      0.1812482827E+00       0.3406258162E+00       0.1221817127E+00
#MS: 3d orbitals 
Kr    D
      0.1284965766E+03       0.6633434386E-02
      0.3700047197E+02       0.5958177963E-01
      0.1455321200E+02       0.2401949582E+00
      0.6651312517E+01       0.4648114679E+00
      0.3310132155E+01       0.3434092326E+00
      0.1699958288E+01       0.5389056980E-01 
END