I am trying to code a simple UKS program. For RKS code, the AO basis functions are set of the spatial part of the wavefunction of every atom involved in the molecule. For ${H_2}$, this is the two Slater-type orbitals (STO) of each H. If you have a molecule involving an atom with a singulet electron (unfilled orbital like Li, B or N), what is the AO basis of the matrices in the ROHF and UKS case?

  • $\begingroup$ UKS=Unrestricted Kohn-Sham? $\endgroup$
    – Ian Bush
    Aug 12, 2023 at 21:36
  • $\begingroup$ Yes, it is the case. $\endgroup$
    – mle
    Aug 13, 2023 at 19:11
  • $\begingroup$ Since someone wrote an answer based on your first version of the question, changing the question will mean the answer will have to be changed. I recommend that you ask a new question if you want a new answer, so I rolled back your edit. $\endgroup$ Aug 13, 2023 at 20:08

1 Answer 1


You mention three different acronyms of electronic structure methods

  • UKS = Unrestricted Kohn-Sham
  • RKS (or ROKS) = Restricted open-shell Kohn-Sham
  • ROHF = Restricted open-shell Hartree-Fock

They differ in whether they are using different orbitals for spin alpha and beta electrons (unrestricted) or the same orbitals but with different occupation numbers (restricted). They also differ in the underlying Hamiltonian coming from Kohn-Sham density functional theory (KS) or Hartree-Fock (HF).

They do not say anything about the underlying basis of the electronic wave function - you can use the same basis for all three.

  • $\begingroup$ I understand your answer. I edited my questions so that the concepts can be applied to examples. $\endgroup$
    – mle
    Aug 13, 2023 at 9:05

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