This question is a follow-up of this post.
The basis set to approximate the overlap, kinetic, electron repulsion and proton-electron attraction matrices is to be choosed by the user depending on the method. What I want is to code a STO-6G UKS code. Let's take two examples so that I can understand and then implement these ideas afterwards :
Example $NO_2$ :
The valence orbitals of $N$ : $2p_x$, $2p_y$ and $2p_z$ and the valence orbitals of $O$ : $2p_x$, $2p_y$ and $2p_z$ with one of the p orbitals filled.
I will not take the frozen approximation of the s-orbitals.
I denote : $\chi^{orbital}_O$ and $\chi^{orbital}_N$ the spatial part of the atomic orbitals for orbital $\in \{1s, 2s, 2p_x, 2p_y, 2p_z \}$.
Then what is the spatial-spin orbital basis set of the overlap, kinetic, Coulomb (Exchange) and proton attraction operators/matrices for each electronic structure methods by only using 1s, 2s and 2p orbitals?
What I think atm :
RKS case
The basis are the same for $\alpha$ and $\beta$ spin orbitals. The the energy is simply the total energy of the $\alpha$ molecular orbitals mutiplied by two since the density is supposed to be the same for $\alpha$ and $\beta$ molecular orbitals.
ROKS/UKS case
I think that the matrices of one of the spin will be at least one size larger.
Example $O_2$ :
Same question for $O_2$.