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I was wondering if anyone can tell me if or if not the wavefunctions used to construct the electron density in density functional theory contains hybridizied orbitals.

I have been working with a planewave pseudopotential code and in the input file of a pseudopotential, say Nickel, it only contains values for l=0 (s-orbital), l=1 (p-orbital) and l=2 (d-orbital). If I would want to calculate NiO, I would include another pseudopotential input file, Oxygen, which contains simply the s and p orbital terms.

Thus, as I understand it, the wavefunctions for Ni and O are built only from their respective atomic orbitals. My question is, do they get hybridizied? Is there an algorithm for these atomic orbitals to somehow be made into a t2g or eg orbital, thus initializing a new wavefunction to be fed into the DFT calculation?

Thank you for any help and I welcome any corrections to my understanding.