# Are multiplet free atoms multireference?

In general, my understanding is that free radicals and non-equilibrium molecules sometimes need multireference electronic structure calculations, mainly because of different electronic states being close in energy.

When I want to describe the electron density of a free atom with a multiplicity given by Hund's rule (that is, triplet carbon and sulfur, for example), then there's two arguments that I could be making:

• There is degeneracy, but only in the ground state, but the degenerate states are completely equivalent by symmetry; and
• From experimental spectroscopy I can assume that there's a large HOMO-LUMO gap.

The first argument would point me to the need of multireference (but not convincingly), but the second point suggests that a single determinant is enough.

So, in general, can I get correct electron densities for free atoms from let's say coupled cluster calculations, or do I need to do multireference?

Open shell atoms are multireference pretty much by definition. Take fluorine, for example, which has a $$1s^2 2s^2 2p^5$$ electron configuration and a $$^2P$$ ground state. We know that the electronic Hamiltonian commutes with the $$\hat{L}^2$$, $$\hat{S}^2$$ and $$\hat{L}_z$$ operators. If you use a single-determinant method such as Hartree-Fock (HF) or Kohn-Sham density functional theory (DFT), you will not get an eigenstate of $$\hat{L}^2$$ or $$\hat{S}^2$$; instead, you will get symmetry breaking.
PS. Note that the atomic physics community has a different definition for HF: their HF is not a single-determinant method, but a single (atomic) configuration method where the wave function ansatz is a proper eigenstate of $$\hat{L}^2$$ and $$\hat{S}^2$$. Similarly, DFT people tend to assume spherical symmetric densities for atoms; this amounts to using fractional occupations in the calculation so one is screwing up physics to some extent. The same words are used for different methods, so one has to be careful about which meaning is used in what context.