Are multiplet free atoms multireference?

Question

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?

Answer 1

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.

However, this is not considered a huge issue in practice; DFT practitioners happily carry out calculations on open shell atoms to determine singlet-triplet gaps or atomization energies, for instance. The calculations can just be hard to converge due to the plethora of local minima caused by open shells, especially for transition metals or lanthanides and actinides.

Coupled cluster theory is exact in principle. The question there is whether you are going to high enough rank in the excitations to capture the effects of strong correlation. For main group elements single reference CCSD is already quite accurate, as far as I know, and it is also commonly used by the atomic physics community. CCSD was also used in the famous study by Medvedev et al to calculate reference electron densities for ions with 2, 4 and 10 electrons. It should also be feasible to compute electron densities with CCSDT or CCSDTQ with modern quantum chemistry codes, and doing so observe how the density converges with improved description of electron correlation.

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.