# How to find out the multiplicities of molecules containing d and f block species?

I know that the U atom has four unpaired electrons. Therefore it has a total spin S of 2. This means its multiplicity is 2S+1 = 5. Now consider a complicated molecule such as $$UF_6$$. In theory all I need to do is calculate how many unpaired electrons exist and then for each un paired electron assign a value of 0.5 in order to get the toal spin S and then use the fact that the multiplicity is 2S +1. However when dealing with d and f block elements things get much trickier and I am unable to work the multiplicity out. Is there a straighforward way to determine the multiplicity of $$UF_6$$, or better still an online database that contains this information for many different molecules (as I would also like to eventually determine the multiplicities of Uranium and Tungsten oxides) .

Thanks.

With metals, they can often exist as different multiplicities depending on the compound they are in and it is not always simple to predict the correct multiplicity. More often than not, determining the multiplicity of the ground state is either done experimentally or by comparing the energies of likely multiplicities computationally.

In your case, it seems be to well established [1-3] that $$\ce{UF6}$$ has a closed shell (and thus singlet) ground state. For other metal compounds, you should generally seek out an experimental value first and if you can't find one, you will essentially need to brute force the problem, calculating all possible multiplicities to determine which is the global minimum.

1. P. Jeffrey Hay , "Ab initio studies of excited states of polyatomic molecules including spin‐orbit and multiplet effects: The electronic states of UF6", The Journal of Chemical Physics 79, 5469-5482 (1983) https://doi.org/10.1063/1.445665
2. Fan Wei, Guo-Shi Wu, W. H. Eugen Schwarz, and Jun Li "Excited States and Absorption Spectra of UF6: A RASPT2 Theoretical Study with Spin–Orbit Coupling" Journal of Chemical Theory and Computation 2011 7 (10), 3223-3231 https://doi.org/10.1021/ct2000233
3. Shao-Wen Hu, Xiang-Yun Wang, Tai-Wei Chu, and Xin-Qi Liu The Journal of Physical Chemistry A 2008 112 (37), 8877-8883 https://doi.org/10.1021/jp804797a
• +1 But it looked a bit odd to see perhaps for the first time, a question with an answer but 0 votes. Is there anything we can do to edit/improve the question to earn your upvote? Jul 29, 2021 at 19:46
• @NikeDattani Just an oversight on my part. This started as a comment, but I wound up finding these papers that I felt were worth including in answer, just forgot to upvote until after I had finished typing up the answer.
– Tyberius
Jul 29, 2021 at 19:48
• +1. Just a small comment: it is sometimes non-trivial to even determine all the "possible multiplicities". Some chemical intuition is still needed for determining the maximum possible spin multiplicity, so that only a finite number of calculations need to be done. Many people have heard of the rule "try spin multiplicities 1, 3, 5, 7, ... for even-electron systems, and 2, 4, 6, 8, ... for odd-electron systems", but unfortunately some of them neglect the ellipses, and just blindly try all multiplicities till 7 (or 8) and stop. I've actually seen such a case where the correct multiplicity is 11. Sep 9, 2022 at 7:19

To obtain the spin multiplicity of the ground electronic state of a molecule, can be extremely hard.

In your question you mentioned $$\ce{UF6}$$ which has 7 atoms, and not all of them being of the same element. But even for a very simple homonuclear (all atoms being of the same element) diatomic molecule like $$\ce{Fe2}$$, my answer to "Total spin and/or multiplicity for transition metal ions?" shows that several papers from 1975-2015 were dedicated to trying to figure out the ground state spin configuration and still there was no consensus.

A table that I presented in my answer to "How to determine occupied and closed orbitals for a Molpro CASSCF calculation?" shows that $$\ce{Fe2}$$ is not the only homonuclear diatomic molecule for which the spin state remained unknown even after more than a century of modern spectroscopy and quantum mechanics.

Unfortunately to determine the ground state spin multiplicity of a complicated molecule, one needs to either:

• calculate many energies of the molecule, each time assuming a different spin multiplicity, until you have considered all of the possible candidates, and pick the one that has the lowest energy; or

• do spectroscopy experiments and find the ground state (most stable version of the molecule) that way.