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Is there a way to work out the geometries for the $\ce{UO_x}$ and $\ce{WO_x}$ species for ($x=1-3$).

I know that deducing the multiplicity (the number of unpaired electrons) in d and f block containing molecules is difficult however I believe that the multiplicity can directly affect the geometry of molecules. So I was wondering how can one deduce the geometry of such molecules if they can't determine the multiplicity.

Also, if anyone has any sources concerning the multiplicities/ geometries (or ideally both) for $\ce{UO_x}$ and $\ce{WO_x}$ ($x=1-3$), I would greatly appreciate it if they could provide me with them.

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    $\begingroup$ The safest way is to optimize the geometry under all possible multiplicities, and pick the one that has the lowest energy $\endgroup$
    – wzkchem5
    Aug 19, 2021 at 11:32
  • $\begingroup$ +1. What is the motivation for getting the multiplicities/geometries of UOx and WOx? People may feel more inspired to put effort into helping you with that if they know the motivation for it! $\endgroup$
    – Nike Dattani
    Aug 19, 2021 at 19:38
  • $\begingroup$ I am trying to look at ionisation scattering cross sections for these molecules by using the binary encounter bethe method. The multiplicity effects the cross sections computed so I would like to use the correct ones. $\endgroup$
    – DJA
    Aug 20, 2021 at 0:07

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You are correct that the optimum geometry for one spin multiplicity will in general be different for another spin multiplicity. Therefore if you want to know the geometry of the lowest-energy state of a molecule, a pre-requisite is to first know the electronic configuration (spin multiplicity and spatial configuration) of the lowest-energy state of the molecule, then optimize the geometry of the molecule in that specific electronic state. Since you don't know what the lowest-energy state of the molecule is, you might want to do a geometry optimization for all states.

Perhaps you were hoping that you could optimize the geometry at any multiplicity and deduce the geometry of the lowest-energy state based on that, but this is not correct at all. Even for a diatomic molecule (in this case $\ce{Na2}$, with the figure being from this paper), the lowest $^3 \Sigma_g$ state has a potential energy minimum at least 1 Bohr larger than the potential energy minimum for the lowest $^1 \Sigma_g$ state.

enter image description here

This type of difference is even worse in some cases, though much milder in other cases, but in any case, even a 0.5 Bohr difference in an equilibrium bond length of a diatomic can be considered enormous.

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