# Symmetry group of p-benzoquinone

I am trying to calculate the UV-visible spectrum of p-benzoquinone. In the literature, the point group of p-benzoquinone is $$D_{2h}$$, but when I optimize this molecule in the ground state with Gaussian software, I obtain the $$C_s$$ group symmetry.

I used a semi-empirical method # opt freq am1 geom=connectivity, than used this geometry as starting point for a DFT calculation # opt freq rb3lyp geom=connectivity and than # opt freq rb3lyp/6-31g(d) geom=connectivity. I tried changing the z-matrix, but I still have a $$C_s$$ group.

Is there any fault with my calculation? What can I do to have a $$D_{2h}$$ symmetry? If I use the $$C_s$$ geometry I obtained, will the UV-visible absorption spectrum be false?

Here are the links to the out-log files of my calculations:

• Related discussion of considerations for optimizations with symmetry when using the Wavefunction program: downloads.wavefun.com/FAQ/converge.html. This won't necessarily address what commands to use in Gaussian, but may give you some insight into what changes could be made to your initial geometry or how much of a problem the inexact symmetry could cause.
– Tyberius
Commented Dec 29, 2021 at 14:19
• @Tyberius Thank you very much for your comment, it is very helpful. Commented Dec 29, 2021 at 14:44

tldr: For a UV/Vis spectra, it shouldn't matter much.

I've found that Gaussian's AM1 / PM3 implementation often breaks symmetry during optimization. So I'm not surprised at your finding.

Moreover, in many cases, it's good to start with the expected symmetry geometry. For example, if I open the output in Avogadro, I can use Properties => Symmetry => Symmetrize to correct to $$D_{2h}$$ .. it seems very, very close. GaussView has a similar feature, as do many other interfaces (WebMO, etc.)

As mentioned in the comment, optimizations can break symmetry. In Gaussian, you can use, e.g.:

Symm=(Loose,Follow)


This loosens the symmetry perception in the initial step and requests that the point group (hopefully $$D_{2h}$$) is retained during optimization.

When you convert to a z-matrix, you can also force a symmetry by using symbolic notation to ensure corresponding bonds and angles are kept equivalent. The documentation gives the example of hydrogen peroxide:

H
O 1 R1
O 2 R2 1 A
H 3 R1 2 A 1 D
Variables:
R1 0.9
R2 1.4
A 105.0
D 120.0


Notice that the two H-O-O angles are defined as the same variable (A), and the H-O bond lengths are defined as identical (R1), ensuring symmetry no matter the optimized values.

It's a bit tedious, but you could do this for your benzoquinone. It looks like some of the bond angles are a tiny bit off, which is why Gaussian has optimized it into the $$C_s$$ point group.

Your question, though, is whether it will matter for UV/Vis spectra. In my experience, due to orbital symmetry, you might see some issues with excitation intensities (i.e., transitions that might be "forbidden" in the higher symmetry, but weak in the low-symmetry group). But in real life, molecules are dynamic, leading to such symmetry breaking anyway. So a symmetry-forbidden UV/Vis transition is usually just a weak excitation in an experimental spectra.

I'd worry much more about getting an accurate geometry and potential errors in your choice of methods. I don't remember G09 that well, but you should try to use a larger basis set (e.g., def2-TZVP) and ideally a dispersion-corrected functional (B3LYP-D3BJ if you want B3LYP) for the geometry. I'd also look at different methods for your TD-DFT calculations. This will matter more than a geometry in a symmetric subgroup.