Sulfuric acid symmetry point group

On the following page: https://cccbdb.nist.gov/pglist.asp It appears that the point symmetry group of sulphuric acid is $$C_2$$. I know that $$C_2$$ means that there is an axis of symmetry of order 2 (180 degree rotation). But, I am not able to visualize it in the molecule.

In fact, you can see $$C_2$$ and other symmetry elements for yourself in 3D by opening the CIF [1, COD-2005680] with Mercury (free, available for Windows, Linux, MacOS):

Figure 1. Unit cell of crystalline sulfuric acid $$\ce{H2SO4}$$. Green lines parallel to crystallographic axis $$b$$ depict $$C_2$$ rotation axes.

This can be achieved by drawing the unit cell content with Calculate → Packing/Slicing… and adding symmetry elements of interest via Display → Symmetry Elements….

Figure 2. Single molecular unit $$\ce{H2SO4}$$ in two projections with the $$C_2$$ placed in drawing plane (left) and perpendicular to drawing plane (right).

References

1. Kemnitz, E.; Werner, C.; Trojanov, S. Reinvestigation of Crystalline Sulfuric Acid and Oxonium Hydrogensulfate. Acta Crystallographica Section C Crystal Structure Communications 1996, 52 (11), 2665–2668. https://doi.org/10.1107/S0108270196006749.
• How I can a draw the molecule on Mercury? @andseliskç – aprendiendo-a-programar Mar 31 '19 at 12:54
• @aprendiendo-a-programar I updated the answer with the link to CIF, which you can open with Mercury. This is an experimentally determined structure which you are not supposed to "draw" yourself. – andselisk Mar 31 '19 at 13:09
• @aprendiendo-a-programar No prob. Figure 2 is a compilation of two screenshots of a single molecule depicted in Mercury along two separate crystallographic axes which I added a "$C_2$" label in Inkscape (image editor) to. I decide to do so for clarity for those users who won't bother opening the structure in Mercury:) – andselisk Mar 31 '19 at 15:51
• Mercury is just a viewer (and certain functions are not available in free version), and it just takes the symmetry info from the CIF. However, Mercury is probably the best crystallographic tool for the beginners I ever encountered (the rest is even more cumbersome or costs money). As for ammonia, here is one I found by adding "H3" and "N" to "1 to 8 elements" field and "2" and "2" to "number of distinct elements min and max" (search hints). Unfortunately, no COD structures have H assigned. – andselisk Mar 31 '19 at 16:21
• I'd suggest to have a look at online tutorials such as Chemtube3d/Symmetry and Symmetry@Otterbein. Both offer similar 3D interactivity via JSmol, a JavaScript library for crystal structures, a desktop alternative to which is Jmol. You can also search Chemistry.SE (this site), I remember even I answered a couple of similar/related questions before. – andselisk Mar 31 '19 at 16:32

In the structure as drawn here, the axis is perpenducular to the plane of the paper passing through the sulfur atom.

• But, if I turn around that axis, every 180 degrees the molecule would not be as it was initially. @Oscar Lanzi – aprendiendo-a-programar Mar 31 '19 at 10:34
• Which atoms would be out of place? Look again... . – Oscar Lanzi Mar 31 '19 at 11:30