# Finding Symmetry number of a molecule [closed]

An isotopic variant of the molecule SF$$_6$$ is S$$^{19}$$F$$_4^{18}$$F$$_2$$, with the two $$^{18}$$F nuclei oriented axially, so that the $$^{18}$$F-S-$$^{18}$$F angle is 180°and the four $$^{19}$$F nuclei form a square in a plane perpendicular to the $$^{18}$$F-S-$$^{18}$$F axis. All of the bond lengths are equal. In the figure, the regions surrounding the $$^{18}$$F nuclei are shown in blue, and the regions around the $$^{19}$$F nuclei are shown in green.Two of the moments of inertia of S$$^{19}$$F$$_4^{18}$$F$$_2$$ are identical, and the third is slightly larger: I$$_A$$= I$$_B$$ = $$2.9942 ×10^{-45}$$ kg m$$^2$$ and I$$_C$$= $$3.0749×10^{-45}$$ kg m$$^2$$. Wikipedia describes SF$$_6$$ as an “extremely potent greenhouse gas.”

What is the symmetry number of S$$^{19}$$F$$_4^{18}$$F$$_2$$?

I have considered it and think there is one 4-fold axis, and two 2 fold axes, but still unsure if that is right

• Welcome to Chemistry Stack Exchange! Please edit your question to show your efforts at solving the problem Mar 19, 2020 at 0:04
• I made one edit, but haven't really been able to get anywhere as I am very confused! Mar 19, 2020 at 0:23
• One way to think about it is: Start from SF$_6$ without any isotope labeling, and see what point group you get. What symmetry operations do you lose when you change the two axial fluorines to $^{18}$F? Mar 19, 2020 at 0:37
• See chemtube3d.com/octahedral-sulfur-hexafluoride-sf6-symmetry for exploring the O$_h$ symmetry of the untagged (all $^{19}$F SF$_6$. Which operations do you lose when you do the replacement I mentioned above? Mar 19, 2020 at 3:37
• If you assume that your molecule is of the form $\ce{AB4C2}$ then one form is that shown in your figure and belongs to the $D_{4h}$ point group, the other has the two blue atoms at 90 deg to one another and belongs to $C_{2v}$ Mar 19, 2020 at 10:08