What are the symmetry elements and point group of #"CF"_4#, #"CClF"_3#, and #"CBrClF"_2#? What symmetry elements are lost in the descent from #"CF"_4# to #"CClF"_3# and then to #"CBrClF"_2#?

Question
Answer 1

Warning! Long Answer.
1. 4 #"C"_3# axes, 6 #σ_text(d)# mirror planes, and 3 #"S"_4# improper axes
2. 1 #"C"_text(3v)# axis and 2 #σ_text(v )# planes

Point group for #"CF"_4#

#"CF"_4# has a tetrahedral geometry. It belongs to point group #"T"_text(d)#, like methane.

It has four #"C"_3# axes, three #"C"_2# axes, three #"S"_4# improper axes, and six #σ_text(d)# mirror planes.

(a) #"C"_3 # axes

If you place the model on a table and look "down" the vertical #"C-F"# bond, we can see that each bond is a #"C"_text(3)# axis of rotation.

You can rotate the molecule 120°# about the axis and get an indistinguishable configuration of the molecule.

(b) #"C"_2# axes

The image below shows one of the four #"C"_text(2)# axes.

The axis bisects a #"C-F"# bond angle.

You can rotate the molecule 180° about this axis and get an indistinguishable configuration of the molecule.

(c) #"σ"_text(d)# planes

The image below shows the two of the six #σ_text(v)# planes.

One is the plane of the screen. The other is a plane perpendicular to the screen and bisecting an #"F-C-F"# bond angle.

(d) #S"_4# axes.

An #"S"_text(n)# improper rotation is a rotation of #(360°)/n# about a #C"_n# axis, followed by reflection in a plane perpendicular to that axis.


(Adapted from slideshare.net)

There are four of these axes in the molecule.

#bb(1.)color(white)(m)"CF"_4# to #"CClF"_3#

The structure of #"CClF"_3# is

We see that the molecule has a #"C"_text(3v)# axis and two #σ_text(v )# planes of symmetry.

#"C"_text(3v)# axes

The three-fold axis is more obvious if you look down the #"C-Cl"# with the #"Cl"# atom closest to your eye.

You can rotate the molecule 120° left or right and get a new configuration that is indistinguishable from the original.

#sigma_text(v)# planes

Each #σ_text(v)# includes a #"Cl-C-F"# bond. Here the mirror plane is the plane of the screen.

A reflection converts the molecule into an indistinguishable form of the original.

In going from #"CCl"_4# to #"CClF"_3#, the molecule has lost four #"C"_3# axes, six #σ_text(d)# mirror planes, and three #"S"_4# improper axes

**#bb(2.)color(white)(m)"CClF"_3# to #"CBrClF"_2#

The structure of the molecule is

Thus, it is in point group #"C"_text(s)#. It has only a #σ_text(v )# plane of symmetry.

#σ_h# plane

The plane contains the #"Br-C-F"# bonds and bisects the #"Cl-C-F"# bond angle#.

One half of the molecule is a mirror image of the other half.

Thus, in going from #"CClF"_3# to #"CBrClF"_2#, the molecule has lost a #"C"_text(3v)# axis and two #σ_text(v )# planes of symmetry.

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