Question

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`?

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

Explanation:

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.