Are there different types of symmetry?

Question

What factor does the symmetry of a molecule play?

For example, I know water is asymmetric so does this therefore make water polar (I know in fact that is is)? It may sound ignorant due to my lack of knowledge but considering one can draw a line through a water molecule, it appears as if if is symmetrical? Why exactly is water asymmetric and how can one tell? I have heard that it is due to its bent shape and lone pair of electrons but this is too general. Just because a shape is bent does not mean it lacks symmetry?

Finally, is there a concept to finding if a given molecule is symmetrical or asymmetrical?

There are quite a few different kinds of symmetry out there; some forbid polarity, some don't. — Ivan Neretin, Jul 01 '16 at 07:48
As you may already have seen, "symmetry" is not a very specific term, just saying a molecule is "symmetric" doesn't actually tell you anything about the molecule at all. Neither is "asymmetric" a good description of water. — orthocresol, Jul 01 '16 at 16:35

score 3 · Answer 1 · answered Jul 01 '16 at 09:17

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Symmetry is a very broad topic, and as was mentioned in the comments there are many kinds of symmetry. However, when dealing with molecules you should focus on point group symmetry. A good place to start is this link.

But let's get back to the question:

You mention that you know water is asymmetrical and is therefore polar but at the same time you also note that you CAN draw a line through it to cut it into two equal halves. In that way, you can say water has a mirror plane and is therefore symmetric. This type of symmetry is more precisely defined as $C_{2V}$. Ammonia has $C_{3V}$, Benzene has $D_{6h}$, and so on and so forth.

Now, symmetry and polarity do have some relation but you can't tie them together, the case in point being the hydrocarbon $\ce{CHMeEtPr}$. From the point of view of symmetry, this is definitely not a symmetric molecule. And despite its complete asymmetry this is definitely what we would call a non-polar molecule.

So are there any properties related to symmetry? Yes - the ability for a molecule to rotate plane polarized light. We measure this and call it optical activity, and call the asymmetric molecules chiral.

Hope that helps!

answered Jul 01 '16 at 09:17

IT Tsoi

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Thanks for the comment! So when we say water is asymmetric exactly how is it asymmetric, in what context? Orbital electrons? Again as you and i noted previously, it is asymmetric yet a line can be drawn through it so how then in that case is it asymmetric? Thanks for the link as well! – Atticus283blink Jul 02 '16 at 22:22
Hi @Atticus283blink, symmetry is described in terms of symmetry elements and few molecules have all symmetry elements. Water, for example, has the C2 symmetry element but not inversion ($\ce{i}$) or improper rotation ($\ce{S_n}$) – IT Tsoi Jul 03 '16 at 00:19
Thanks again! Just a follow up; Firstly, can you clarify what you wrote after the word "inversion" and after "rotation?" As you can see the text font is not correct. Furthermore, on that link you sent me it references sigma many times as shown here: https://imgur.com/a/pvz7X What exactly does this symbol mean in chemistry or symmetry for that matter? – Atticus283blink Jul 03 '16 at 20:40
Sigma refers to "reflection on a mirror plane". Inversion is followed by a small letter i, and Improper Rotation has the symbol of S_n. – IT Tsoi Jul 07 '16 at 05:18
Thanks so much! In my textbook (Chemistry The Central Science Brown) it does not talk about symmetry and Sigma. Is this concept for more advanced chemistry? I just find it strange it doesnt cover this. I am in first semester inorganic chemistry would this make sense? – Atticus283blink Jul 11 '16 at 02:09
@Atticus283blink knowledge of symmetry mainly required in chemistry where geometry plays an important role, and in most cases you can survive through undergraduate university with just passable knowledge, so it is entirely possible that it is a topic reserved for a later semester. – IT Tsoi Jul 11 '16 at 03:28

score 1 · Answer 2 · answered Jul 01 '16 at 14:29

Symmetry is a huge subject. In chemistry we deal mainly with point- groups, which is the symmetry about a point in space as the name suggests. Crystals are described by space-groups and translation is additionally allowed. Have a look at at almost university level physical chemistry textbook for an introduction.

Two main areas that it mainly influences molecules are (a) whether spectroscopic transitions are allowed or forbidden, and (b) whether orbitals can combine to form molecular bonds.

A more familiar property, and one that is easier to explain, is the dipole moment of a molecule. While individual bonds can have a dipole (C-Cl for example), whether the whole molecule has a dipole depends on the overall symmetry. To be polar the molecule must not have a centre of inversion. This is the only condition and this restricts the point groups that it can belong to.

The common point groups with a centre of inversion are $C_i, D_{2h} ,D_{4h}, D_{6h}, D_{8h}, D_{3d}, D_{5d}, S_6, T_h, O_h, I_h$ & $D_{\infty h} $ and so a molecule with any of these point groups does not have a dipole moment. (Symmetry notation is very condensed so have a look at a text book. If you want to try assigning point groups I found this site molecule-viewer.com which has many molecules to try and 3D pictures of symmetry elements.)

Another familiar example is chiral molecule. This has four different atoms or groups attached to one of its carbon atoms. The molecule should then only have the lowest symmetry (called $C_1$ which indicates 360 degree rotation). A nice example is limonene.

Are there different types of symmetry?

2 Answers2