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Is a molecule with no symmetry necessarily polar?

Can a polar molecule still have some elements of symmetry (i.e. mirror image is the same as itself)? I think so ... because we can have achiral tetrahedral carbon molecules that are polar - i.e. methylene chloride.

So, is it proper to say that a molecule that lacks symmetry is necessarily polar?

Or can a more nuanced statement based on symmetry be made? Is there a "minimum" level of symmetry needed to achieve non-polarity?

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    $\begingroup$ There appears to be a lot of negative inversions in this post. All asymmetric molecules are polar to some degree. Some polar molecules with have symmetry elements. $\endgroup$ – Lighthart Oct 31 '14 at 21:50
  • $\begingroup$ @Lighthart can you expand this into an answer? $\endgroup$ – Dissenter Oct 31 '14 at 21:53
  • $\begingroup$ The answer to this question depends on what your threshold is for polar or what context you mean. For example, diethyl ether is more polar than hexane, but I wouldn't really consider either polar. If you mean polar as in having a non-zero dipole moment, then you're probably correct, but that's nearly every single compound. $\endgroup$ – jerepierre Oct 31 '14 at 22:12
  • $\begingroup$ I mean non dipole moment @jerepierre $\endgroup$ – Dissenter Oct 31 '14 at 22:13
  • $\begingroup$ No two atoms have exactly the same electronegativity. Consequently any molecule that is not symmetric has a nonsymmetric distribution of electron density, and as such is formally polar. Others have suggested that there is a threshold of polarity, underneath which the nonsymmetric distribution of electron density is not sufficiently nonsymmetric so as to create a dipole of meaningful magnitude. Compare t-butane to t-butylchloride, for example. $\endgroup$ – Lighthart Nov 3 '14 at 18:57
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Let's start by defining a polar molecule as a molecule with a dipole moment.

Is a molecule with no symmetry necessarily polar?

Yes, a molecule with no symmetry belongs to point group $\ce{C_1}$ (e.g. the only symmetry element it contains is a $\ce{C_1}$ axis, rotation of the molecule 360/1 degrees converts the molecule back into itself). The molecule is asymmetric and polar.

Can a polar molecule still have some elements of symmetry (i.e. mirror image is the same as itself)? I think so ... because we can have achiral tetrahedral carbon molecules that are polar - i.e. methylene chloride.

Yes, methylene chloride, vinyl chloride, methanol, chloroform, etc. all contain planes of symmetry, but are still polar.

So, is it proper to say that a molecule that lacks symmetry is necessarily polar?

If I understand correctly, this is a repeat of your first question.

Or can a more nuanced statement based on symmetry be made? Is there a "minimum" level of symmetry needed to achieve non-polarity?

Yes

  • All asymmetric molecules are polar. Such molecules belong to point group $\ce{C_1}$
  • Molecules belonging to point group $\ce{C_{n}}$ with n>1 are polar. 1,3-dimethylallene is an example (it has $\ce{C_2}$ symmetry, rotate it by 360/2 degrees about its $\ce{C_{2}}$ axis and it converts back to its original representation)
  • Molecules belonging to point group $\ce{C_{s}}$ are polar. A sigma plane either contains or bisects molecules in this point group, and this plane is the only symmetry element. Methanol, bromocyclopropane, vinyl chloride, etc. belong to this point group and are polar.
  • Molecules belonging to point group ${C_{nv}}$ are polar. Formaldehyde and methylene chloride (both ${C_{2v}}$), chloroform (${C_{3v}}$) and hydrogen chloride (${C_{\infty v}}$) are examples. This point group contains a ${C_{n}}$ axis and n sigma planes containing the axis.

If the molecule is not in one of these point groups, then it is not polar and does not have a dipole moment (or said differently, molecules in all other point groups [${D_n, S_n, C_{nh}, D_{nd}, D_{nh}, T_d, O_h}$ and higher] are not polar and do not have dipole moments).

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  • $\begingroup$ "All asymmetric molecules are polar." but I thought earlier in your post you said that some polar molecules contain elements of symmetry $\endgroup$ – Dissenter Nov 1 '14 at 1:50
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    $\begingroup$ Asymmetric molecules belong only to point group ${C_1}$, the only symmetry element they possess is a ${C_1}$ axis. They are all chiral, polar and have dipole moments. As described above, other non-asymmetric point groups that contain other symmetry elements may also be polar. $\endgroup$ – ron Nov 1 '14 at 2:02
  • $\begingroup$ 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} $. $\endgroup$ – porphyrin Jul 1 '16 at 13:57
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Consider the following (absolutely imaginary) molecule: $\ce{CX^1X^2X^3X^4}$ where the $\ce{X}$ atoms are all of a different kind but have the same electronegativity.

This molecule is asymmetrical but has no dipole moment.

While an imaginary example is nice and well, I think that in reality, electronegativities will always differ, if even ever so slightly. As a result, there will be a total dipole moment on a molecule with no symmetry. The question you really have to ask now is: What is the threshold for a molecular dipole moment to consider the molecule polar?

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  • $\begingroup$ what's the geometry of this 5-atomed molecule? $\endgroup$ – Dissenter Oct 31 '14 at 21:55
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    $\begingroup$ The first atom is a carbon, so I'd say tetrahedral ;) $\endgroup$ – tschoppi Oct 31 '14 at 22:54

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