Symmetry and Chirality explained using 3D models

It was during my school days when I was studying Stereochemistry of molecules. Chirality, Enantiomers, Fischer Projections etc. in organic chemistry. The first requirement of this particular topic is that you should have a very good spatial (the way groups are oriented in 3D space) understanding of a molecule and I was clearly lost as I couldn’t decipher the very basic geometry i.e. a tetrahedron which was a must to understand molecular structure in organic chemistry.

The main problem was in imagining different molecules from various angles, the molecules were sometimes so complicated! that it got impossible to understand and work them out. The reason for my failure to understand was very clear as I had never seen a real molecule (or a representative structure as nobody has seen a real one) in my life so solving problems based on geometry was a far fetched dream. Finally! my long ordeal ended when my teacher brought ball and stick model of methane in the class. He showed us the planes of symmetry, the carbon and hydrogen atoms lying in one plane, the angle between two hydrogen atoms etc. And there it was, the moment of truth where everything resolved and I was able to understand a lot more just with the help of that simple model.

With the same approach in my mind, I have tried to explain chirality of a molecule with the help of 3D models so that you can figure out most of the things in stereo-isomerism. Finally, I would like to encourage you to make your own 3D models using simple matchsticks and erasers as anything that you and see and touch can never be replaced by a model. 

STRUCTURE OF METHANE

Take a good look at the tetrahedron structure of methane (CH4)molecule. Click on the play button and then move around in space to see the arrangement of atoms, bonds and their relative spatial location. See as many times as you like but make sure that you understand this basic geometry and we will be seeing a lot of it.

An introduction on symmetry elements in a molecule and how is symmetry related to chirality? If you are already familiar with this then you may skip.

Center of Symmetry

The center of symmetry ‘i’ is a point in space such that if a line is drawn from any part (atom) of the molecule to that point and extended an equal distance beyond it, an analogous part (atom) will be encountered.

An example of point of symmetry is 1,3-trans-disubstituted cyclobutane, below. Note that the chiral G substituent is inverted on both sides of the point of symmetry. This symmetry element is sometimes also called “the point of inversion”.

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Fig 1: Center of symmetry about a point ‘i’

Plane of Symmetry

A plane of symmetry is a reflection plane which brings into coincidence one point of the molecule with another one through the mirror reflection.

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Fig 2: Here xz plave is the plane of symmetry

Apart from the two there is also “Axis of Symmetry” but it is not required for chirality. If you want read about it you can click here.

The existence of a reflective symmetry element (a point or plane of symmetry) is sufficient to assure that the object having that element is achiral.

Now, go back to Methane’s 3D model and try to observe the point(s) of symmetry and plane(s) of symmetry. Did you find any of them? Is the methane molecule chiral or achiral?

ANS: Methane has no center of symmetry but has 6 planes of symmetry each having 2 H atoms and 1 C atom in the middle (Fix the carbon centre and number the hydrogens, now to select two hydrogens from four the possible ways are 4C2 = 6, hence the number of planes are 6). So we can easily say that the molecule is achiral.

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Fig 3: Plane of symmetry in a methane molecule

STRUCTURE OF ETHANE

Interesting property of carbon is its C-C bond formation ability owing to incredibly high bond dissociation energy. So naturally there are large number of other organic molecules having C-C bond. The simplest of them all has to be ethane (C2H6) molecule. Have a look for yourself to understand the structure of ethane.

Its like two methane molecule joined together with C-C sigma bond and two hydrogen atoms removed. See! tetrahedron geometry is the most basic building block of entire Alkane family. Since two groups joined with a sigma bond can undergo free rotation thus, ethane exhibits Conformational Isomerism. The above displayed form is Staggered (Gauche) in which dihedral angle is 60 degrees.

So how many point(s) of symmetry you find? And what about the plane(s) of symmetry?

ANS: Planes of Symmetry = 3, Point of Symmetry = 1, Hence  the molecule is achiral.

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Fig 4: Three planes of symmetry in ethane molecule

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Fig 5: One center of symmetry in ethane molecule

Getting bored! Let’s try something different. Let’s take the case of Cyclo-Hexane.

STRUCTURE OF CYCLO-HEXANE CHAIR CONFORMATION

As per Wikipedia, In the basic chair conformation, the carbons C1 through C6 alternate between two parallel planes, one with C1, C3 and C5, the other with C2, C4, and C6. The molecule has a symmetry axis perpendicular to these two planes, and is congruent to itself after a rotation of 120° about that axis.

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Fig 6: Plane of symmetry explained in Chair conformation of Cyclo-Hexane

Pick any two diametrically opposite carbon and their corresponding 2 hydrogen and pass a plane through them, you’ll get a plane of symmetry. And there is one center of symmetry right at the middle of the molecule.

ANS: Total Planes of Symmetry = 3, Center of Symmetry = 1, Hence the molecule is achiral.

I hope that you have learnt to identify the centers and planes of symmetry in a molecule. This blog might be useful to you in helping you to visualize things but don’t get dependent on it as in long run its your own imagination that will serve you the best.

BIBLIOGRAPHY:

  1. Solomons & Fryhle Organic Chemistry
  2. http://www.cem.msu.edu/~cem251/F96/alkane_conformations/cem2.html
  3. http://tigger.uic.edu/~kbruzik/text/chapter2.htm
  4. http://research.cm.utexas.edu/nbauld/teach/cyclohex.html
  5. https://en.wikipedia.org/wiki/Cyclohexane_conformation
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