Symmetry

By Aamarpali Puri

Symmetry means agreement in proportion/ agreement in dimensions when a certain portion of an object looks exactly like another portion of the same object. Symmetry is exhibited everywhere i.e crystal cubes, designing, in plants, structure of flowers, water droplets and even in music. It leads to pleasing proportions, regularity, harmonious arrangements.

In chemistry systematic discussion of symmetry is termed Group Theory. Molecules are classified according to their symmetry. The collection of symmetry elements present in a molecule forms a “group”, typically called a point group. A point group has all the symmetry elements (points, lines, and planes) which intersect at a single point.

Symmetry helps us in determination of structure of molecules and understanding their Stereochemistry. Symmetry helps in Analysis of Molecular Vibrations, finding out the Chirality and polarity of a molecule.

To understand the symmetry of various elements it is necessary to know the geometry of various molecules. This can be obtained by Valence Shell Electron Pair Repulsion (VSEPR) theory, which helps in prediction of the shapes of molecules and bond angles of these molecules. Various shapes of molecules are Linear (Carbon dioxide), Bent (Water), Planar (Boron Trifluoride), Pyramidal (Nitrogen Trifluoride), Square Planar (Xenon Tetrafluoride), Tetrahedral (Carbon Tetrachloride), Pentagonal (not known to exist) and Octahedral (Sulphur hexafluoride) etc.

Symmetrical molecules have Symmetry elements (imaginary geometrical entities) such as points, lines and planes. Some geometric operations are reflection, rotation or inversion, when performed on molecules gives rise to indistinguishable configuration of same molecule. So molecules can have configurations which are alike in all respects except chemical nature. Linear elements have an infinite number of planes of symmetry. If in a molecule x, y, z coordinates are changed to –x, -y, -z and if after that too molecule presents an indistinguishable configuration then origin is called Centre of Symmetry. If an imaginary line is drawn from an atom to the centre of the molecule and extended on the other side by the same distance and meets a similar atom, the molecule is said to have centre of symmetry. Example: a cube. All linear molecules when rotated through any angle with respect to the bond axis, present an indistinguishable configuration possess an Axis of Symmetry. Example HCl

Radial symmetry is rotational symmetry around fixed point (Centre of Symmetry) Radial symmetry can be termed as cyclic or dihedral symmetry. The notation for Cyclic Symmetries is Cn. Example: Star fish, Hibiscus flower.

Strip Pattern Symmetry can be classified into following patterns Translational symmetry, Horizontal mirror symmetry, vertical mirror symmetry, Rotational Symmetry, Glide Reflection Symmetry. Example: Snakes.

Bilateral symmetry is symmetry across a line of reflection. Two halves are mirror images of each other exhibits Bilaterally Symmetrical.

Some Beautiful examples of symmetry in nature are: Honey Comb, Sunflower, Peacock, Spider Webs and Pine Cones etc.

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