Symmetry Elements, Operations

The symmetry of the molecules can be described in terms of electrons of symmetry and the corresponding symmetry operations.

Clearly some molecules, like H2O and CH4, are symmetric. Now we shall develop a clear and precise way of describing such symmetries. Consider, for example, the plane containing the H2O molecule and the perpendicular plane shown in fig. 1.these planes are examples of planes of symmetry. You can test, what is here quite obvious, that the molecule is symmetric with respect to each plane by reflecting the molecule through the plane. This problem consists of treating the plane as a mirror. This reflection through the mirror, in both directions, produces a result that is indistinguishable from that existing originally. The reflection process is an example of a symmetry operation. It is the symmetry operation associated with a plane of symmetry. The plane of symmetry is an example of an element of symmetry.

As this example suggests, we can describe the symmetry of a molecule in terms of the elements of symmetry of the molecule. That a molecule has any particular element of symmetry can be checked by carrying out the symmetry operation associated with each symmetry element. If the operation does nothing more than leave the positions of atoms unchanged or carries one atom of a set of identical atoms into a position of another atom of the set, the result will be indistinguishable from that existing initially. When this is the result of the symmetry operation, the molecule does indeed have the corresponding symmetry element.

Planes of symmetry: the general symbol for a plane of symmetry is σ. If we draw the planes vertically, we refer t them as vertical planes of symmetry. Such planes are given the symbol σv. As if the plane of symmetry is drawn horizontally, we refer to it as a horizontal plane and label isσh, as if it is drawn in a way that can be described as diagonal, it is labeled σd.

Center of symmetry: now let us consider some other elements of symmetry and the symmetry operations associated with them. A molecule is said to have a center of symmetry if the operation of investigation through the center produces a result indistinguishable from that occurring originally. 

Axis of symmetry: a molecule is said to have an axis of symmetry if rotation of the molecule about that axis gives us back our initial situation. A twofold axis is one for which a rotation by360/2 degrees, or ½ revolution, produces a result like axis of rotation denoted by C2. A threefold axis is one for which a rotation, say clockwise, by a 1/3 revolution. The other is a clockwise rotation by 2/3 revolution or a counterwise rotation by 1/3 revolution.

The element of symmetry described as a fourfold axis consist of rotations by ¼, 2 (1/4) and 3(1/4) revolution. A C4 axis implies a C2 axis since the operation consisting of a rotation by 2/4 revolution is equivalent to rotation by ½ revolution.

A sixfold axis of symmetry as the discussion of the fourfold axis suggests, a sixfold axis implies coincident two fold and three fold axes.

If a single molecule has a single axis of rotation, we agree to draw the molecule to that this axis is in the vertical direction. If a molecule has more than one axis of rotation, we draw the molecule so that the highest order axis is vertical. The ax of rotation of the benzene molecule, drawn in accordance with this rule is followed. 

Rotation reflection axis: with only one additional type of symmetry and precisely indicated by stating the number and relative orientations of the four kinds of symmetry elements that have been described. Thus instead of saying, for example, that H2O is a symmetric molecule, we now can show the elements of symmetry of the molecule.

Molecular symmetry: the symmetry of a molecule is completely and precisely indicated by stating the number and relative orientations of the four kinds of symmetry elements that have been described. Thus instead of saying, for example, H2O is a symmetric molecule, we now can show the elements of the H2molecule.

One additional element of symmetry, which adds nothing to a description of the symmetry of a molecule but is helpful for an organised treatment of the consequences of this symmetry, should now be added. This symmetry element is called the identity and is given the symbol E. the symmetry operation associated with this symmetry element can be said to consist of no change. (Alternatively the operation can be described as a rotation about any axis by 360°.) Thus all molecules have the symmetry element E. (You will see that inclusion of this identity element is not as frivolous as it seems.)

   Related Questions in Chemistry

  • Q : Pressure and power for adiabatic

    a) Air flowing at 1 m3/s enters an adiabatic compressor at 20°C and 1 bar. It exits at 200°C. The isentropic efficiency of the compressor is 80%. Calculate the exit pressure and the power required. b) Steam enter

  • Q : Mole fraction of benzene Choose the

    Choose the right answer from following. In a solution of 8.7g benzene C6H6 and 46.0 gm toluene ,(C6, H5, CH3) the mole fraction of benzene in this solution is: (a)1/6 (b)1/5 (c)1/2 (d)1/3

  • Q : Mole fraction of hydrogen Give me

    Give me answer of this question. In a mixture of 1 gm H2 and 8 gm O2 , the mole fraction of hydrogen is: (a) 0.667 (b) 0.5 (c) 0.33 (d) None of these

  • Q : Dipole moment direction for the methanol

    Briefly describe the dipole moment direction for the methanol?

  • Q : Simulate the column in HYSYS The

    The objective of this work is to separate a binary mixture and to cool down the bottom product for storage. (Check table below to see which mixture you are asked to study). 100 kmol of feed containing 10 mol percent of the lighter component enters a continuous distillation column at the m

  • Q : Illustrations of the reversible reaction

    What are the various illustrations of the reversible reaction? Explain briefly?

  • Q : What are condensation polymers? Give

    These types of polymers are formed as a result of condensation reaction between monomer units. Some common examples are being discussed here: 1. Polyesters 2047_condensat</span></p>
                                        </div>
                                        <!-- /comment-box -->
                                    </li>
   
   </td>
	</tr><tr>
		<td>
       
      <li>
                                        <div class=

    Q : Molecular crystals Among the below

    Among the below shown which crystal will be soft and have low melting point: (a) Covalent  (b) Ionic  (c) Metallic  (d) MolecularAnswer: (d) Molecular crystals are soft and have low melting point.

  • Q : Question of vapour pressure Choose the

    Choose the right answer from following. Vapour pressure of a solution is: (a) Directly proportional to the mole fraction of the solvent (b) Inversely proportional to the mole fraction of the solute (c) Inversely proportional to the mole fraction of the solvent (d

  • Q : Basicity order order of decreasing

    order of decreasing basicity of urea and its substituents

©TutorsGlobe All rights reserved 2022-2023.