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Introduction to Chirality and Symmetry

All objects may be categorized with respect to a property we describe chirality. A chiral object is not similar in all respects (that is superimposable) with its mirror image. An achiral object is the same with (superimposable on) its mirror image. Chiral objects have a "handedness", for an instance, corkscrew, golf clubs, shoes and a scissors. So, one can buy right or left-handed golf clubs and scissors. Similarly, shoes and gloves come in pairs, a right and a left. Achiral objects do not have a handedness, for an instance, a baseball bat (no writing or logos on it), a plain round ball, a pencil, a T-shirt and a nail. The chirality of an object is associated to its symmetry and to this end it is helpful to understand specific symmetry elements that may be related with a given object. A symmetry element is a line, a plane, or a point in or from an object, about which a rotation or reflection leaves the object in an orientation identical from the original. Few instances of symmetry elements are displayed below.

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The face playing card provides an instance of a center or point of symmetry. Starting from this type of point, a line drawn in any direction encounters similar structural characteristics as the opposite (180º) line. Four random lines of this type are displayed in green color. An instance of a molecular configuration having a point of symmetry is (E)-1, 2-dichloroethene. The other method of describing a point of symmetry is to note that any point in the object is reproduced by reflection from the center onto the other side. In these two examples the point of symmetry is colored magenta.

The boat conformation of cyclohexane displayed two intersecting planes of symmetry (labeled σ) and an axis of symmetry (labeled C2 in the diagram). For symmetry axis the notation is Cn, where n is an integer chosen so that rotation about the axis by 360/nº returns the object to a position identical from where it started. In this example the rotation is by 180º, so n=2. A plane of symmetry splits the object in such type of way that the points on one side of the plane are equal to the points on the other side by reflection via the plane. Further than this, the point of symmetry that is noted earlier, (E)-1, 2-dichloroethene also have a plane of symmetry (the plane defined by the six atoms) and a C2 axis, passing from the center perpendicular to the plane. The presence of a reflective symmetry element (a point or plane of symmetry) is enough to assure that the object having that element is achiral. So Chiral objects, do not consist of any reflective symmetry elements, but may have rotational symmetry axes, because these elements do not require reflection to operate. As well as the chiral vs. achiral distinction, there are two other terms frequently employed to refer to the symmetry of an object. These are illustrating below:

(i)                  Dissymmetry: All dissymmetric objects are chiral.The absence of reflective symmetry elements.

(ii)               Asymmetry: All asymmetric objects are chiral. The absence of all symmetry elements.  

Symmetry in Organic Chemistry

The symmetry of a molecule is described from the existence of symmetry operations performed with respect to symmetry elements. A symmetry element is a plane, a line, or a point in or via an object, on which a rotation or reflection leaves the object in an orientation the same from the original. A plane of symmetry is entitled by the symbol σ, and the reflection operation is the coincidence of atoms on one side of the plane with consequent atoms on the other side, as though reflected in a mirror. A point or center of symmetry is labeled as i, and the inversion operation exhibits coincidence of each atom with an identical one on a line passing from and an equal distance from the inversion point. At last, a rotational axis is entitled Cn, where the degrees of rotation that restore the object is 360/n (C2= 180º rotation, C3= 120º rotation, C4= 90º rotation, C5= 72º rotation). C1 is called the identity operation E since it returns the original orientation.

Asymmetric is an object that having no symmetry elements other than E is. This type of  an object is essentially chiral. Because a point or plane of symmetry involves a reflection operation, the presence of such type of an element makes an object achiral. One or more rotational axes of symmetry may exist in chiral, dissymmetric and achiral objects.

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