Symmetry operations and symmetry elements
Symmetry is a property of molecules consisting of more than one atom of similar type, with equal bond angles and/or bond lengths. For instance the high symmetry of the SF6 molecule (diagram 1. arises from the six equal S-F bonds disposed at angles of 90° to each other. In order to make the notion more exact we make use of the idea of a symmetry operation. For instance rotating SF6 by 90° about an suitable axis, it appears identical after the rotation. The axis concerned is termed as the symmetry element. Rotations that do not leave the molecule looking similar are not symmetry operations.
The dissimilar types of symmetry operation and their subsequent symmetry elements are listed in Table 1. By convention the identity operation E is included for mathematical completeness. It includes no change at all and is a symmetry operation for any system. The remaining, the non-trivial types of operation are demonstrated for the case of SF6 in Fig. 1. The C4 rotation is similar 90° rotation considered to above. SF6 has two another C4 axes and also various C2 (180°) and C3 (120°) axes not displayed. The influences of reflection (σ) and inversion (i) should be clearly differentiated. In the previous case the symmetry element is a plane that reflects like a mirror and does not influence atoms lying in the plane.
Operation of inversion from a center however takes everything from the center and out to similar distance on the opposite side. A rotation-reflection (Sn) is an operation which combines a Cn rotation with a reflection in a plane perpendicular to the rotation axis. Occasionally the individual components are themselves symmetry operations: for instance the C4 axes of SF6 are also S4 axes like the molecule has reflection planes perpendicular to each C4 axis. Though, in the case that is demonstrated in Fig. 1 that is not so. The axis demonstrated is a C3 axis but not a C6. Though combining a 60° rotation with a reflection creates the S6 symmetry operation displayed.
Rotations are termed as proper symmetry operations where the operations involving inversion and reflection are not proper. Proper symmetry operations might be performed physically using molecular models, where the not proper operations can only be visualized. The molecule possessing no improper symmetry elements is differentiable from its mirror image and is termed as chiral. Chiral molecules consist of the property of optical activity that means that when polarized light is passed from a solution the plane of polarization is rotated. In organic molecules, chirality comes when four distinct groups are tetrahedrally bonded to a carbon atom. Inorganic instances of chiral species include six- coordinate complexes with bidentate ligands. Molecules with not proper symmetry elements cannot be chiral such as the operations concerned convert the molecule into its mirror image that is therefore indistinguishable from the molecule itself. Most frequently such type of achiral molecules has a reflection plane or an inversion center but more seldom they have a Sn rotation-reflection axis with no inversion or reflection alone.