ABSTRACT
Some objects look exactly like their mirror image and we say that they are symmetrical or, more precisely, that they have reflection symmetry. Objects can also have rotational symmetry; for example, the letter ‘T’ is such that if we turn it over by rotating it through 180° about the upright axis it will look the same. Rotation and reflection symmetries are based on geometrical shape, and they are described in a precise way by introducing rotation and reflection symmetry operations. Complete sets of such symmetry operations form point groups, and the symmetry of a geometrical figure can be classified according to which point group it belongs. If we think of a molecule as being a rigid object of fixed structure, then its symmetry can be described in terms of a point group and this is useful for molecules having small amplitude vibrations in isolated electronic states.
