Symmetry species of translations

In the sixth column of the main body of the character table is indicated the symmetry species of translations (7) of the molecule along and rotations (R) about the cartesian axes. In Figure 4.14 vectors attached to the nuclei of H2O represent these motions which are assigned to symmetry species by their behaviour under the operations C2 and n (xz). Figure 4.14(a) shows that... 

The symmetry species of translations and rotations are used so frequently that they are generally included in the character tables. 

The last two columns of the character table provide information about IR and Raman activities of normal vibrations. One column lists the symmetry species of translational motions along the x, y and z axes (Tx, Ty and Tz) and rotational motions around the x, y and z axes (Rx, Ry and Rz). The last column lists the symmetry species of the six components of polarizability. As will be discussed in Section 1.14, the vibration is IR-active if it belongs to a symmetry species that contains any T components and is Raman-active if it belongs to a symmetry species that contains any a. components. Pairs of these components are listed in parentheses when they belong to degenerate species. 

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