Irreducible representations triatomic molecules

These nine irreducible representations correspond to the nine motional degrees of freedom of the triatomic water molecule. To obtain the symmetry of the genuine vibrations, the irreducible representations of the translational and rotational motion have to be separated. This can be done using some considerations described in Chapter 4. The translational motion always belongs to those irreducible representations where the three coordinates, x, y, and z, belong. 

From the Czv character table, the three translations span Ai, Bi, and Bj, and the three rotations span Ai, Bi, and Bi. If these are taken away from eqn [75], this leaves 2Ai and Bi- The three normal vibrations of the bent triatomic molecule, therefore, span these irreducible representations. (See Figure 9 the antisymmetric stretch is Bi.)... 

Figure 7.3 Nodal patterns and qualitative energies of MOs in linear and bent triatomic molecules according to Walsh [4]. The lowest three MOs, composed of 1s AOs on the constituent atoms (Fig. 7.2), participate little in the chemical bonding and are excluded. Horizontal coordinate is the bending angle 6. Orbital occupancies are shown for linear CO (0 = 180°) and for bent NO2 (0 = 134°). Irreducible representations are given for the MOs in and C v point groups at left and right, respectively.

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