Molecular Orbitals and Walsh Diagrams

Following Walsh [1], we rationalize the fact that molecules like H2O and CH2 

We now recognize that the symmetry point group of the bent molecule is all four operations of which leave X in place. Two of them, E and cr, (zx), also leave the H atoms in place and the other two, C2(x) and ad yz), exchange 

2 Symmetry Coordinates of a Symmetric Ttiatomic Linear Molecule 

The symmetry of nuclear displacements arises most commonly in connection with vibrational spectroscopy of polyatomic molecules [7]. Let us compare the nuclear displacements of a symmetric linear triatomic, XYX, illustrated in Fig. 4.2, with those shown in Fig. 3.9 for a homonuclear diatomic molecule, which also has cylindrical symmetry. It was pointed out that in the latter case there is no way of reducing the symmetry of the potential energy of X2 below Doo/i by nuclear motion in the case of the triatomic molecule, there is. 

Since each of its three atoms can move parallel to any one of the three coordinate axes, we can construct nine symmetry coordinates. Assuming the molecule to be linear, and artificially reducing its symmetry from Dooh to D2/1 as 

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Chapter 4. Formation and Deformation of Polyatomic Molecules 4.1.1 Molecular Orbitals and Walsh Diagrams... 

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