XH2 is that the -bonding character in orbitals 1 and
2 is spread over all three atoms, indicating that the
bonding character is delocalized over the HXH framework.
Delocalized bonding is a general result within MO
theory.
MO approach to bonding in linear XH2:
working from molecular symmetry
The method shown above for generating a bonding description
for linear XH2 cannot easily be extended to larger
molecules. A more rigorous method is to start by identifying
the point group of linear XH2 as D1h (Figure 4.13a). The
D1h character table is used to assign symmetries to the orbitals
on atom X, and to the ligand group orbitals. The MO
diagram is then constructed by allowing interactions between
orbitals of the same symmetry. Only ligand group orbitals
that can be classified within the point group of the whole
molecule are allowed.
Unfortunately, although a linear XH2 molecule is structurally
simple, the D1h character table is not. This, therefore,
makes a poor first example of the use of group theory in
orbital analysis. We can, however, draw an analogy between
the symmetries of orbitals in linear XH2 and those in homonuclear
diatomics (also D1h). Figure 4.13b is a repeat of
Figure 4.11, but this time the symmetries of the orbitals on
atom X and the two ligand group orbitals are given. Compare
these symmetry labels with those in Figures 1.19 and
1.20. The construction of the MO diagram in Figure 4.13b
follows by allowing interactions (bonding or antibonding)
between orbitals on atom X and ligand group orbitals with
the same symmetry labels.