character table (Table 4.3). The four ligand group orbitals
therefore have a1 and t2 symmetries; the t label designates
a triply degenerate set of orbitals. Normalized wavefunctions
for these LGOs are given by equations 4.18–4.21.
ða1Þ ¼ 1
2 ð 1 þ 2 þ 3 þ 4Þ ð4:18Þ
ðt2Þ1 ¼ 1
2 ð 1 2 þ 3 4Þ ð4:19Þ
ðt2Þ2 ¼ 1
2 ð 1 þ 2 3 4Þ ð4:20Þ
ðt2Þ3 ¼ 1
2 ð 1 2 3 þ 4Þ ð4:21Þ
These four LGOs are shown schematically in Figure 4.20b.
By comparing Figures 4.20a and 4.20b, the symmetries of
the four ligand group orbitals can be readily matched to
those of the 2s, 2px, 2py and 2pz atomic orbitals of the C
atom. This allows us to construct a qualitative MO diagram
(Figure 4.21) in which the interactions between the carbon
atomic orbitals and the ligand group orbitals of the H4 fragment
lead to four MOs with delocalized -bonding character
and four antibonding MOs.