876 21 The Electronic Structure of Polyatomic Molecules
equilibrium bond angle of 109.5◦instead of the experimental bond angle of 104.5◦.
The 1sorbital of each of the hydrogen atoms forms a bonding molecular orbital with
one of the 2sp^3 hybrid orbitals:ψσAcOψ 2 sp (^3) (2)+cHψ 1 sA (21.3-2a)
ψσBcOψ 2 sp (^3) (3)+cHψ 1 sB (21.3-2b)
where the H atoms are denoted by A and B. From the fact that oxygen is more elec-
tronegative than hydrogen we can assume that
|cO|>|cH| (21.3-3)
This also corresponds to the fact that the oxygen 2sp^3 hybrid orbitals are lower in
energy than the hydrogen 1sorbitals.
Acorrelation diagramfor the H 2 O molecule is shown in Figure 21.7. In this diagram
the energies of the unhybridized atomic orbitals are shown with broken lines, because
they have been used to construct the hybrid orbitals and are no longer available for use
in LCAOMOs. The energies of the 2sp^3 hybrids are shown with solid lines. In addition
to the bonding orbitalsσA andσB, the correlation diagram shows the energies of the
corresponding antibonding orbitalsσ∗A andσ∗B, which have larger coefficients on the
hydrogen end, and which remain vacant in the ground-state.
The 1sorbital of the O atom is occupied by a nonbonding pair of electrons and each
of the bonding molecular orbitals is occupied by two electrons. Two 2sp^3 hybrids are
Orbital energy (schematic)
Hydrogen
atomic
orbitals
1 sHA 1 sHB
2 pO (replaced)
A B
A B
2 sp^3
2 sO (replaced)
Moleculer
orbitals
1 sO
Oxygen
atomic
orbitals
(with
hybridization)
Molecular
orbitals
Hydrogen
atomic
orbitals
Figure 21.7 Correlation Diagram for the Water Molecule Using 2sp^3 Hybrid Orbitals.