Physical Chemistry Third Edition

872 21 The Electronic Structure of Polyatomic Molecules

at the origin, one of the H atoms on thexaxis, and the other H atoms in thexyplane

with bond angles of 120◦as shown in Figure 21.3. In order to make LCAOMOs that

contain only two atomic orbitals, we require hybrid orbitals that have orbital regions

pointing in the directions of the H atoms. These hybrid orbitals are called the 2sp^2

hybrid orbitalsand are constructed from the 2s,2px, and 2pyorbitals:

ψ 2 sp (^2) (1)−

√

1

3

ψ 2 s+

√

2

3

ψ 2 px (21.2-1a)

ψ 2 sp (^2) (2)−

√

1

3

ψ 2 s−

√

1

6

ψ 2 px+

√

1

2

ψ 2 py (21.2-1b)

ψ 2 sp (^2) (3)−

√

1

3

ψ 2 s−

√

1

6

ψ 2 px−

√

1

2

ψ 2 py (21.2-1c)

The directions of maximum extension of these hybrid orbitals lie in thexyplane, 120◦

apart. They overlap with the 1sorbitals of the hydrogen atoms, as shown in Figure 21.4a.

Figure 21.4b shows a cross section of the orbital region of one of them. The orbital

region resembles those of the 2sphybrid orbitals.

x

B

H

y

H

H

Figure 21.3 The BH 3 Molecule.

EXAMPLE21.1

Predict the electronic structure of the BH 3 molecule that would likely agree roughly with a

Hartree–Fock–Roothaan calculation.

Solution

The 1sB orbital is much lower in energy than the other orbitals, so it is used as a nonbonding

orbital and occupied by a pair of electrons. Each of the 2sp^2 hybrid orbitals is combined with

a1sorbital on a hydrogen atom to form a bonding LCAOMO and an antibonding LCAOMO.

These orbitals should resemble the orbitals obtained by energy localization of the canonical

orbitals from the Hartree–Fock–Roothaan procedure. The bonding orbitals are occupied by

pairs of electrons and the antibonding orbitals remain unoccupied. The electronegativity of

boron is 2.0 and that of hydrogen is 2.1, so these bonding orbitals should exhibit only a small

polarity, with the coefficient for the hydrogen 1sorbitals slightly larger in magnitude than

that for the 2sp^2 orbital.

z

y

y

z 5 0 plane

x

x

2 sp^2 (3)

2 sp^2 (1)

2 sp^2 (2)

2 sp^2 (1)

120 °

(a) (b)



Figure 21.4 Thesp^2 Hybrid Orbitals.(a) Directions of the symmetry axes of the orbital

regions of the 2sp^2 hybrid orbitals. (b) A cross section of an orbital region.