Chemistry - A Molecular Science

s*(2p) p*(2p) p(2p) s(2p) *(2s)s (2s)s

2s

2s

2p

2p

O^2

Figure 6.23 MO diagram for O

2

The MOs are in the yellow region

, while the AOs used to construct

them are shown on either side. The notation

σ(2s) is used to show

that the

σ molecular orbital is formed by mixing of the two 2s

atomic orbitals as represented by the dotted lines.

Energy

1s

1s

s* s

1s

1s

s* s

(a) H

2

(b) He

2

Figure 6.22 MO diagrams for H

and He 2

2

Note the dotted lines simply show which atomic orbitals are used to construct each molecular orbital.

Electrons occupying bonding orbitals lower the energy of the system and make the
MO more bonding, while those occupying antibonding orbitals raise the energy and make the MO less bonding. Indeed the bond order (BO)

is defined in term

s of the difference

between the number of bonding and antibonding electrons in the bond as follows:

BO =

1 /^2

(number of bonding electrons -

number of antibonding electrons)

As an example of the use of a diagram like

the one shown in Figure 6.21, we examine

the differences predicted for the H

and He 2

molecules (Figure 6.22). Each H atom has one 2

electron in its 1s orbital, so two electrons must be placed in the diagram for H

. Both 2

electrons occupy the

bonding orbital, so the H-H bond order = σ

1 /^2

(2 - 0) = 1.

Consequently, H

has a single bond and is a stable molecule. An He atom has two 2

electrons in its 1s orbital, so four electrons

would have to be placed into the diagram for

He

, which fills both the 2

and σ

• orbitals. The He-He bond order would be σ

1 /^2

(2 - 2) = 0,

which means that, consistent with observation, there is no He-He bond and He

is not a 2

stable molecule.

In the valence bond description of O

described in Figure 6.14, all of the electrons are 2

paired. However, O

molecules are paramagnetic (they are deflected in a magnetic field), 2

which means that O

molecules contain unpaired electrons. This observation was a major 2

dilemma for the valence bond model, and its explanation was a major victory for molecular orbital theory. We now present the MO description of O

to see how it 2

explained the paramagnetism of O

. We start by determining the order of the energy levels 2

in Figure 6.23.

-^

The 2s orbitals interact to form the

(2s) and σ

*(2s) orbitals. The 2s orbitals are the lowest σ

energy valence orbitals in an oxygen atom, so

the two MO’s are the lowest energy MO’s

derived from the valence AO’s.

-^

The 2p orbitals that are directed along the bonding axis interact in a head-on manner similar to that shown in Figure 6.19 to produce the

(2p) and σ

*(2p) orbitals. Head-on σ

interactions are usually stronger

than side-on interactions, so the

(2p) is the lowest σ

energy MO derived from the 2p interactions, while the

σ

*(2p) is the highest energy MO.

(^) •
The remaining 2p orbitals interact in a side-on fashion as shown in Figure 6.20 to produce a pair of
(2p) and a pair of π
*π
(2p) orbitals. Note that the
members of each pair have the
same energy because the two
(2p) orbitals are identical except for their orientation π
relative to one another.
Each oxygen atom has six valence electrons (2s
2 2p
4 ), so a total of 12 electrons must be
placed into the energy diagram. The electrons
are placed in the same manner as they are
into the orbitals of an atom, so the lowest
energy orbitals are occupied first while obeying
Chapter 6 Molecular Structure & Bonding
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