Chemistry - A Molecular Science

Chapter 6 Molecular Structure & Bonding

the Pauli Exclusion Principle and Hund’s rule. The result of adding 12 electrons in the diagram is shown in the figure. Many of the properties of a molecule are dictated by the nature of its

H

ighest

O

ccupied

M

olecular

O

rbital

or

HOMO

and its

Lowest

Unoccupied

M

olecular

Orbital

or

LUMO

. Three important predictions

can be made based on this

diagram:

1. There are a total of eight bonding elec

trons and four antibonding electrons, so the O-O

bond order is

1 /^2

(8 - 4) = 2, which is the same prediction made from valence bond theory.

2. Unpaired electrons in the

π* orbitals account for the paramagnetism of O

. This prediction 2

was a major success for MO theory.

sX sX sX

sC

sXB s

sXA XC

Energy

sA

X

B

X

A

X

C

sB

(a) (b) (c)

DE

AX

DE

XB

DE

XC^

Figure 6.24 Mixing AOs of different energy The relative sizes of the spheres

represent the contributions of

the AOs in each MO. The cont

ribution of each AO in the

bonding MO increases relative to that of X as t

he energy of the

AO gets lower. (a) A is higher in energy than X, so the contribution of X (sphere size) to the bonding MO is greater. (b) B is lower in energy than X, so

the contribution of B to the

bonding MO is greater. (c) C is lowest in energy, so the contribution of s

is the greatest. C

3. The HOMO is the

π*(2p) and the LUMO is the

σ*(2p).

The two nuclei in

heteronuclear diatomic molecules

are nuclei of different elements,

so the AOs that mix to form the bonding MO

are at different energies. Whereas the two

atoms of a homonuclear diatomic molecule make equal contributions to each MO in the molecule, the energy difference between the AOs in a heteronuclear diatomic molecule results in MOs that are not composed of equal amounts of the AOs. Instead, the AOs mix in the ratio that achieves th

e lowest energy possible for

the bonding MO. The lowest

energy MO is produced when the AO at lower energy contributes more to the MO than does the AO at higher energy. Consider the

bonding between of atom X to atoms A, B,

and C as described in Figure 6.24. •

Figure 6.24a: The energy of s

(the s orbital atom X) is less than that of sX

by an amount A

EΔ

. sXA

is the lower energy AO, so it contributes more to the bonding MO (X

σXA

) than does

SA

, which is shown by the relative sizes of t

he spheres describing the MO. The larger sphere

on X means that there is more electron densit

y on atom X in the bond, so the XA bond is

polar with atom X carrying the negative charge.

-^

Figure 6.24b: s

is lower in energy than sB

by an amount X

ΔE

. sXB

is the lower energy orbital, B

so it contributes more to the bonding MO (

σXB

). The XB bond is polar with atom B carrying the

negative charge.

(^) •
Figure 6.24c: s
is lower in energy than sC
by an amount X
EΔ

. XC

EΔ

> XC

EΔ

, so sXB

contributes C

even more to the XC bond than did s

to the XB bond. The small sphere representing the B

contribution of s

to the X

σXC

MO indicates that only a small

amount of the electron density in

the bond resides on atom X. The

result is that the XC bond is

more polar than the XB bond.

Recall that electronegativity is a measure of how well an atom attracts the bonding

electrons, but, as shown in the preceding paragraph, the electron density in a bond is greater around the atom with the lower energy orbital;

i.e.,

the atom with the lower energy

orbital attracts the electrons more, so it is the more electronegative atom. This is why we

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