Chemistry - A Molecular Science

Chapter 6 Molecular Structure & Bonding

(b) out-of-phase combination = * MO

s

(a) in-phase combination =

MOs

= =

Figure 6.19

σ bonds from end-on combinations of p orbitals

+

b) out-of-phase

= * orbitalp

=

+

a) in-phase= orbital

p

=

Nodal plane perpendicular to bondingaxis makes the orbital antibondingNodal planes containing the bondingaxis makes the orbital a orbital

p

Figure 6.20

π bonds from side-on combinations of p orbitals

DE

DE*

ss

s* s

Energy

= =

Figure 6.21 MO diagram for combining two s orbitals

While the color of each AO in diagrams su

ch as Figure 6.18 represents its phase in the

combination, the

size of the sphere represents its relative contribution to the MO

. The fact

that the two AOs are the same size in Figure 6.18 means that the two AOs contribute equally to the MO, which means that the electr

on density in the MO is distributed equally

over both atoms. MOs can be represented by e

ither the resulting combination as shown on

the right of Figure 6.18 or as the combining orbitals as shown on the left of Figure 6.18. We will use the latter method, where spheres

showing the sign and relative magnitude of

the contributing AOs will be shown rather than the resulting MO.

As shown in Figure 6.18,

and σ

• MOs are formed from the combination of two s σ

orbitals on different atoms. However,

σ

interactions are also pr

oduced by the head-on

combination of p orbitals. The combination of

orbitals that mixes lobes of the same phase

(Figure 6.19a) increases electron density

on the bonding axis, so it is a

bonding orbital. σ

The combination in which lobes of opposite phase interact (Figure 6.19b) annihilates electron density between the two atoms to produce a nodal plane perpendicular to the bonding axis, so it is a

• antibonding orbital. σ

The side-on combination of two p orbitals (Figure 6.20) results in no electron density

on the bonding axis, so both co

mbinations are classified as

. The combination of orbitals π

of the same phase increases electron density

between the bound atoms, so it is the

π

bonding orbital. The combination in which

lobes of opposite phase interact produces a

nodal plane perpendicular to the bonding axis, so it is an antibonding

• orbital. π

DIATOMIC MOLECULES The two nuclei in a

homonuclear diatomic molecule

are nuclei of the

same

element, so

the interacting atomic orbitals (AOs) are id

entical and contribute equally to the MO.

Consequently, the electron density in each MO

is symmetric and the bonds are nonpolar.

Each MO is characterized by an energy level, and electrons occupy the molecular orbitals in the same manner that they do atomic orbitals;

i.e.

, they fill the molecular orbitals at

lowest energy while obeying both Hund’s ru

le and the Pauli Exclusion Principle.

The energies of the

and σ

• orbitals relative to the s orbσ

itals used to construct them

are shown in an MO diagram. Three important characteristics of MO diagrams like those in Figure 6.21 are:

1. The energy of bonding interactions is

lower than that of the atomic orbitals (

E). Δ

2. The energy of antibonding orbitals is

higher than that of the atomic orbitals (

E*). Δ

3.

E* > Δ

E. Δ

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