Physical Chemistry , 1st ed.

2 selectrons will occupy the g 2 sbonding molecular orbital (and have oppo-

site spins). A molecular orbital diagram for Li 2 is shown in Figure 12.21.

Example 12.15

Borrowing from the molecular electron configuration of H 2 , what is the elec-

tronic configuration of Li 2?

Solution

Since we have two electrons in the g 1 smolecular orbital, two electrons in

the *g 1 santibonding orbital, and two electrons in the g 2 smolecular orbital,

the electron configuration is

(g 1 s)^2 (*g 1 s)^2 (g 2 s)^2

Note that sigma orbitals arise from the combination of the 2satomic orbitals

as well.

When porbitals participate in making molecular orbitals, a new considera-

tion arises. Because of the directionality of the porbitals, there are two possi-

bilities when porbitals combine. One porbital from each atom (arbitrarily the

pzorbital) can combine in a head-on, axial fashion (Figure 12.22a). The other

two porbitals (pxand py) must combine in a side-on, off-axis fashion (Figure

12.22b). Although the two side-on-overlapping pcombinations are degenerate,

these molecular orbitals do nothave the same energy as the axially overlapping

molecular orbital. The axially overlapped molecular orbital, with increased

electron density within the internuclear axis, is also a orbital; bonding and

antibonding orbitals are also produced by this combination of two patomic

orbitals.

The four side-on-overlapping porbitals make pi( ) molecular orbitals,

whose electron densities exist outside the intermolecular axis. (In fact, the in-

ternuclear axis represents a node for orbitals.) The combination of the four

patomic orbitals produces two degenerate bonding orbitals and two degen-

412 CHAPTER 12 Atoms and Molecules

px or py px or py

pz pz orbital

+

+

 orbital

(a)

(b)

Figure 12.22 (a) The pzatomic orbitals interact head-on, yielding bonding and antibond-

ing orbitals. (b) The pxand pyatomic orbitals interact in a side-on fashion, yielding orbitals

whose electron density is outside the internuclear axis. The different shades of the lobes indicate

different phases of the wavefunctions.

(^)
Li
2 s 2 s
Energy
Li
Li 2
(^)
Li
1 s 1 s
Li
Figure 12.21 A molecular orbital diagram for
Li 2 , showing that 1satomic orbitals interact with
1 sorbitals, and 2sorbitals interact with 2sor-
bitals. Although this is an additional approxima-
tion, it helps us understand the wavefunctions of
these simple molecules.