Physical Chemistry Third Edition

20.4 Heteronuclear Diatomic Molecules 851

20.18For each of the following ions or molecules, give the
bond order and the number of unpaired electrons in the
ground state:
a.C+ 2
b.B+ 2
c.Be+ 2

20.19For each of the following ions or molecules, give the
bond order and the number of unpaired electrons in the
ground state of:
a.O− 2
b.N+ 2
c.F+ 2

20.20Give the electron configuration, bond order, and term
symbol for the ground state of:
a.O 2
b.O− 2
c.O+ 2

Which will have the shortest bond? Which will have the

largest vibrational frequency? Explain your answers.

20.21The ionization potential is defined as the energy required

to remove an electron from a gaseous atom or molecule.

Sketch a rough graph of your predictions of the ionization

potentials of the homonuclear molecules Li 2 through F 2

as a function of atomic number. Explain.

20.22The electron affinity is defined in Chapter 19, and applies

to molecules as well as to atoms. It is energy given off

when a gaseous atom or molecule gains an electron.

Decide which of the homonuclear diatomic molecules

from Li 2 through F 2 would likely have a positive electron

affinity (spontaneously attract an electron) and give your

reasoning.

20.23If a hydrogen molecule is somehow excited into the state

with configuration (σg 2 s)^2 will the molecule dissociate?

Explain.

20.24An important excited state of O 2 is a singlet state. It is

highly toxic and biological organisms have defenses

against it. Write the electron configuration and the

term symbol for the lowest-energy singlet state of O 2.

20.4 Heteronuclear Diatomic Molecules

Heteronuclear diatomic molecules are not as symmetrical as homonuclear molecules,

and we cannot evaluate coefficients in LCAO molecular orbitals by requiring that the

orbitals have the proper symmetry. Variational, SCF, or density functional calculations

must be used to evaluate the coefficients.

z

r1H

r2H

r3H

r4H

r3Li

r4Li r2Li

r1Li

H nucleus

Electron 1

Electron 3

Electron 4

Electron 2

Origin of coordinates

x Li nucleus

y

Figure 20.13 The LiH Molecule Sys-

tem.

Lithium Hydride

The simplest stable heteronuclear molecule is lithium hydride, LiH. Like He 2 , LiH

has two nuclei and four electrons. We say that these two molecules areisoelectronic

(have the same number of electrons). However, LiH is a stable molecule in the ground

state while He 2 is not. Figure 20.13 shows the LiH system. We apply the Born–

Oppenheimer approximation and place the nuclei on thezaxis and place the origin

of coordinates at the center of mass of the nuclei. The zero-order electronic Hamil-

tonian operator for the LiH molecule is (omitting the constant internuclear repulsion

termVnn)

̂He(0) 1 Ĥ 1 (1)+Ĥ 1 (2)+Ĥ 1 (3)+Ĥ 1 (4) (20.4-1)

whereĤ 1 (i) is a one-electron Hamiltonian operator for electron numberi:

̂H 1 (i)−h ̄

2

2 m

∇^2 i+

e^2

4 π 0

(

1

riH

+

3

riLi

)

(i1, 2, 3, 4) (20.4-2)