12.12 & 12.13 Molecular Orbitals;
More Diatomic Molecules
12.39.Explain how we know that the first in equation
12.43 is the wavefunction for the bonding orbital, and that
the second in equation 12.43 is the wavefunction for the an-
tibonding orbital.
12.40.From Figure 12.23, give molecular electronic configu-
rations for all diatomic molecules shown.
12.41.Use Figure 12.23 to determine electron configurations
for O 22 , O 2 , and O 22 .
12.42.Use molecular orbital arguments to decide whether or
not the difluoride dianion, F 22 , should exist as a stable ion.
12.43.What is the bond order for the NO molecule? Use
Figure 12.24 to determine an answer.
12.44.Use a math software program to determine the sym-
bolic determinant of the 4 4 determinantal wavefunction for
a Be atom, which has four electrons. Can you write the wave-
functions represented by the individual terms and identify the
quantum numbers for each function?
12.45.Numerically evaluate the integral in Example 12.8 for
E(1)and demonstrate how much agreement there is to the
given value of the energy correction of 5.450 10 ^18 J.
12.46.Use a symbolic math program to evaluate the trial
wavefunction given in Example 12.11. Do you get the same
value for Z?
12.47.Evaluate the energies of the wavefunctions that are
linear combinations of three terms whose energy and overlap
integrals have the following values (in arbitrary units):
H 11 18 S 11 0.55
H 22 14 S 22 0.29
H 33 13.5 S 33 0.067
H 12 2.44 S 12 0.029
H 13 1.04 S 13 0.006
H 23 0.271 S 23 0.07712.48.Evaluate equations 12.46 and 12.47 versus R, as R
varies from 0 to 5 Å. Determine the value of Rthat minimizes
the energy. What is the value of the energy at this minimum-
energy distance?418 Exercises for Chapter 12
Symbolic Math Exercises