Chapter 5 problems
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6.
The Molecular Orbital Theory
a. What are the three approximations to the molecular orbital theory that
were discussed in class?
b. Explain each approximation in some detail.
What are the three conditions for effective overlap of atomic or molecular
orbitals?
Interactions between d and p orbitals can be important in transition metal
complexes. As discussed in class, however, the symmetry of the combining
orbitals must match to form bonding and antibonding orbitals. Identify (and
show pictorially) these possible combinations between the d and p orbitals.
To answer parts a-e consider the C2+1 species.
a. Prepare a molecular orbital energy diagram or interaction diagram
(without the aid of Spartan) for this species, including the orbital shapes
and the number of electrons in each orbital. Do you predict significant
orbital mixing (e.g. between s and pz orbitals)?
b. Now, using Spartan construct the molecular orbital diagram (including the
calculated orbital shapes) and compare to the one constructed without the
aid of the software. Perform all calculations at the semi-empirical/AM1
level. The multiplicity of C2+1 is 2 (i.e. doublet). It has an unpaired
electron.
c. Write down the wavefunctions for the molecular orbitals (lowest energy to
highest). Explain how these wavefunctions indicate or do not indicate
significant orbital mixing between the s and pz orbitals.
d. Identify the HOMO and LUMO.
e. Would you predict C2+1 to be more or less stable than C2+2? Why?
Perform a calculation on both species and compare bond lengths. Discuss.
The hypofluorite ion, OF-, can be observed only with difficulty. Use Spartan
to help you answer the questions below. Calculations will be performed at the
semi-empirical/AM1 level.
a. Prepare a molecular orbital energy diagram for this ion. Be sure to
indicate with dashed lines the significant interactions. Fill this diagram
with the available valence electrons.
b. This ion is not very stable. Why?
c. Where would you predict the higher electron density; near the fluorine or
oxygen? Using Spartan construct an electrostatic potential map. Discuss
this map with reference to your prediction made earlier.
d. Write the wavefunctions for the HOMO and LUMO. What is the most
likely position for adding H+ to the OF- ion (to the oxygen and fluorine
end)? Explain your answer.
For the compound XeF2:
a. Sketch the valence shell group orbitals for the fluorine atoms (with the z
axes collinear with the molecular axis).
b. For each of the group orbitals, determine which outermost s, p, and d
orbitals of xenon are of suitable symmetry for interaction and bonding.
7.
c. The approximate orbital energies for Xe are -76.7, -25.8, and -12.1 eV for
the 4d, 5s, and 5p orbitals, respectively. The applicable orbital energies
for fluorine are on page 134. Do you predict a significant interaction
between the d orbitals of Xenon and any of the valence orbitals of
fluorine? Explain.
d. Perform an HF/3-21G calculation on XeF2. Examine and sketch the
HOMO and the next five molecular orbitals that are lower in energy. Do
you see any evidence for d orbital contribution from the Xe atom to these
molecular orbitals? Explain.
To answer the below questions, consider the compound GaF3:
a. Draw the Lewis structure and from this structure determine the point
group of the molecule (make sure you answer this correctly).
b. Draw the 2py atomic orbitals on the fluorine atoms. Recall that the y axes
on the ligands point toward the center atom on nonlinear molecules.
Determine the reducible representation for this group of atomic orbitals.
c. Using a calculator or any other method, determine the group orbitals (i.e.
SALC’s) from the reducible representation.
d. Which orbitals (s, p, or d) on the center atom have the appropriate
symmetry to interact with these group orbitals? Indicate clearly.
e. Assuming the energies between the group orbitals/SALC’s constructed for
the 2py atomic orbitals and the valence orbitals (s, p, and d) on Ga to have
similar energies construct a molecular orbital diagram to illustrate the
possible interactions.
f. Perform an HF/3-21G calculation on GaF3. Examine the various orbital
contributions to the HOMO and the next four molecular orbitals that are
lower in energy. Do you see any evidence for d orbital contribution from
the Ga atom to these molecular orbitals? Explain.