VSEPR (valence state electron pair repulsion) theory was formulated to
anticipate the local geometry about an atom in a molecule (see discussion in
Section 25.1). All that is required is the number of electron pairs
surrounding the atom, broken down into bonded pairs and nonbonded (lone)
pairs. For example, the carbon in carbon tetrafluoride is surrounded by four
electron pairs, all of them tied up in \(\mathrm{CF}\) bonds, whereas the sulfur
in sulfur tetrafluoride is surrounded by five electron pairs, four of which
are tied up in SF bonds with the fifth being a lone pair.
VSEPR theory is based on two simple rules. The first is that electron pairs
(either lone pairs or bonds) will seek to avoid each other as much as
possible. Thus, two electron pairs will lead to a linear geometry, three pairs
to a trigonal planar geometry, four pairs to a tetrahedral geometry, five
pairs to a trigonal bipyramidal geometry, and six pairs to an octahedral
geometry. Although this knowledge is sufficient to assign a geometry for a
molecule such as carbon tetrafluoride (tetrahedral), it is not sufficient to
specify the geometry of a molecule such as sulfur tetrafluoride. Does the lone
pair assume an equatorial position on the trigonal bipyramid leading to a
seesaw geometry, or an axial position leading to a trigonal pyramidal
geometry?
The second rule, that lone pairs take up more space than bonds, clarifies the
situation. The seesaw geometry in which the lone pair is \(90^{\circ}\) to two
of the SF bonds and \(120^{\circ}\) to the other two bonds is preferable to the
trigonal pyramidal geometry in which three bonds are \(90^{\circ}\) to the lone
pair.
Although VSEPR theory is easy to apply, its results are strictly qualitative
and often of limited value. For example, although the model tells us that
sulfur tetrafluoride adopts a seesaw geometry, it does not reveal whether the
trigonal pyramidal structure (or any other structure) is an energy minimum,
and if it is, what its energy is relative to the seesaw form. Also it has
little to say when more than six electron pairs are present. For example,
VSEPR theory tells us that xenon hexafluoride is not octahedral, but it does
not tell us what geometry the molecule actually assumes. Hartree-Fock
molecular orbital calculations provide an alternative.
a. Optimize the structure of \(\mathrm{SF}_{4}\) in a seesaw geometry
\(\left(C_{2 v} \text { symmetry }\right)\) using the HF/3-21G model and
calculate vibrational frequencies (the infrared spectrum). This calculation is
necessary to verify that the energy is at a minimum. Next, optimize the
geometry of \(\mathrm{SF}_{4}\) in a trigonal pyramidal geometry and calculate
its vibrational frequencies. Is the seesaw structure an energy minimum?
What leads you to your conclusion? Is it lower in energy than the
corresponding trigonal pyramidal structure in accordance with VSEPR theory?
What is the energy difference between the two forms? Is it small enough that
both might actually be observed at room temperature? Is the trigonal pyramidal
structure an energy minimum?
b. Optimize the geometry of \(\mathrm{XeF}_{6}\) in an octahedral geometry
\(\left(\mathrm{O}_{\mathrm{h}} \text { symmetry }\right)\) using the HF/3-21G
model and calculate vibrational frequencies. Next, optimize \(\mathrm{XeF}_{6}\)
in a geometry that is distorted from octahedral (preferably a geometry with
\(\left.C_{1} \text { symmetry }\right)\) and calculate its vibrational
frequencies. Is the octahedral form of \(\mathrm{XeF}_{6}\) an energy minimum?
What leads you to your conclusion? Does distortion lead to a stable structure
of lower energy?
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