Created by Margret J. Geselbracht, Reed College (mgeselbr@reed.edu) and posted on VIPEr
(www.ionicviper.org) on May 31, 2009. Copyright Margret J. Geselbracht 2009. This work is licensed
under the Creative Commons Attribution Non-commercial Share Alike License. To view a copy of this
license visit http://creativecommons.org/about/license/.
MOLECULAR ORBITALS AND JAHN-TELLER DISTORTION OF THE XENON TRIFLUORIDE ANION
1. The molecular anion [XeF3]– has been observed in the gas phase in mass spectrometry
experiments, although it has never been isolated in the condensed phase nor structurally
characterized. Recently, computational studies were carried out to predict the structure and
understand the bonding in [XeF3]–. The researchers examined three possible structures,
shown below, one with D3h symmetry and two different distorted models, a T-shaped
molecule (predicted from VSEPR) and the Y-shaped molecule.
F
F
distort
Xe
Xe
F
F
F
F
F
F
Xe F
Xe
F
distort
F
F
T-shaped molecule
Xe
F
F
Y-shaped molecule
(a) Start by drawing the -only MO diagram for the undistorted D3h version of [XeF3]–. Only
consider the use of the valence ns and np atomic orbitals on Xe: No d orbitals allowed!
Determine the representation for -bonding, reduce it, draw the well-labeled MO
diagram, fill in the right number of electrons and draw cartoons of all the MOs.
D3h
E
 = 3
2 C3
3 C2
h
2 S3
3 v
0
1
3
0
1
F
 = A1’ + E’
The bonding MOs will involve the Xe 5s, the Xe 5px and 5py orbitals. The Xe 5pz orbital
will be nonbonding.
To gauge the relative energies of the Xe AOs and the SALCs made from the F 2p
orbitals, consider first, the relative ionization energies (source: www.webelements.com)
of Xe (1170 kJ/mol) and F (1681 kJ.mol). These values tell us that the Xe 5p orbitals are
higher in energy than the F 2p orbitals (not too surprising). The relatively large effective
nuclear charge felt by electrons in the Xe 5s orbital, will lower the energy of this orbital
substantially such that we might expect the Xe 5s orbital would be at least of comparable
energy to that of F 2p. In reality, the Xe 5s orbital (-23.4 eV) is actually slightly lower in
energy than F 2p (-18.6 eV) (source: J. Am. Chem. Soc. 2000, 122, 2780-2783.).
According to this source, by the way, the Xe 5p orbitals are at -12.56 eV.
Note that while it is not important that you know exactly what the energies of the Xe
orbitals are, if you consider that the Xe 5s is much higher in energy, than you will
unlikely be able to correctly predict the triplet diradical state for this molecule. The trick
is that you need to have the 2a1’* MO end up lower in energy than the 2e’* MOs.
Whether or not 2a1* is lower or higher in energy than 1a2”nb is less critical.
Created by Margret J. Geselbracht, Reed College (mgeselbr@reed.edu) and posted on VIPEr
(www.ionicviper.org) on May 31, 2009. Copyright Margret J. Geselbracht 2009. This work is licensed
under the Creative Commons Attribution Non-commercial Share Alike License. To view a copy of this
license visit http://creativecommons.org/about/license/.
This MO diagram will be filled with 12 e-‘s. How you do the “book keeping” on those
electrons on either side of the MO diagram is
not really that important. In the case below, I
h
2e'*
a
v
2e'*
e
c
5p
E'
A2"
1a2"nb
2a1'*
E
E'
A1'
F SALCs
5s
A1'
1e'
ounted
8
electrons
from
a
neutral Xe,
2 neutral F
atoms
contributing
1 e- each
and then 1
F–
contributing
2 electrons.
Xe
1a1'
1a2" nb
1e'
1a1'
(b) What would be the formal bond order in the [XeF3]– anion?
Note the electrons in the 1a2” nb MO do not contribute to the bond order.
2a1'*
Created by Margret J. Geselbracht, Reed College (mgeselbr@reed.edu) and posted on VIPEr
(www.ionicviper.org) on May 31, 2009. Copyright Margret J. Geselbracht 2009. This work is licensed
under the Creative Commons Attribution Non-commercial Share Alike License. To view a copy of this
license visit http://creativecommons.org/about/license/.
Bond order = ½ (6 – 4) = 1 divided over 3 positions
So average bond order of only 1/3 for each bond.
(c) Now consider the effects of each distortion. Starting with the MOs you have drawn for
the symmetric molecule, draw a correlation diagram to show any energy changes that you
would expect for each molecular orbital, labeling the MOs in the new point group of the
distorted molecule. In other words, do the MOs go down in energy, go up in energy, or
stay the same after the distortion has occurred? Briefly explain the origin of any energy
changes you show. Notice that in the distorted molecules, there are unequal Xe–F bond
lengths. You should do this for each of the two distorted structures.
In both the T-shaped and Y-shaped distortions, the point group changes from D3h to C2v.
In the pictures below, I have changed the symmetry labels of the MOs accordingly. The
MO symmetries were assigned according to the symmetries of the Xe AO. Note that the
x, y, and z axes change orientations in C2v. The z axis now points along the C2 axis and
the molecule is defined to lie in the yz plane.
T-shaped distortion:
a1
a1 *
a1
F
b2
F
a1*
F
F
b2* F
The energies of the a1 MOs should change very little due to
the spherical symmetry of the Xe 5s orbital. The shortened
bond lengths on the bottom of the T will lower the bonding
MO slightly (enhancing bonding overlap), but it should also
raise the antibonding MO slightly (enhancing antibonding
overlap).
These MOs are no longer degenerate in C2v. The bonding MO on
the left should go up in energy, because the small amount of
bonding overlap with the lower half of the orbital is lost as the two
F atoms move into the nodal plane of the Xe p orbital. The
bonding MO on the right should go down in energy since the
orbital overlap becomes more effective as the F orbitals move up
to the point of maximal overlap with the Xe p orbital.
The opposite energy changes will occur for the antibonding MOs.
F
There should be no change in the energy of the nonbonding MO, although the symmetry
label changes (since it is now based on the Xe 5px orbital). These energy changes are
summarized below.
Created by Margret J. Geselbracht, Reed College (mgeselbr@reed.edu) and posted on VIPEr
(www.ionicviper.org) on May 31, 2009. Copyright Margret J. Geselbracht 2009. This work is licensed
under the Creative Commons Attribution Non-commercial Share Alike License. To view a copy of this
license visit http://creativecommons.org/about/license/.
2b2*
2e'*
4a1*
1b1 nb
1a2"nb
3a1*
E
2a1'*
2a1
1e'
1b2
1a1
1a1'
D3h
T-shaped C2v
Y-shaped distortion:
a1
a1
a1*
The energies of the a1 MOs should change very little due to the
spherical symmetry of the Xe 5s orbital. The shortened bond length
on the top of the Y will lower the bonding MO slightly (enhancing
bonding overlap), but it should also raise the antibonding MO
slightly (enhancing antibonding overlap).
a1*
b2
F
b2 * F
These MOs are no longer degenerate in C2v. The bonding MO on the
left should go down in energy, because the bonding overlap with the
lower half of the orbital will be slightly improved as the two F atoms
move away from the nodal plane of the Xe p orbital and the bonding
overlap with the top F atom should improve as the bond length
decreases. The bonding MO on the right should go up in energy since
the orbital overlap becomes less effective as the F orbitals move down
off the points of maximal overlap with the Xe p orbital.
The opposite energy changes will occur for the antibonding MOs.
There should be no change in the energy of the nonbonding MO,
although the symmetry label changes (since it is now based on the Xe
5px orbital). These energy changes are summarized below.
Created by Margret J. Geselbracht, Reed College (mgeselbr@reed.edu) and posted on VIPEr
(www.ionicviper.org) on May 31, 2009. Copyright Margret J. Geselbracht 2009. This work is licensed
under the Creative Commons Attribution Non-commercial Share Alike License. To view a copy of this
license visit http://creativecommons.org/about/license/.
4a1*
2e'*
2b2*
1b1 nb
1a2"nb
3a1*
E
2a1'*
1b2
1e'
2a1
1a1
1a1'
D3h
Y-shaped C2v
Created by Margret J. Geselbracht, Reed College (mgeselbr@reed.edu) and posted on VIPEr
(www.ionicviper.org) on May 31, 2009. Copyright Margret J. Geselbracht 2009. This work is licensed
under the Creative Commons Attribution Non-commercial Share Alike License. To view a copy of this
license visit http://creativecommons.org/about/license/.
(d) The D3h triplet state was found to be 60-110 kJ/mol higher in energy than the ground state
structure, which turned out to be the Y-shaped molecule. (The range in energies
depended on the details of the atomic orbital basis sets chosen for the Xe and F atoms.)
Can you explain why there would be such a significant gain in energy upon distortion for
this molecule? If you can, please do so. 
As seen in part c, for either type of distortion, the total energy of the electrons are
lowered relative to the symmetric D3h structure. The important change in energy involves
the two highest energy electrons which are stabilized by the distortion as one of the MOs
becomes more bonding as the overlap increases upon distortion. Unfortunately, this
qualitative picture does not explain why the Y-shaped distortion is lower in energy than
the T-shaped distortion. A more quantitative measure of the energy changes for each
distortion is required, in other words, a complete calculation.