Download Project 3 - Illinois State Chemistry

Chemistry 362
Fall 2015
Dr. Jean M. Standard
November 11, 2015
Project 3: Molecular Orbital Calculations of Diatomic Molecules
In this project, you will investigate the molecular orbitals and molecular orbital energies of the homonuclear
diatomic molecules N2 and O2 in both ground and excited states. Molecular orbital energy diagrams will be
constructed and geometry optimizations of the compounds will be performed in order to compare and contrast their
structures, orbitals, and energies.
The computer program that you will use for these simulations is a software package called Gaussian for the
quantum mechanical calculations and a software package called Avogadro for visualization. You will be able to
access Gaussian and Avogadro in the computer lab located in Julian Hall Room 216. Please note that the computers
in the JH 216 are usually available at any time during the day; however, they are occasionally reserved for classes as
noted on the schedule posted on the door.
This project requires you to complete calculations for a number of molecules using the Avogadro/Gaussian software
packages. You may use any of the Macintosh computers in JH 216 to access the Avogadro/Gaussian programs
(instructions are provided later in this handout). In fact, you can use one Macintosh for one part of the project, and
another Macintosh for another part of the project since none of the data is stored on the Macs. All the calculations
actually will be carried out on Linux workstations that you will connect to from the Macintosh through the internet.
This project is worth 25 points and is due on Monday, November 30, 2015.
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USING THE COMPUTERS AND THE AVOGADRO SOFTWARE PACKAGE
This section contains instructions for logging in to the Macintosh computers in JH 216 and accessing the Linux
computers on which the calculations will be performed. In addition, it provides instructions on how to start the
Avogadro software package. The use of the Gaussian software package will be described later.
Logging In
To log in to one of the Macintosh computers in JH 216, enter your ISU ULID and password.
Starting X11
In order to access the Linux workstations to run the Avogadro/Gaussian software packages, you must run a software
package on the Mac called X11. To start the X11 application, click on the "X" icon located in the Dock on the Mac
desktop. A single white window should appear on the screen; this is called an "xterm" window, or simply a terminal
window.
Logging on to the Linux Computers
You may use any one of the six available Linux computers for the project. To log on to one of the Linux computers,
type the following command in the xterm window:
ssh –Y [email protected]
Here, "ssh" stands for secure shell; this application provides a secure connection to the remote Linux workstation.
Also, hostname is the name of one of the six Linux computers. The password is "wavefun". Enter the password as
prompted. Once you have done this, you are connected to the Linux computer.
Starting the Avogadro Program
To start the Avogadro program, type "avogadro" in the xterm window and hit the return key. A window for the
Avogadro software package should appear on your screen. At this point, you are ready to begin the project.
PROJECT 3 PROCEDURE: MOLECULAR ORBITALS OF DIATOMIC MOLECULES
In this project, you will explore the molecular orbitals (MOs) and molecular orbital energies of the homonuclear
diatomic molecules N2 and O2. In particular, you will construct the MO energy diagrams and perform geometry
optimizations of the compounds to explore their structure. Example MO diagrams can be found in Chapter 23 of
your textbook. In addition, you will characterize the molecular orbitals as sigma bonding or antibonding, pi bonding
or antibonding, or core orbitals.
The parts of the project that involve direct use of the Avogadro/Gaussian software packages are marked with an
asterisk. Other parts may require analysis of the results of the Avogadro/Gaussian calculations, comparison with
literature values, or use of information from class or your textbook.
1.
Construction of MO energy diagrams of N2 and O2
1a. Using the handout provided in class or information in Ch. 23 of your textbook, sketch the MO energy diagrams
of N2 and O2. Make sure to label and fill the atomic orbitals as well as the molecular orbitals. Include these
sketches in your project. Be careful of the energy ordering of the 1π and 3σ molecular orbitals––they switch
order between N2 and O2.
1b. Report the multiplicities of N2 and O2 that are predicted by your MO energy diagrams.
1c. Compute and report the bond order of N2 and O2 from the MO energy diagrams. The bond order is defined as
BondOrder =
# Bonding electrons − # Antibonding electrons
.
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Sketch the Lewis dot structures of N2 and O2. Discuss whether or not the bond order predicted from the Lewis
dot structure €
agrees with the calculation from the MO energy diagram.
2.
Geometry Optimizations and Energy Calculations of N2 and O2
In this part of the project you will employ the Avogadro/Gaussian software packages to obtain the equilibrium
geometries and energies of the singlet and triplet states of N2 and O2.
*2a. To begin, you will need to build the N2 molecule using the Avogadro software package. To construct an initial
structure for the N2 molecule, start the program and click on the Drawing Tool,
. Set the Element to
Nitrogen, Bond Order to Triple, and make sure that "Adjust Hydrogens" is turned off. Click with your mouse in
the drawing window to place a single nitrogen atom. Then place a second nitrogen atom on the screen adjacent
to the first one, as shown in Figure 1.
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Figure 1. Placement of nitrogen atoms on the screen to form the beginnings of the N2 molecule.
Now, use the mouse to draw a bond between the nitrogen atoms in order to complete the construction of the N2
molecule. When finished, your structure should look similar to that shown in Figure 2.
Figure 2. Completed drawing of the N2 molecule.
*2b. Next, perform a quantum mechanical calculation of the singlet state of the N2 molecule using the Gaussian
software package. The equilibrium geometry, energy, and molecular orbitals of the molecule will be
determined. From the Avogadro menus at the top of the window, select "Extensions → Gaussian". Use the
following settings:
Calculation: Geometry Optimization
Theory: RHF
Charge: 0
Processors: 4
Basis: 3-21G
Multiplicity: 1
Also, make sure that the "Checkpoint" button is clicked (this enables viewing of the molecular orbitals,
which will be carried out in step 4).
Once the settings are correct, click "Compute". You will be prompted to enter a filename. Use the filename
'n2singlet-XYZ.com', where 'XYZ' corresponds to your initials. After the filename is entered, click "Save".
The calculation will begin and you should see a popup window appear that says "Running Gaussian
calculation…". When the popup window disappears, your calculation of the N2 molecule should be complete.
*2c. The results that you need for the singlet N2 molecule include the equilibrium bond length and electronic energy.
The optimized N2 molecule should have automatically loaded into the Avogadro window (there will be a listing
of MOs to the right of the structure, which you will investigate later in the project). To obtain the equilibrium
bond length, use the Measure Tool,
, to measure the equilibrium bond and report it.
To obtain the electronic energy of N2, you will have to search the results file directly. To do this, first close
Avogadro by selecting "File → Quit". You may be asked to save changes, but you can safely discard any
changes because the file you need is already saved.
Next, in the terminal window, type "gedit n2singlet-XYZ.log" (where 'XYZ' corresponds to your initials).
You will see a window open on the screen similar to that shown in Figure 3. The file you are viewing contains
the results from the Gaussian calculation that you ran for singlet N2.
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Figure 3. Results file from a Gaussian calculation of the N2 molecule.
To obtain the electronic energy, search the file for the string 'GINC' by selecting "Search → Find" from the
menu. This takes you almost to the end of the file and you will see a block of text that looks something like the
following:
1\1\GINC-FRODO\FOpt\RHF\6-31G(d)\N2\STANDARD\2-Nov-2015\0\\#N RHF/6-3
1G(D) OPT\\Title\\0,1\N,-0.5379161752,0.0369894235,0.\N,0.5379161752,0.0369894235,0.\\Version=AM64L-G03RevC.02\State=1-SGG\HF=-108.9439495\
RMSD=9.984e-10\RMSF=1.632e-06\Dipole=0.,0.,0.\PG=D*H [C*(N1.N1)]\\@
The energy listed in the block shown above, HF=–108.9439495, is the electronic energy. Record this value; it
is given in hartrees.
When you are finished, select "File → Quit" to close the results file.
*2d. Repeat steps 2a-2c to build and perform a quantum mechanical calculation of the singlet state of O2. You
should record the equilibrium bond length and electronic energy.
*2e. Next, you will build and perform a quantum mechanical calculation of the triplet state of N2. To do this, first
build a new copy of the N2 molecule using the same procedure as in step 2a.
Then, perform a quantum mechanical calculation of the triplet state of the N2 molecule using the Gaussian
software package. The equilibrium geometry, energy, and molecular orbitals of the molecule will be
determined. From the Avogadro menus at the top of the window, select "Extensions → Gaussian". Use the
following settings:
Calculation: Geometry Optimization
Theory: RHF
Charge: 0
Processors: 4
Basis: 3-21G
Multiplicity: 3
Make sure that this time the "Multiplicity" is set to 3 to select the triplet state. Also, make sure that the
"Checkpoint" button is clicked.
In addition, you must change one line in the setup window as shown in Figure 4.
Figure 4. Setup window for a Gaussian calculation of triplet N2.
You should see on the third line in the white input box the following text:
#n RHF/3-21G Opt
Edit the line so that it has the following form (you are just replacing RHF with UHF):
#n UHF/3-21G Opt
Once the settings are correct, click "Compute". You will be prompted to enter a filename. Use the filename
'n2triplet-XYZ.com', where 'XYZ' corresponds to your initials. After the filename is entered, click "Save". The
calculation will begin and you should see a popup window appear that says "Running Gaussian calculation…".
When the popup window disappears, your calculation of the triplet state of the N2 molecule should be complete.
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Finally, repeat step 2c in order to measure and record the equilibrium bond length and electronic energy of
triplet N2.
*2f. Repeat step 2e to build and perform a quantum mechanical calculation of the triplet state of O2. You should
record the equilibrium bond length and electronic energy.
2g. Prepare a table of results for singlet and triplet N2 and O2. Your table should include the equilibrium bond
length and electronic energy of each of the four species.
Which is lower in energy, singlet or triplet N2? The lower energy species is the most stable. Does this result
agree with your prediction of the multiplicity from MO energy diagram in Part 1?
Which is lower in energy, singlet or triplet O2? Does this result agree with your prediction of the multiplicity
from the MO energy diagram in Part 1?
3. Comparisons with Experiment
In this part of the project, the computed bond lengths and electronic energies of singlet and triplet N2 and O2 will be
compared with experiment.
3a. Obtain literature values from experiment for the equilibrium bond lengths of singlet and triplet N2 and O2.
NIST is a good place to look, but you also can find the values elsewhere. Compare your results to the literature;
use percent differences.
3b. How much does the bond length change in singlet vs. triplet N2 and singlet vs. triplet O2? When comparing the
singlet state to the triplet state bond lengths for each species, which molecule exhibits the larger change between
the singlet and triplet bond lengths, N2 or O2? Discuss why one species might exhibit a large change in bond
length between singlet and triplet while another might not.
3c. Use the MO energy diagrams that you constructed in Part 1 to discuss whether or not the bond orders are
different for singlet vs. triplet N2 and singlet vs. triplet O2. Explain whether or not your findings correlate with
the bond length differences observed in step 3b.
3d. Obtain literature values for the experimental singlet-triplet energy difference for N2 and O2. Again, NIST is a
good place to look. You will need to find the energy difference between the lowest singlet and triplet states for
each molecule; many are shown. On the NIST web site, the states are ordered from lowest to highest in energy,
with the lowest energy states at the bottom of the listing. The lowest, or ground, state is always labeled X and
the next highest is labeled A or a. The energy difference is denoted Te and is reported in cm–1.
Compare the literature energy spacing between the singlet and triplet states for N2 and O2 with your computed
results. The energy difference between the singlet and triplet states from the computer simulations may be
obtained by taking the difference between the singlet and triplet electronic energies reported in step 2f (just use
the absolute value of this number); the conversion from hartrees to cm–1 is 1 hartree = 219474.6 cm–1.
Is there good agreement between experiment and calculation? You may find that in one case there is, but not in
the other.
What are the magnitudes of the singlet-triplet energy differences for N2 and O2? Are the differences similar for
N2 and O2, or is there an order of magnitude difference (you might want to consider the experimental values for
this discussion)? Why is one singlet-triplet energy difference so much larger than the other one? Use the MO
energy diagrams that you constructed in Part 1 to explain.
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3e. Finally, it is known experimentally that singlet O2 is a very highly reactive species and is important in some
natural and biological processes. Provide two or three examples of the role singlet oxygen is thought to play in
some key processes.
4. Classification of Molecular Orbitals of N2 and O2
In this part of the project, you will view the three-dimensional shapes of the occupied molecular orbitals of the
ground electronic states of N2 and O2 and classify them as core, sigma or pi, and bonding or antibonding.
*4a. To view the molecular orbitals of singlet N2, start the Avogadro program and select "File → Open". The file
type should be set to "Computational Chemistry Output", and the filename you select should be 'n2singletXYZ.log' (where 'XYZ' corresponds to your initials). Click "Open" and the singlet N2 molecule should appear
in the Avogadro window.
The list of MOs should appear to the right of the molecule in the Avogadro window. However, if the list does
not appear, select "Extensions → Molecular Orbitals".
Click on the listing for the HOMO in the window. The highest occupied molecular orbital (MO#7 for singlet
N2) should be displayed (blue is negative, red is positive with respect to the sign of the orbital). If it does not
appear, click the "Render" button below the MO list. Make a sketch of the orbital. You may use the left mouse
button to rotate the orbital on the screen in order to get a better view if necessary.
Note: If you prefer to obtain screenshots of the MOs instead of sketching them, you may use Command-Shift-4
on the Mac. A crosshair cursor will appear that you may use to drag over the region of the screen that you wish
to capture. The snapshot will be saved the to Mac desktop in PNG image format.
*4b. Repeat step 4a for each of the remaining 6 occupied molecular orbitals in turn by selecting MO 6, MO 5, . . .,
MO 1. Note that if you display them in sequence from MO 7 to MO 1, you are displaying the molecular
orbitals from highest to lowest energy, respectively.
*4c. Repeat steps 4a+b to open the results file and display and sketch the occupied MOs of triplet O2. Note that in
this case there are 8 occupied MOs. Also note that due to approximations in the calculations that you performed
in this project, the ordering of the 3σ and 1π orbitals is incorrect in this step. However, the goal here is for you
to sketch and classify the MOs, so do not be concerned if the ordering does not quite match the energy level
diagram that you constructed in step 1.
4d. In your report, include the sketches of each occupied MO of singlet N2 and triplet O2, along with a classification
as to the type of orbital for each one. Your classification should include whether the MO is a core type, sigma
type or pi type, and whether it is a bonding or antibonding orbital.
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