Chemistry 362 Spring 2018 Dr. Jean M. Standard April 20, 2018 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 N 2 and O 2 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 30 points and is due on Wednesday, May 2, 2018.
2 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 find the X11 application, use Launchpad in the Dock at the bottom of the screen and search for X11. Start the X11 package. 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 Each person will be assigned one of the six available Linux computers to use for the project. To log on to the Linux computer to which you were assigned, type the following command in the xterm window: ssh Y che362@hostname.che.ilstu.edu Here, "ssh" stands for secure shell; this application provides a secure connection to the remote Linux workstation. Also, hostname is the name of the Linux computer to which you were assigned (options: frodo, samwise, gandalf, aragorn, legolas, gimli). 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 3 In this project, you will explore the molecular orbitals (MOs) and molecular orbital energies of the homonuclear diatomic molecules N 2 and O 2. 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 N 2 and O 2 1a. Using the handout provided in class or information in Ch. 23 of your textbook, sketch the MO energy diagrams of N 2 and O 2. 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 N 2 and O 2. 1b. Report the multiplicities of N 2 and O 2 that are predicted by your MO energy diagrams. 1c. Compute and report the bond order of N 2 and O 2 from the MO energy diagrams. The bond order is defined as BondOrder = # Bonding electrons # Antibonding electrons 2. Sketch the Lewis dot structures of N 2 and O 2. 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 N 2 and O 2 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 N 2 and O 2. *2a. To begin, you will need to build the N 2 molecule using the Avogadro software package. To construct an initial structure for the N 2 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.
4 Figure 1. Placement of nitrogen atoms on the screen to form the beginnings of the N 2 molecule. Now, use the mouse to draw a bond between the nitrogen atoms in order to complete the construction of the N 2 molecule. When finished, your structure should look similar to that shown in Figure 2. Figure 2. Completed drawing of the N 2 molecule.
*2b. Next, perform a quantum mechanical calculation of the singlet state of the N 2 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: 5 Calculation: Geometry Optimization Processors: 4 Theory: RHF Basis: 3-21G Charge: 0 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 N 2 molecule should be complete. *2c. The results that you need for the singlet N 2 molecule include the equilibrium bond length and electronic energy. The optimized N 2 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 N 2, 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. The file you are viewing contains the results from the Gaussian calculation that you ran for singlet N 2. 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-2017\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 O 2. You should record the equilibrium bond length and electronic energy.
6 *2e. Next, you will build and perform a quantum mechanical calculation of the triplet state of N 2. To do this, first build a new copy of the N 2 molecule using the same procedure as in step 2a. Then, perform a quantum mechanical calculation of the triplet state of the N 2 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 Processors: 4 Theory: RHF Basis: 3-21G Charge: 0 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 3. Figure 3. Setup window for a Gaussian calculation of triplet N 2. 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 N 2 molecule should be complete.
7 Finally, repeat step 2c in order to measure and record the equilibrium bond length and electronic energy of triplet N 2. *2f. Repeat step 2e to build and perform a quantum mechanical calculation of the triplet state of O 2. You should record the equilibrium bond length and electronic energy. 2g. Prepare a table of results for singlet and triplet N 2 and O 2. 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 N 2? 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 O 2? 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 N 2 and O 2 will be compared with experiment. 3a. Obtain literature values from experiment for the equilibrium bond lengths of singlet and triplet N 2 and O 2. 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 N 2 and singlet vs. triplet O 2? 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, N 2 or O 2? 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 N 2 and singlet vs. triplet O 2. 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 N 2 and O 2. 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 T e and is reported in cm 1. Compare the literature energy spacing between the singlet and triplet states for N 2 and O 2 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 N 2 and O 2? Are the differences similar for N 2 and O 2, 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.
8 3e. Finally, it is known experimentally that singlet O 2 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 N 2 and O 2 In this part of the project, you will view the three-dimensional shapes of the occupied molecular orbitals of the ground electronic states of N 2 and O 2 and classify them as core, sigma or pi, and bonding or antibonding. *4a. To view the molecular orbitals of singlet N 2, 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 'n2singlet- XYZ.log' (where 'XYZ' corresponds to your initials). Click "Open" and the singlet N 2 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 N 2 ) 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 O 2. 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 N 2 and triplet O 2, 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.