Computational Chemistry at GVSU

An Exploration of Methods and Basis Sets

In this laboratory, we will be exploring the accuracy of different methods and basis sets in determining the order of the molecular orbital levels of F₂. First we will use the semi-empirical method AM1, to calculate the electronic structure of F₂. We will then more accurately calculate its electronic structure using ab initio methods.

Using Cerius2, build F₂ and clean the structure. Measure the interatomic distance (Geometry: Measurement) and record it in Row 1 of Table 1.

Geometry Optimization

1. Get the MOPAC menu card by choosing "Quantum 1" menu deck, and then click the MOPAC card forward. Choose "Run". Set the spin multiplicity to one.

Note: The spin multiplicity, M, is 2S + 1, where S is the total spin angular momentum quantum number. If all electrons are paired, S = 0 and M = 1. This is called a singlet state. If one electron is unpaired, S = 1/2 and M = 2, giving a doublet state. If two electrons are unpaired, S = 1 and M = 3, giving a triplet state.

In Cerius², M = 0 means that you want the program to choose the spin multiplicity based on what its algorithms indicate is most likely.

2. Set the File Prefix to "F2AM1", and choose "AM1" as the Method. Choose "Geometry Optimization" as the Task and then click on the "Run" button.
   
   
3. In Table 1, Row 2, record the amount of CPU time it took to run the geometry optimization calculation, found at the bottom of the MOPAC output window (gray).
(Occasionally the gray window doesn't pop up. Check the Command window, at the bottom left below the Model window, to make sure your job ran correctly. If no error messages are present, the job may simply have run too fast to pop up a window. If this is the case, record the CPU time as ~0 seconds.)


4. Energies: Once the calculation is complete, choose "Analyze –>" in the "MOPAC" Deck, and then "Files". You will see a Summary of Calculation, giving the AM1 Heat of Formation (H°_f) for your F₂ conformation. Record this in Row 2 of Table 1.

Comparing Energies: Each suite of programs (MOPAC, Gaussian) has its own reference energy state, and all energies are calculated relative to this reference enery.

• For MOPAC, the reference state is the Heat of Formation (H°_f). This is the energy required or given off when the molecule is assembled from the appropriate elements in their "standard states" at 25°C. Someone (actually a committee) has assigned standard states for each element, e.g., the standard state for carbon is graphite, and for oxygen it's O₂ gas.
• For Gaussian, the reference state is the Total Energy, the energy required or given off when the molecule is assembled at absolute zero from individual particles (electrons, nuclei) at infinite distance from each other. The total energy is usually a very large number, since assembling atoms is usually favorable.
  
  

Only if two energies have the exact same reference state can they be compared. This requires the energies be for the same number and type of atoms. For example, the cis vs. trans energy of butadiene can be compared using H°_f from MOPAC, but the energy of butadiene cannot be compared to that of butane (they have a different atom set). The energy of butadiene from MOPAC cannot be directly compared to an energy from Gaussian, since they have a different reference energy.

If an equation is balanced, the sum of the energies of the reactants can be compared to the sum of the energies of the products, since each side of the reaction has the same number and type of atoms.

5. Record the F-F distance in Row 2.

Q 2. Has the interatomic distance improved?

 

 

Analyzing Structures

6. Molecular Orbitals (MO): Let’s further analyze the geometry-optimized structure. Back in the MOPAC Deck card, choose "Analyze —>" again. Select "Orbitals". You can then select any one of the orbitals shown, and push the upper left "Calculate" button. A Molecular Orbital will be displayed. You can choose "Surfaces" in the "Analyze—>" menu and set the transparency to ~ 70% to see the underlying structure. You can also change the isosurface value to vary the size of the orbitals plotted.

Let each sigma orbital be named ns, where n =1, 2,… indicates the lowest to highest energy sigma orbitals (e.g., 1s, 2s*,…). If the orbital is antibonding, superscript it with an asterisk (*). Name the pi orbitals similarly (e.g., 1p, 2p*,…). Write the order of the orbitals from lowest to highest energy in Table 1, last column.

Since AM1 is so fast, we will use it to explore electron density.

7. Electron Density: Choose "Density" in the "Analyze —>" menu, and select the "Calculate Total Charge Density" button. The electron density is the number of electrons per unit volume; the surface shown is an isosurface, i.e., a contour connecting all points that have a particular number of electrons per volume.



8. Slices: Under "Analyze —>", select "Slices". Click on "Create New Slice" and see what happens. Move the slice position. Return it to the original spot and click on "Create Slice Plot in Graph Window".



9. Deleting Surfaces and Slices: You can "Delete Surface" in the Surface box (Analyze->: Surfaces), and "Delete Slice" in the Slice box to prepare for the next exercise.

 

B. Testing the Accuracy of Quantum Mechanical Methods: A comparison of the semi-empirical AM1 method and various ab initio methods.

In the next part of the lab, we will explore the ability of various Quantum Mechanical (QM) methods to reproduce the experimentally observed order of orbitals for F₂. This order is given in your textbook (Reference 3), Fig. 14.29, p. 401, or from a web page at the Chemistry Dept at the University of Florida. Write this order in the "Experimentally Determined" row (Row 7) of Table 1.

Q 3. Does AM1 reproduce the correct order? Verify with your neighbors. Write this order in Row 2.

 

 

Running Gaussian Electronic Structure Calculations

To improve the results, we'll use ab initio methods. These methods typically calculate orbitals for all electrons, not just the valence electrons. To do this,

10. select the "Gaussian" card under "Quantum 1".
    
    
11. Choose the upper right "Options" box in the Run dialog box, and enter "pop=full" in the last box of the window that pops up. This tells the Gaussian program to print out the contributions of each atomic orbital in the basis set to the resulting molecular orbital.
    
    
12. Choose "Single Point Energy" as the Task.
    
    
13. Choose HF (Hartree-Fock) as the Method, and 3-21G as the Basis Set.
    
    
14. Name the files "F2HF1" instead of "Gaussian". Make sure the charge and spin multiplicity are set correctly, and then choose "Run".




Analyzing Structures

15. Find the energy for the molecule, as in Energies (4.), above. Note, however, that instead of computing the heat of formation for a molecule, the Gaussian program calculates the total energy. You may have to scroll down in the "Analyze" window to see this number.
    
    
16. Fill in the reported Total Energy, U, in Row 2 of Table 1. This is the HF/3-21G total energy, but for the AM1 geometry.
    
    
17. Next we'll allow the atomic coordinates to optimally adjust themselves by repeating the above calculation but with the Task set to "Geometry Optimization". Record the F-F distance, and the Total Energy, U, value in the Row 3 in Table 1.

Q 4. Has the energy changed much? What does this mean?

 

 

 

18. Also record the order of orbitals (found as in Molecular Orbitals (6.) above).
    
    
19. Use the molecular orbital coefficients listed in the Gaussian logfile (the gray data window) to determine which atomic orbitals are mixed, and use these to construct a Molecular Orbital Energy Level diagram for the HF/3-21G data.

Note: The Gaussian program subscripts each s orbital with a "g" if it is bonding ("SGG") and a "u" if it is antibonding ("SGU"). The pi orbitals have a subscript "u" indicating bonding orbitals ("PIU") and "g" ("PIG")indicating antibonding orbitals. Details of the "u" and "g" designations are given in your Atkins textbook on p. 404 (Reference 3).

Q 5. Does HF/3-21G reproduce the correct order? Verify with your neighbors.

 

Q 6. Record the F-F distance in Table 1. Has the interatomic distance improved?

 

 

Using More Accurate Methods

20. To improve the order of the orbitals, we’ll first try improving the basis set by using more Gaussian orbitals to better approximate the atomic orbitals, and we’ll also include d orbitals in addition to the s and p orbitals. This can be done by choosing 6-31G(d) as the basis set instead of 3-21G. Find the geometry-optimized conformation and record your results in Row 4 of the table. Also record the basis set's atomic orbitals.
    
    
21. Next, improve the method by including electron correlation. One method that does this "cheaply" (i.e., without using a lot of computer time) is a Density Functional Theory method (DFT) called B3LYP. Use this instead of Hartree-Fock (HF). Find the geometry-optimized conformation and record your results in Row 5.
    
    
22. Let's try one more increase in basis set. Repeat the above calculations, but with B3LYP/6-31+G(d). The "+" means there are extra "diffuse" orbitals have been added. Fill in the data in Table 1.

Q 7. Which methods above give the right order of orbitals, and why?

Q 8. Was there any improvement in the interatomic distance as the level of accuracy in method increased?