Computational Chemistry at GVSU

Introduction to Quantum Mechanical Calculations

In this laboratory, we will be exploring electronic structure calculations, carried out using quantum mechanical-based methods in Cerius2. First we will use a semi-empirical method, called AM1, to calculate the electronic structure of the diatomic molecule hydrogen fluoride, HF. We will then more accurately calculate the electronic structure of HF using ab initio methods and examine the set of atomic orbitals that are linearly combined to create the molecular orbitals.

Note: Like hydrogen fluoride, the ab initio method "Hartree-Fock" is also abbreviated "HF". Which HF is meant should be clear from the context in which it is used.

Getting Started
  1. After logging in, open a UNIX Shell Window (In the upper left stack of menu bars, choose "Desktop" and then "Open Unix Shell").
  2. With the cursor within the Unix Shell window, type

    3. cerius2

    If you get a message with "unlock" mentioned, that means last time you logged out off the machine before first exiting cerius2. Hence, cerius2 thinks it is still running. And won't start up a second time. To fix this, type

    cerius2  -unlock

    Make sure you put a space between cerius2 and the dash.
  3. Build HF and clean the structure.

A. Using the Semiempirical Method AM1 to Find a Good Starting Structure.
  1. Click on the Menu Deck Bar (which by default is set at "Builders 1"), and choose "Quantum 1".
  2. Within the Quantum 1 set of cards, choose "MOPAC". The MOPAC card will come forward.
  3. Choose "Run". The card that appears is your interface for setting up the electronic structure calculation.

    4.  

    Geometry Optimization: AM1
  4. Change the following items on the Run card:

    5. a) Set the File Prefix to "HFAM1" (by default, it is "mopac"). All files that the electronic structure program calculates will now start with HFAM1.

    b) Set the Task to "Geometry Optimization". Geometry Optimization allows the atom centers to be shifted around until the most optimal conformation is found (of course, it might only be a local minimum rather than the true global minimum).

    c) Set the Method to "AM1".

    d) Set the charge to zero.

    e) Set the spin multiplicity ("Spin") to one. Spin multiplicity, M, is 1 + the number of unpaired electrons a molecule has. Hence M = 1 corresponds to a singlet state, M = 2 corresponds to a doublet state, etc. In class you will learn that M = 2S + 1, where S in the spin quantum number.

    You could also leave M set to zero in Cerius2, which allows the program to choose the spin multiplicity that its algorithms indicate is most likely.

  5. Select the "Run" button on the Run Card to submit the calculation.
    6.

     

B. Using the ab initio Methods to Determine Optimal Geometry and Analyze Molecular Orbitals.

    Running Gaussian Electronic Structure Calculations
  1. Select the "Gaussian" card under "Quantum 1"
  2. Select "Run" and then choose "Gaussian 94" in the upper right of the pop-up Run card. Then choose "Job Control" on the Gaussian Card, and click on the triangle at the top of the pop-up Job Control card. Choose "local host" as the host machine (i.e., the actual machine that will run the calculations). Close this dialog box.
  3. Return to Gaussian's "RUN" dialog box. Click on the upper right "Options" box, and enter "pop=full" in the "Additional Gaussian Keywords" box. This tells the Gaussian program to print out the contributions of each atomic orbital in the basis set to the resulting molecular orbital.
  4. Choose Geometry Optimization as the Task.
  5. Choose HF (Hartree-Fock) as the Method, and 3-21G as the Basis Set. The selection of the type of method used (HF, MP2, B3LYP, etc.) and the size of the basis set (3-21G, 6-31G(d), etc.) can affect the amount of computer resources needed to complete a calculation (i.e., time, amount of memory). Note that both the Methods and the Basis Sets in the program are generally listed in order of increasing computational time required.
  6. Name the files "HFHF1" instead of "Gaussian".
  7. Make sure the charge and spin multiplicity are set correctly, and then choose "Run". Do not close the gray HFHF1.log window that pops up!

    8.  

    Analyzing Structures
  8. Total Electronic Energy: Find the energy for the molecule, by Choosing "Analyze->" in the "Gaussian" Deck, and then "Files". You will see a "Summary of Calculation" box - scroll down to find the total energy. This is the energy required to assemble a molecule at absolute zero from electrons and nuclei at infinite distances from one another. Note that these energies are always large and negative, as assembling a stable molecule from electrons and nuclei is always a favorable process.

  9. Molecular Orbitals: Analyze the orbital structure of HF. To do this, choose

    10. "Analyze->" and then "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 make the orbitals "see-through" by choosing "Surfaces" in the "Analyze->" menu and setting the transparency to ~70%.

  10. Answer the following questions and verify your answers with your neighbors:
    11.
    1. What is the number of electrons in HF? _______________

    2. How many electrons are in an orbital? _______________

    3. What number of orbitals in HF should be occupied? _______________

    4. According to Gaussian, how many orbitals are occupied? _______________

    5. Are the number of occupied orbitals consistent with your expectations? ____
      6.

    6. The lowest energy orbitals holds the 1s2 electrons of hydrogen fluoride. How many orbitals are needed in the molecule to hold these electrons? Is the orbitals shape consistent with a 1s2 orbital? Is the orbital bonding, non-bonding or anti-bonding?

      7.  

       

    7. As the orbitals increase in energy, discuss whether they are bonding, non-bonding, or anti-bonding orbitals, and whether the bonding portions have sigma
      8.  vs. pi character. Record your answers for each orbital below. (Remember, sigma orbitals have density along the bond axis, while pi orbitals have density above and below the bond axis.)

       

       

       

    1. Look at the LUMO. Is this orbital bonding, non-bonding, or anti-bonding? Is this expected?

      2.  

       

    2. In previous classes, you have spoken of atomic orbitals mixing to produce the valence molecular orbitals. Which occupied orbitals are produced by mixing?
      3.

 

 

 

 

 

 

Now we will look at which atom orbitals are being mixed by Gaussian to produce molecular orbitals. Gaussian linearly combines the atomic-like orbitals specified in the basis set to create each molecular orbital. To examine this, we need to enter into the gray window containing mumbo-jumbo looking output data that Gaussian produces. We will do this in a "follow the leader fashion", so take a break until all students catch up. The instructor will give further instructions...

k) What atomic orbitals is Gaussian mixing to form the bonding molecular orbitals? Is this what you predicted?
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