In the physical chemistry laboratory it is common for students to measure and analyze the gas phase IR spectrum of HCl and DCl. Less common is the measurement and analysis of the spectra of more complicated molecules like NH₃ or C₂H₂, but these experiments are beginning to appear in standard laboratory texts[1] and Raman spectroscopy is becoming more available as well. This exercise describes the modeling of the vibrations of molecules (with acetylene as the example) using a standard molecular modeling package such as CAChe[2]. (A separate page gives instructions for using MacSpartan+.) The exercise may be done independently or in conjunction with the experimental determination of the gas phase IR and/or Raman spectra of one or more of the molecules.

Drawing the Molecule

If you are not familiar with the drawing program you are using, ask your instructor for assistance. These directions describe one way to construct C₂H₂ in CAChe Plus.

1. Open the CAChe Editor.

2. Select Atom Tool from the Tool menu.

3. Select C from the Atom menu

4. Click once in the work space to place the first carbon atom and then, starting at the center of that atom, click and drag some distance and release the mouse. You should see two carbon atoms, singly bonded.

5. Draw the triple bond by carefully clicking, dragging and releasing between the two atomic centers two more times.

   Note: The hybridization codes in the atom (and periodic table) menu appear to have no useful function for this purpose and physically drawing the triple bond seems to work best for drawing this molecule.

6. Select Select Tool from the Tool menu, click in an open area of the work space, and select Comprehensive from the Beautify menu.

7. Save your model in an appropriately named file.

Optimizing the Geometry

1. Select Mechanics in the Applications menu. A box will pop up with the information for the calculation. Accept the default job and parameters by clicking on OK. The calculation is finished when the Stop button is no longer highlighted.

   Note: This calculation will add a folder named "your file name_f" to the location where you stored your model file and you can recover the results of the calculation at any time by exploring this folder.

Calculating Vibrational Frequencies

1. Choose MOPAC from the Applications menu.

2. A dialog box will pop up. Change the settings to match the figure below:

   Figure 2

3. Click on Details in this box and change the settings in the resulting pop-up box to match the figure below:

   Figure 2

4. Click on Done in this box and click on Run in the MOPAC box to which you�ll be returned. You may receive some warnings about overwriting files or about the imperfections that may result due to atom numbering, but just click on OK . You should receive a calculation status screen and the calculation is finished when the Stop button is no longer active.

Displaying and Analyzing the Vibrational Spectrum

1. Select Visualizer in the Applications menu.

2. Select Vibrational Spectra in the Analyzemenu. A vibrational spectrum will pop up and there will be markers along the trace which locate the normal modes. How many markers do you see? How many vibrational modes should there be for this molecule (C₂H₂)? If there is a marker along a flat portion of the trace, what does this mean?

3. Though a bit tedious, you can analyze this display quite nicely. Double clicking exactly on the horizontal axis allows you to "bracket" regions around the markers with almost any resolution you choose. Thus you can extract the actual frequencies of the modes.

4. Clicking on the markers will display a sketch of the molecule with vectors that indicate which mode is responsible for that frequency.

5. Which (if any) of these modes should be IR active? Which ones (if any) should be Raman active? (See item #2 above.) Can you figure out what kind of spectrum CAChe is actually displaying here?

6. If experimental equipment is available, run the gas phase IR and Raman spectra of C₂H₂ and compare the fundamental vibrations you have calculated with the absorptions in the experimental spectra. Be sure that you realize that the experimental spectra will be enriched with rotational structure which this modeling method has not addressed.

   BONUS EXERCISEDepending upon the graphics programs available, you may be able to include the displayed spectrum (with important regions enlarged) and the images of the molecule with the vibrational vectors for each mode in your laboratory report.

1. Shoemaker, D. P.; Garland, C. W.; Nibler, J. W., Experiments in Physical Chemistry, 6th edition, McGraw-Hill, 1996.
2. It does not appear to be possible to work with isotopically substituted molecules in CAChe.