CHEM 345-Debye
Molecular Vibrations

11/23/2004

With this worksheet, you will see computer simulations of the internal vibrational motions of various molecules and see how one can sometimes identify vibrational modes with particular bonding groups. The overall motion of a molecule can be divided up into three types of motion: translation, rotation, vibration:


1. Translational Motion- subdivided into motions along the x-, y-, and z-axes with motion along each axis contributing ½RT to the average molar translational energy of a substance where T is the temperature in kelvin and R is a constant (called the ideal gas constant) equal to 8.31415 J K^-1 mol^-1. The total average energy stored in translational motion for a mole of any substance at temperature T is then 
   E_trans = ½RT + ½RT + ½RT = (3/2)RT
    
2. Rotational Motion - subdivided into rotations around the x-, y-, and z-axes with each such rotation contributing ½RT to the average molar rotational energy. However, rotational motion stores energy only if the rotational motion involves a nucleus located off the axis of rotation. A monatomic substance has its mass located directly on all three axes and cannot store energy in any rotational motion. A linear molecular has two such qualified rotations (rotation around the bond axis does not qualify because the nuclei of the two atoms are located directly on the rotation axis). A non-linear molecule can store energy in rotational motions around all three axes. In summary:
     E_rot(monatomic) = 0
   
   E_rot(linear) = ½RT + ½RT = RT
   
   E_rot(non-linear) = ½RT + ½RT + ½RT = 3RT/2
    
3. Vibrational Motion - subdivided into normal modes of vibration which rapidly increase with the number of atoms in the molecule. Each of these normal vibrational modes contributes RT to the average molar energy of the substance and is a primary reason why heat capacities increase with molecular complexity. A monatomic substance can have no internal vibrations as such motion would involve a movement of its center of mass and be called translation.The number of vibrational modes ( X_vib ) is calculated from the number of atoms (N) in the molecule as follows:
   X_vib(linear) = 3N - 5
   
   X_vib(non-linear) = 3N - 6
   For example, the linear O=C=O molecule contains 3 atoms (N=3) so that X_vib=3(3)-5= 4 normal modes of vibration. The 4 vibrations of this simple molecule can be clearly separated into two "bond stretching" motions which are called the "symmetric stretch" and the "asymmetric stretch" (or "antisymmetric stretch"), respectively,
                       
            Symmetric stretch                                  Antisymmetric stretch
   and into two equivalent "bond bending" motions where one bending motion is in the plane of the screen (or paper) and the other is in a plane perpendicular to the screen (or paper):                     
   In one bending mode, the oxygens are "wagging" up and down; in the other bending mode, the oxygens are wagging in and out of the screen (or paper).
   
   Although it is easy to separate the internal vibrations of small molecules into well-defined bond stretching and bending modes, this is not true for larger molecules. As you will discover, larger molecules have some internal vibrations which are predominantly bond stretching motions, others which are predominantly bond bending (wagging) motions, but also vibrations which clearly are mixed stretching and bonding motions. In this computer simulation worksheet, you are asked to examine the normal modes of vibrations of various molecules and classify the vibrations as being predominantly stretching, bending, or mixed motions as well as identify (by frequency) vibrational motions which are predominantly symmetric and asymmetric stretchings of particular bonds.

You will be looking at the increasing numbers and features of the normal modes of vibration as molecules become larger in size and more complex in their structure. To a large extent, it is these internal molecular vibrations which are responsible for the increased heat capacity of substances composed of larger molecules.

Here is a summary of the above discussion:


• Monatomic Substance - A monatomic substance can store energy only in translational motion. There are neither rotational nor vibrational modes.
   
• Linear Molecule - A linear molecule of N atoms can store translational energy in three ways, rotational energy in two ways (rotation around two axes) and vibrational energy in 3N-5 ways.
   
• Non-linear Molecule - A non-linear molecule of N atoms can store translational energy in three ways, rotational energy in three ways (rotation around all three axes) and vibrational energy in 3N-6.ways.


Particular vibrational modes often are found to be dominated by either bending motions or stretching motions and chemists label them as such. Some vibrational modes appear to involve combinations of significant amounts of bending and stretching motions and cannot easily be identified as being one or the other. Here some examples showing the calculation of the number of vibrational modes of some molecules:



Molecule or Atom	Geometry	Vibrational Modes	Total Average Molar Energy (E)	Molar Cv (=dE/dT)
Ar	monatomic	3N - 3 = 0	3RT/2 + 0 + 0 = (3/2)RT	(3/2)R
H2	linear	3N - 5 = 1	3RT/2 + 2(½RT) + (1)RT = (7/2)RT	(7/2)R
CO2	linear	3N - 5 = 4	3RT/2 + 2(½RT) + (4)RT = (13/2)RT	(13/2)R
H2S	non-linear	3N - 6 = 3	3RT/2 + 3(½RT) + (3)RT = (6)RT	(6)R
CH4	non-linear	3N - 6 = 9	3RT/2 + 3(½RT) + (9)RT = (12)RT	(12)R
C4H10	non-linear	3N - 6 = 36	3RT/2 + 3(½RT) + (36)RT = (39)RT	(39)R
C6H6	non-linear	3N - 6 = 30	3RT/2 + 2(½RT) + (30)RT = (65/2)RT	(65/2)R


You have two options for obtaining the molecular data files required by the SpartanPC molecular simulation software loaded on the computers in the Chemistry Learning Center (CLC): (a) You can download the two data files linked on this page (F2.spartan, C6H6.spartan) plus the eleven data files linked on the Report Table and bring the data files to the CLC on a floppy disk, 100Mb ZIP disk or on a CD-ROM. (b) You can borrow a floppy disk from the instructor containing the data. The computers in the CLC are "protected" so as to prevent you from downloading and using the data files directly from the course Website.

PROCEDURE:
Peliminary (for practice):
1. Begin the Spartan molecular modeling program and maximize the window.
2. Under the File pull-down menu, click on Open and open the file for the F₂ molecule (F2.spartan). The molecule should appear on your screen.
3. Notice how you can rotate and move the molecule around on the screen with your mouse
4. Under the Display pull-down menu, click on Vibrations. A small window should open listing the frequency (in cm^-1) of the single vibrational mode of this diatomic molecule along with a check-box. Click on the check-box and you will see the animated vibration of this simple molecule. Is this a stretching or bending mode?
5. Under the File pull-down menu, click on Close and answer NO if asked if you wish to store any changes to your file.
6. Repeat Step 2 and bring up the file (C6H6.spartan) for the benzene (C₆H₆) molecule.
7. Choose the Vibrations option from the Display pull-down menu and investigate the many vibrational modes for this complex molecule.
8. When finished, Close the file without saving any changes.

The Real Thing (for grade):
You are now ready to proceed with the experiment. For each molecule identified in your Report Table, use the Open option to bring up a new molecule. Make sure that you have first cleared the screen of the previous molecule with the Close option. Fill in the missing information in the table. For the larger molecules, you may find more than one mode of vibration which the indicated bond stretches; in this case, enter the frequency of the vibration mode which involves more stretching of the bond(s). The completed table will be your laboratory report.