Quantum Calculations for Ethylene
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C2H4 Optimized Geometry
The most optimal geometry was determined by the conformation with the lowest energy. MOPAC was used to guess an initial geometry, which was then given to MacMolPt to set up calculations. The calculations were run in GAMESS at three different levels of theory. After each theory calculation, the lowest energy conformation was used as the beginning guess for the next level.  When the calculation finally converged at the DZV level, that conformation had the lowest energy and was determined to be the best geometry.

According to these calculations, the most optimal geometry for C2H4 has a bond length of 1.33 Angstroms between the carbons and an angle of 116.4 degrees between the hydrogens on each carbon.

Lit comparison:For the literature3, an experimental value of 1.339 Angstroms between the carbons was found.  As well as and experimental value of 117.6 degrees between the hydrogens on each carbon.  The calculated values vary slightly from the experimental values, which is to be expected because the calculations are based on approximations, not exact values.
 

C2H4 HOMO 
The highest energy molecular orbital that is occupied by electrons is called the HOMO. The HOMO of C2H4 is shown to the left.
 IR spectrum of C2H4

Motion of C2H4 at 1110cm-1
Vibrational frequencies are the frequencies at which a molecule vibrates.  In the presence of Infrared Radiation, the vibrations can be detected.  The frequency of this motion is 1110cm-1, and corresponds to the peak closest to 1000 above4.
 

Motion of C2H4 at 1619cm-1
The frequency 1619cm-1 corresponds to the motion depicted on the left, and corresponds to the peak shown second from the right above4.
 

Motion of C2H4 at 1811cm-1
The frequency 1811cm-1 corresponds to the motion depicted on the right, and corresponds to the peak shown near 1900 above4.
 

Motion of C2H4 at 3335cm-1
The frequency 3335cm-1 corresponds to the motion depicted on the left, and corresponds to the large peak furthest to the left above4.
 

Motion of C2H4 at 3462cm-1
The frequency 3462cm-1 corresponds to the motion depicted on the right, and corresponds to the large peak furthest to the left as well4.


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