Wilson's GF Method (molecular vibrations)

In summary, the FG matrix method developed by Wilson can be applied to both linear and nonlinear molecules. However, the G matrix elements for linear molecules may need to be derived or doublechecked, as they are not specifically tabulated for linear molecules. This can be done by referring to the relevant sections in textbooks such as "Molecular Vibrations" by Wilson, Decius and Cross or "Molecular Symmetry and Spectroscopy" by Bunker and Jensen. Fortunately, many of the matrix elements are zero for linear molecules, making the application of the FG matrix method possible.
  • #1
jaejoon89
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Can Wilson's GF (FG) Matrix Method be applied to linear molecules as well as nonlinear? For example, can it be applied to a linear chain of hydrocarbons? What are some of the restrictions?
 
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  • #2
I don't see why not. Can you get more detailed?
 
  • #3
1. A chain of hydrocarbons is not linear (unless the carbons are triple-bonded). For a singly-bonded chain of hydrocarbons, the geometry of the bonds on each carbon are approximately tetrahedral so the bond angles are about 109 degrees.

2. Yes, the FG matrix method works for linear molecules. However, G matrix elements tabulated by Wilson, Decius and Cross are not written for linear molecules. (For example, they depend on torsion angles which aren't defined at linear geometry), so you might have to derive/doublecheck the validity of your G matrix elements (for guidance on this, see section 4-2 of "Molecular Vibrations" by Wilson, Decius and Cross. For a more modern text on FG matrix methods, I recommend Chapter 10 of "Molecular Symmetry and Spectroscopy" by Bunker and Jensen). Luckily, many of the matrix elements are zero at linear geometry. (For example, all stretch-bend G matrix elements will be zero because these coordinates are orthogonal when the molecule is linear.)

Hope this is helpful to readers of this forum.
 

Related to Wilson's GF Method (molecular vibrations)

1. What is Wilson's GF Method for molecular vibrations?

Wilson's GF Method is a mathematical approach used to calculate the vibrational frequencies of molecules. It takes into account the connectivity of atoms, bond strengths, and atomic masses to predict the vibrational motions of molecules.

2. How does Wilson's GF Method differ from other methods for calculating molecular vibrations?

Unlike other methods, Wilson's GF Method considers the entire molecular structure, rather than just individual bonds. It also takes into account the force constants of bonds, which gives a more accurate prediction of vibrational frequencies.

3. Can Wilson's GF Method be used for all types of molecules?

Yes, Wilson's GF Method can be used for any type of molecule, as long as the connectivity of atoms is known. It has been applied to simple diatomic molecules as well as complex organic molecules.

4. What is the accuracy of Wilson's GF Method?

The accuracy of Wilson's GF Method depends on the input parameters used, such as bond strengths and atomic masses. In general, it has been found to have a good agreement with experimental data, with an average error of around 5-10%.

5. How is Wilson's GF Method useful in the field of chemistry?

Wilson's GF Method is useful in understanding the vibrational properties of molecules, which is important in many areas of chemistry. It can help in identifying unknown compounds, studying chemical reactions, and determining molecular structures. It is also used in spectroscopy to interpret vibrational spectra of molecules.

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