Wilson's GF Method (molecular vibrations)

[jaejoon89]

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?

 

[DrDu]

I don't see why not. Can you get more detailed?

 

[bapark]

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.