I would like to determine the frequencies of the normal modes from the force constant matrix printed as "Force constant in Cartesian coordinates" in the Gaussian .log file. How to perform it? Are the square roots of its eigenvalues proportional to the frequencies? If so, what is the factor which converts them into frequencies?
Hi Roland,
first, may I ask what you need to do this analysis for? Maybe there's an easier way to achieve what you want. Gaussian has the freqchk utility which lets you redo a frequency analysis from a checkpoint file. If you're not just asking for purely academic purposes but really need the results for something specific, that tool would probably be the easiest way to go.
Anyway, to clarify the theory a bit: Yes, the frequencies are indeed proportional to the square root of the force constants, which you obtain by diagonalizing the Hessian matrix (i.e., the second derivatives of the energy). There's an additional factor of 1/(2*pi*c) and some unit conversions to cm-1 in there. A simple way to approximate that factor would be to take the square root of the eigenvalues and compare those to the wavenumber output from Gaussian itself.
However, there's also the reduced vibrational mass that enters the equation. The force constant matrix you pull from the log file may or may not be mass-weighted already, so you'll have to be careful with your results. If it is, just taking the root of the eigenvalues will give you the frequencies. If it's not, things are going to get quite a bit more complicated. Again, you could manually take the root of the eigenvalues and try to relate them to wavenumbers in the log file. If you don't get roughly the same conversion factor for all vibrations, you know that you're missing the mass scaling in the Hessian.
Note also that Gaussian will first try to project the translations and rotations out of the Hessian before diagonalizing it. You may notice some deviations between your manual results and the ones from Gaussian, because vibrations and rotations are in principle not fully separable and whether or not you keep them in your Hessian before diagonalization will make a difference. That's why getting the conversion factor in the simple way I described will only be an approximation, you should try to reconstruct it again. I did that before, unfortunately I can't remember what exactly the factor was and which unit conversions it contained. Once you have an approximate value for it, that should be easy to determine through some experimentation though.
For further info look at the Gaussian whitepaper here: http://gaussian.com/vib/
Hi,
is this what you want?
InternalModes
Print modes as displacements in redundant internal coordinates. IntModes is a synonym for this option.
You'd use the keyword freq=InternalModes on an optimised geometry
u can use phonopy package, it is very easy
https://atztogo.github.io/phonopy/index.html
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