Energy corresponding to the peak of velocity power spectrum

Question

I ran a MD simulation for a number of N molecular hydrogen. I used the velocity time history of system for each atom and subtract the velocity of center of mass of each molecule from the velocity of corresponding atoms. ( I basically did it to take the effect of transnational energy away of my analysis, otherwise the transient behavior which is a nature of diffusive systems make it difficult to visualize velocity time correlation function)

I obtained the velocity correlation function for the overall system and then take the Fourier Transform of it to get the velocity power spectrum. As expected I will end up having a sharp peek with intensity I at frequency w. I need to assign a vibrational energy to this frequency. Is there any way to find the vibrational energy knowing the velocity power spectrum in the way I have obtained it?

So many thanks for your helps.

Best,

HRJ

Answer 1

Possibly?

I think you can use the equipartition theorem to tell you that the energy stored in each degree of freedom is the same (at least for everything that has $E\propto x^2)$ So you should be able to count up all the spring modes, $m$ and then if there are $n$ atoms in your molecule the time average of your spring energy would be $\frac{m}{n}KE$ where $KE$ is the time average sum of the kinetic energy of the atoms.

This might be an inadequate simplification for your system though. Some vibrational modes may not be accessible at your temperatures, but I think figuring out which modes were available would require figuring out their energy levels...