Jaime,

Here are some references on the subject:

-Numerical Recipes (any edition, see the chapter on Fourier Transform

Spectral Methods)

-J. Chem. Phys. 1993, 98, 4984-4990

-J. Chem. Phys. 2003, 119, 11792-11805

The "power spectrum" is defined in Num. Rec. as the square of the

magnitude of the Fourier transform.

The two journal articles define the density of states as the same

integral that you gave, but multiplied by some constants (1/kT terms).

Even in that case I think the square of the magnitude must be used,

otherwise you could see negative values in the density of states.

In either case, I believe that only the real parts of the Fourier

transform should be used. The bigger issue in my opinion is that using

canned FFT routines result in N/2 data points in the power spectrum,

when the original VACF contains N data points. The only suggestion

offered in Num. Rec. is to augment your VACF with zeroes until you have

2N data points.

We're working on code to calculate VACFs from LAMMPS dump files, but we

still need to validate it. Let me know if you want to compare codes.

Regards,

Jeff Greathouse