Fourier

The fourier.x program takes an input file with time-data and calculates the power spectrum / fourier transform of the autocorrelation function. The input file must only have lines of the form

<integer> <dummy 1> <dummy 2> <dummy 3> <data 1> <data 2> <data 3>

where the first four entries are ignored and the autocorrelation and fourier-transform is performed on the last 3 entries of a line. This format corresponds to the DIPOLE file created by DIPOLE DYNAMICSDIPOLE DYNAMICS. The name of the input file as well as other needed quantities are queried by the program interactively. The output file will contain the power-spectrum up to a maximum frequency. The format and contents of this file are:

<frequency> <value1> <value2> <value3> <value4> <value5>

<frequency>   is the frequency in wave numbers.


<value1> 		 is the plain power spectrum of the input data 


normalized to unity in the output frequency range.


<value2> 		 is the power spectrum with a prefactor of 
$\omega ( 1 - \exp(-\beta \hbar \omega) )$
 


corresponding to the classical/Gordon limit. 


<value3> 		 is the power spectrum with a prefactor of 
$\omega \tanh(\beta \hbar \omega/2)$



corresponding to the Kubo correction


<value4> 		 is the power spectrum with a prefactor of  
$\omega \beta \hbar \omega$



corresponding to the high temperature / harmonic limit (recommended).


<value5> 		 is the power spectrum with a prefactor of  
$\omega ( 1 - \exp(-\beta \hbar \omega) ) * \exp(\beta \hbar \omega /2)$
 


corresponding to Schofield's correction

All spectra with their corresponding prefactor are separately normalized in the output range to sum up to unity and the index of refraction of the medium is set to unity.

To compute velocity or other auto-correlations, one first has to process data so it matches the required format. For example to determine the characteristic frequencies of the fictitious electron dynamics of a CPMD run, one can process the ENERGIES file with:
awk ' { print $1, 0.0, 0.0, 0.0, 0.0, 0.0, $2; } ' ENERGIES > ekinc.dat

The source code package for the fourier.x tool contains a small fortran program trajec2atoms.f that can split TRAJECTORY files into individual files, one per atom. Those files can then be processed with fourier.x and then combined to a power spectrum.

The equivalent functionality has been integrated into VMD, e.g. to compute spectral densities (also for subsystems) from dipole auto-correlation functions from IONS+CENTERS.xyz files. See http://www.ks.uiuc.edu/Research/vmd/plugins/irspecgui/http://www.ks.uiuc.edu/Research/vmd/plugins/irspecgui/ for more information.