gmx dielectric calculates frequency dependent dielectric constants from the autocorrelation function of the total dipole moment in your simulation. This ACF can be generated by gmx dipoles. The functional forms of the available functions are:
One parameter: y = exp(-a_1 x), Two parameters: y = a_2 exp(-a_1 x), Three parameters: y = a_2 exp(-a_1 x) + (1 - a_2) exp(-a_3 x). Start values for the fit procedure can be given on the command line. It is also possible to fix parameters at their start value, use -fix with the number of the parameter you want to fix.
Three output files are generated, the first contains the ACF, an exponential fit to it with 1, 2 or 3 parameters, and the numerical derivative of the combination data/fit. The second file contains the real and imaginary parts of the frequency-dependent dielectric constant, the last gives a plot known as the Cole-Cole plot, in which the imaginary component is plotted as a function of the real component. For a pure exponential relaxation (Debye relaxation) the latter plot should be one half of a circle.