Finite Temperature Approximation

        As an approximation to full molecular dynamics (here) this program approximates the effects of molecular vibration by broadening the intermolecular distances with a parameter q which is proportional to temperature.

        The RMS amplitude, l_ij, between two atoms is q*sqrt(r_ij). Then, for example with C₆₀ which has only carbon, the scattered intensity is computed as:
    intensity(s) = Sum over i,j of: f0² * sin(s*(r_ij-l_ij²/r_ij) )/(s*r_ij) * exp(-0.5*(l_ij*s)²)
The l_ij distribution most closely matches Hedberg's T=1003K data with q=0.055.

Notes:

• Note that temperature compensation is specificly tuned to C₆₀.
• The file 'Matching Hedberg's data.xls" (on request) is some simple calculations used to determine the 'q' of q =~ sqrt(T) for approximate temperature variation
• The files "C0.scf" and "He0.scf" are needed in the program directory for computation - scattering factors.