Radial distribution functions from first principle

Perhaps some of the most important information on the mode of molecular packing of water in the liquid state is contained in the radial distribution function, which, in principle, can be obtained by processing X-ray or neutron scattering data. There are, however, several difficulties in extracting the proper information from the experimental data. First, it should be kept in mind that the full orientation-dependent pair correlation function cannot be obtained from such an experiment. Instead, only information on the spatial pair correlation function is accessible. We recall the definition of this function,... 

The first method comprises theories based on a statistical description of ionic liquids in a very rigorous way using radial distribution functions obtained from X-ray diffraction. These are theories based on the principle of corresponding states. 

Therefore, to evaluate the reliability of the SW potential, we must, instead, examine how good the agreement is between properties obtained using it and from experiments or first-principles simulations. Such a comparison is made here on the basis of an extensive literature search of experiments, first-principles simulations and other empirical potential simulations done on liquid silicon. We compare results for density (p), structure factor (S(q)), radial distribution function (g(r)), and diffusivity (D) obtained from various reports with the SW silicon data. 

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