The most common approach to describe the structure of the liquid is through the radial distribution function (RDF), which is a restricted one dimensional representation of the full three dimensional structure of the liquid. Identification of small changes in the three-dimensional liquid structure through their effect on the RDF requires knowledge of it to high accuracy. Typically one dimensional diffraction patterns from the liquid are collected and the liquid structure, S(q), is obtained taking into account a series of approximations and corrections which lead to systematic error of ~5% [1]. In determining the RDF from the structure factor, an addition error is introduced due to the use of a finite range of the transferred momentum, q. This finite cutoff introduces errors into the RDF, most notably short wavelength oscillations, which may be considered as numerical noise. These oscillations may affect the interpretation of the RDF, and in particular prevent identification of small changes therein.

We present a methodology [2] to produce improved RDF's using analytic asymptotic expressions for the structure factor. Also a mathematical formalism is proposed, which can reproduce the asymptotic expressions reported in the literature [3,4,5] and, furthermore, derive a new expression. Then, the stability and convergence of the RDF's obtained by the methodology are tested choosing different asymptotic expressions and q-wavevector cutoffs. Finally, we show implementations for elements of columns IV and V such as bismuth, silicon, germanium and tin at a wide range of temperature. 

[1] North D M, Enderby J E, and Egelstaff P A 1968 J. Phys. C: Solid State Phys. 1 784.

[2] Under preparation.

[3] Vorob’ev Y N and Yur’ev G S 1975 J. Struct. Chem. 16 370-373.

[4] Greenwood DA 1980 J. Phys. C: Solid State Phys. 13 331.

[5] Verlet L 1968 Phys. Rev. 165 201.