In the previous section we took advantage of the fact that there are N (N -1) water-water correlations in the simulation cell, which greatly increases the sampling statistics. However, many scenarios involve a single solute molecule in solution, where the cross term RDFs are then sampled on only N correlations per independent MD frame. Fig. tests the three corrections on a simple The structure factor at low q as a function of sampling time, calculated from RDFs corrected using the Volume correction. The dashed line shows the result of reducing the sampling noise of the 1 ns sample by calculating the scattering using a numerical dr of 0.2 Å. solute-solvent system comprised of a single Ag + ion in water, with RDFs sampled from between 1 ns to 133 ns. If the sampling is too short, the corrections cannot converge the integral. The S c (0; R > 39 Å) values converge with simulation time when either the Volume-and Perera correction is applied, whereas the van der Vegt correction is more unstable. For the 1 ns sampling, the bottom plot shows large artificial oscillations at low q with some ringing even above 1 Å-1 . The dashed curve represents scattering calculated from an RDF sampled with dr = 0.2 Å instead of 0.05 Å, showing that a 4 x increase in numerical bin size of dr in eq. 1 only affects the oscillatory artefacts significantly at q < 0.2 Å-1 .