Finite-size Effects on the Calculation of X-ray Scattering from Molecular Dynamics Simulations

Structural studies using x-ray scattering methods to investigate molecules in solution are shifting focus towards including the role and effects of the surrounding solvent. However, forward models based on molecular dynamics (MD) simulations to simulate structure factors and x-ray scattering from interatomic distributions such as radial distribution functions (RDFs) face limitations imposed by simulations, particularly at low values of the scattering vector q. In this work, we show how the value of the structure factor at q = 0 calculated from RDFs sampled from finite MD simulations is entirely dependent on the size of the simulation cell. We derive a new, simple method to correct the RDFs to eliminate this error, and compare it to two other RDF- correction methods developed for Kirkwood-Buff theory applications. We present a quantitative test to assess the reliability of the simulated low-q scattering signal, and show that our RDF- correction successfully recovers the correct q = 0 limit for neat water. We investigate the effect of MD-sampling time on the RDF-corrections, before advancing to a more realistic example system comprised of a solvated transition metal complex, sampled in a series of water cells with increasing density. We show that our correction recovers the correct q = 0 behaviour for increasing density. Furthermore, we employ a simple continuum scattering model to dissect the total scattering signal from the solvent-solvent structural correlations in a solute-solvent model system to find two distinct contributions: a non-local ’density’-contribution and a local contribution from the solvent shell. We show how the second contribution can be approximated without also including the density-contribution. Finally, we provide a ’best-practices’-checklist for experimentalists planning to incorporate explicit solvation MD simulations in future work, offering guidance for improving the accuracy and reliability of structural studies using x-ray scattering methods in solution.