Noura Dawass

3.5. C ONCLUSIONS 3 63 3.5. C ONCLUSIONS In this chapter, we studied finite size effects related to the computation of KBIs from molecular simulations of finite subvolumes. We presented the uncertain- ties in KBIs due to: (1) effects due to the finite size of the subvolume, and simu- lation box, used to compute the KBIs; and (2) effects related to computing RDFs from molecular simulations of closed systems, in contrast to open systems as defined in the KB theory. We showed that uncertainties in the computations of the KBIs decrease when increasing the size of the simulation box, and hence the embedded subvolume. We varied the system size and find that simulation boxes with lengths larger than 15 σ are sufficient to reduce errors in computed KBIs to below 0.1%. We vary the size of the subvolume, or the maximum distance at which the RDF are computed. We find that a larger distance does not always ensure higher accuracy. In fact, for a given simulation box size, the radius of the spherical subvolume should not be extended beyond half the length of the simulation box. When using an analytic RDF model for the computations of the KBIs, it is relatively straightforward to identify the linear regime in the scaling of finite subvolumes integrals with the inverse size of the subvolume. However, using RDFs computed fromMD simulation of WCA molecules did not necessar- ily result in easily identifiable linear regimes. We presented some guidelines for extrapolating the scaling of finite subvolumes KBIs to the thermodynamic limit. While in some cases small simulation boxes provided a sufficient linear regime, finite–effects caused the resulting KBIs to deviate from these obtained from very large systems. Uncertainties arising from using RDFs of closed systems were evaluated for multiple simulation box sizes, as well as for various RDF correction methods. We demonstrate that using a RDF correction can significantly enhance the convergence of the KBIs and eventually the accuracy of the computations of the integrals. We compare between the RDF correction methods and find that the van der Vegt correction of Ref. [113] achieves the lowest error and is easy to apply.