Noura Dawass

3 40 F INITE -S IZE E FFECTS 3.1. I NTRODUCTION To compute KBIs using molecular simulation, Krüger and co–workers [74] de- rived an expression for KBIs of finite subvolumes, embedded in larger reser- voirs. From the scaling of KBIs of finite subvolumes with the inverse size of these subvolumes, estimates for KBIs in the thermodynamic limit are obtained. When computing KBIs from molecular simulations of closed, and finite systems one must be aware of two system-size effects that originate from: (1) comput- ing finite-volume KBIs from subvolumes embedded in closed and finite simula- tion boxes [122] ; and, (2) using RDFs obtained from finite and closed simulation boxes, in contrast to open, infinite systems as required by the KB theory. For the second effect, RDFs from open systems, g ∞ ( r ), can be estimated from g ( r ) obtained from molecular simulations of closed and finite systems. Previously, Krüger et al. [74] used a correlation based on expanding the difference between g ( r ) and g ∞ ( r ) in a Taylor series in the inverse of the number of molecules. Gan- guly and van der Vegt [113] suggested a correction based on the excess or deple- tion of molecules within a distance, r , around a central molecule. Cortes-Huerto et al. introduced a correlation to compute the KBIs that includes a correction to the RDF finite-size effects [83] . The objective of this chapter is to investigate finite-size effects associated with the computation of KBIs frommolecular simulations (e.g. MD) of finite and closed systems. For the two types of finite-size effects studied (Figure 3.1) , we present the inaccuracies as a function of the simulation box size. Also, we inves- tigate subvolume sizes and provide the distances up to which RDFs need to be calculated. This chapter is organized as follows. The finite-size effects are stud- ied using two sets of simulations. The first set of simulations consider MC sam- pling of KBIs from subvolumes embedded in a larger simulation box. The KBIs in the thermodynamic limit, and the inaccuracies associated with these com- putations are investigated for various sizes for the simulation box. Second, we demonstrate the finite-size effects related to the RDF by performing MD simu- lation of a WCA [112] mixture. Other than varying the simulation box size used to obtain KBIs, we also test various RDF correction methods to estimate RDFs of infinite systems, g ∞ ( r ). In section 3.2 details regarding the simulation methods and specifications of the systems studied are provided. In section 3.4, we present two main sets of results: (1) the appropriate system sizes from which KBIs could be extrapolated and the magnitude of the inaccuracies made when simulating finite subvolumes; and (2) the numerical inaccuracies resulting from comput- ing RDFs using closed and finite simulation boxes, and the effect of applying the discussed correction methods of the RDFs. Our findings are summarized in sec- tion 3.5.