Noura Dawass

3 42 F INITE -S IZE E FFECTS A trunc. = 4 π R · R − 3 µ R − L box 2 ¶¸ , 1 2 < R L box < p 2 2 (3.1) V trunc. = 2 π · 2 3 R 3 − µ R − L box 2 ¶ 2 µ 2 R + L box 2 ¶¸ , 1 2 < R L box < p 2 2 (3.2) To compute the KBIs of the system using the RDF of Eq. (2.6) , MC sampling is performed to numerically evaluate Eq. (1.18) . For simplicity, a brute-force ran- dom sampling algorithm is used instead of importance sampling MC. The simu- lations follow the following algorithm: 1. Specify the size of the cubic simulation box L box , the size of the spherical subvolume, with radius R placed in the center of the box, and the RDF parameters χ and σ . In this study, we fix σ = 1, and test different values of χ ( χ = 1, 2, and 4). 2. Select two random points inside the simulation box, P 1 and P 2 , accept the points if they both fall inside the sphere otherwise, generate new points. 3. Select a random point, P 3 , and accept if the point is outside the sphere. Otherwise, choose a new point P 3 . 4. Calculate the distance between points P 1 and P 2 ( r 12 ), and points P 1 and P 3 ( r 13 ). Find g ( r 12 ) − 1 and g ( r 13 ) − 1 using Eq. (2.6) . 5. Performing steps 2 and 3 results in one cycle. After a sufficient number of cycles (in this study we perform 10 11 cycles), compute the average of the integrals R V R V and R V R L 3 box − V (from Eq. (1.18) and Eq. (1.26) ) over the RDF. 6. Finally, calculate G V αβ (Eq. (1.18) ) and Q (Eq. (1.26) ) using the sampled av- erages of the integrals R V R V and R V R L 3 box − V . 3.3. F INITE - SIZE EFFECTS OF RADIAL DISTRIBUTION FUNC - TIONS While our formulation enables the calculation of KBIs from finite subvolumes, the used RDF has to be of that of an open and infinite system, g ∞ ( r ). Using g ( r ) frommolecular simulation of a closed system results in a systematic error that af- fects the accuracy of the KBIs, thus, the g ( r ) has to be corrected. There are several approaches available to estimate g ∞ ( r ) from RDFs computed in closed systems. In this section, we present the RDF correction methods that we consider in this