Noura Dawass

1.3. K IRKWOOD –B UFF I NTEGRALS FROM MOLECULAR SIMULATIONS 1 15 with internal degrees of freedom. Wedberg et al. [75, 85] presented a method for extending KBIs to the thermodynamic limit using Verlet’s extension of RDFs [86] . The Verlet extension method [86] can be applied to estimate RDFs beyond the size of the finite simulation box, which are then used to extrapolate to KBIs to the thermodynamic limit, by truncating Eq. (1.3) to a value much larger than half the size of the simulation box. The approach of Wedberg et al. [75] was verified for pure Lennard Jones (LJ) and Stockmayer fluids. A drawback of this approach is the complexity of the numerical procedure as it required the effective interac- tion potential for two molecules at distance r . Moreover, it is not trivial to extend the method to systems of molecules with intramolecular degrees of freedom. KBIs can be computed from molecular simulations of finite number of molecules using static structure factors [76, 87] . The structure factor of a liq- uid, S ( q ), is related to the Fourier transform of pair distribution functions, and q is the magnitude of change of a reciprocal lattice vector [23] . Structure factors can be measured from scattering experiments, where q is a function of the wave length and the scattering angle. At the zero wavelength limit, q = 0, structure fac- tors are directly related to KBIs [51, 88] . However, the values of S ( q = 0) cannot be measured directly. Similarly, with molecular simulation, structure factors can be computed for a set of values of q , and then extrapolated to the limit q = 0 to find KBIs. In the work of Nichols et al. [76] , structure factors are computed from fluctuations in the number of molecules of finite systems. Each lattice vector q corresponds to a set of different sampling volumes, or sub-cells inside the simu- lation box, fromwhich density fluctuations are computed. Rather than consider- ing subvolumes formed by a central molecule, Nichols et al. [76] considered fluc- tuations in slab-like regions that resulted from dividing the simulation box. As a result, the whole volume is considered and all the information is used. Fromfluc- tuations, written as a 3 D Fourier series, structure factors are computed and this was used to obtain the thermodynamic properties that relate to KBIs (partial de- viates of chemical potential with respect to composition, partial molar volumes, and isothermal compressibilities). For a LJ fluid, Nichols et al. [76] found that it was difficult to extrapolate structure factors to q = 0. Instead, thermodynamic properties computed from subcells (i.e specific range of q ) were extrapolated to the limit q = 0. Extrapolation of thermodynamic properties is needed to rem- edy finite-size effects. While the method of Nichols et al. [76] provides accurate thermodynamic properties, compared to truncated KBIs, it is computationally involved even for systems with no intramolecular interactions. Structure factors were also used in the work of Rogers [87] to compute KBIs from simulations of closed and finite systems. As in the work of Nichols et al. [76] , information from