Noura Dawass

1.1. T HE K IRKWOOD -B UFF THEORY 1 3 the most important relations that link microscopic structure with macroscopic properties (section 1.1) . This is followed by a discussion of the inversion of the KB theory and its applications (section 1.2) . Also, we present the available meth- ods for computing KBIs frommolecular simulations (section 1.3) and review the applications of KBIs computed frommolecular simulations (section 1.4) . Finally, the scope of the thesis is presented (section 1.5) . 1.1. T HE K IRKWOOD -B UFF THEORY One of the fundamental quantities for describing the microscopic structure of fluids, are RDFs [13, 26] . Essentially, RDFs provide the probability of finding a molecule at a distance r from a central molecule. For homogenous and isotropic fluids, RDFs g αβ ( r ) are defined as [13] : g αβ ( r ) = ρ αβ ( r ) ρ β (1.1) where ρ αβ ( r ) is the local density of component β at a distance r from a cen- tral molecule of type α , and ρ β is the bulk density of component β . RDFs can be determined from scattering experiments as well as from molecular simula- tion. Using molecular simulations, RDFs are frequently computed using parti- cles counting [22] . Alternatively, force–based computations of RDFs can be im- plemented [27– 29] . Commonly, particle counting is adopted in molecular simu- lation packages with RDFs computed from [26] : g αβ ( r ) = V N α N β * N α X i = 1 N β X j = 1 δ ( r − r j + r i ) + (1.2) where N α and N β are the number of molecules of components α and β , respec- tively. δ is the Dirac delta function, r i is the position of atom i , and the brackets 〈 ... 〉 indicate an ensemble average. When α equals β , terms where i = j should be excluded in the double summation of Eq. (1.2) . RDFs are central in the KB theory, where the local structure of fluids is related to macroscopic properties. In this section, we review the most important relations derived by Kirkwood and Buff [12] . For the original formulation of the theory, the reader is referred to the paper by Kirkwood and Buff [12] . A very detailed derivation was presented by Newman [30] , and an alternative derivation was provided by Hall [15] . In the grand-canonical ( µ TV ) ensemble, thermodynamic quantities are re- lated to KBIs G ∞ αβ for an open and infinite system as [12] : G ∞ αβ = Z ∞ 0 d r 4 π r 2 h g ∞ αβ ( r ) − 1 i (1.3)