Noura Dawass

S UMMARY The Kirkwood–Buff (KB) theory is one of the most rigorous solution theories that connects molecular structure to macroscopic behaviour. The key quantity, the so–called KB Kirkwood–Buff Integrals (KBIs), are defined either in terms of fluc- tuations in the number of molecules or integrals over radial distribution func- tions over open subvolumes. In the grand–canonical ensemble, KBIs of infinitely large and open systems are directly related to thermodynamic properties such as partial derivatives of chemical potentials and partial molar volumes. Using molecular simulations, it is only possible to study small systems with a finite number of molecules, and therefore finite–size effects should be considered. In chapter 1, a literature review of studies of KBIs was conducted. This review fo- cused on: (1) inversion of the KB theory, where KBIs are estimated from macro- scopic properties; (2) available methods to compute KBIs from molecular simu- lations, and (3) applications of KBIs to molecular systems. Generally, three levels of estimations for KBIs were used in literature: (1) the easiest, and most com- mon approach is to simply truncate KBIs of open and infinite systems to half the size of the simulation box; (2) a number of mathematical involved methods were developed that are not easily extended to complex molecules; (3) The approach of Krüger and co-workers provides an approach that is more accurate than trun- cating KBIs and with an intermediate difficulty. To compute KBIs from molecu- lar simulations, Krüger and co-workers derived an expression for KBIs of finite and open subvolumes embedded in larger reservoirs. According to thermody- namics of small systems (nanothermodynamics), thermodynamic properties of small systems scale linearly with the inverse size of the subvolume. Extrapolating KBIs to the thermodynamic limit yields KBIs of open and infinite systems. In this thesis, various aspects related to estimating KBIs from molecular simulations of finite and closed systems were investigated. As a result, an improved framework to compute KBIs accurately and conveniently is developed. The methodology was used to compute KBIs of model systems, and realistic solutions. In chapter 2, shape effects of KBIs from molecular simulations are investi- gated. The dependence of KBIs on the shape and dimensionality of the sub- volume is characterised by a weightfunction w ( x ). A method to numerically compute the weightfunction w ( x ) for any arbitrary convex subvolume was devel- oped. We computed KBIs of an analytic Radial Distribution Function (RDF) for 161