Noura Dawass

1 20 A PPLICATIONS OF K IRKWOOD –B UFF I NTEGRALS KBIs can be used for the development and parameterization of force fields [105– 107] . Weerasinghe and Smith provide KB derived force fields (KBFFs) for a number of mixtures, such as sodium chloride in water [106] , urea and wa- ter [108] , acetone and water [109] , and methanol and water [110] . The force fields were parameterized so that KBIs obtained from experimental data are re- produced. More on the use of experimentally obtained KBIs are provided in sec- tion 1.2. The authors of Refs. [105– 107] found that macroscopic properties can be accurately computed using KBFFs, while addressing solute-solute and solvent- solute molecular structure of the systems considered. For instance, in Ref. [105] the derived KBFFs was able to reproduce microstructure of alkaline earth halide salts in water. Ion-ion and ion-water distances provided by the force field were found to agree with those measured by neutron scattering experiments. The same KB force field yielded satisfactory predictions of several macroscopic quan- tities such as partial molar volumes, and partial derivatives of chemical potential with respect to density. Mijakovi´c et al. [111] compared several force fields, in- cluding KBFFs, for ethanol-water mixtures. The authors reported that the KB de- rived force field performed better than other force fields when computing KBIs and several thermodynamic properties such as excess volumes, excess enthalpy, and self-diffusion coefficients. 1.5. S COPE OF THIS THESIS The focus of this thesis is to provide methods to accurately compute KBIs from molecular simulation. In this way, one does not have to rely on experimental data or insertion and deletion of molecules. To successfully estimate KBIs from molecular simulation using Eq. (1.25) , the following effects have to be studied: 1. Shape effects related to the subvolume embedded in the system. 2. Finite–size effects related to the size of the system used to compute KBIs. To obtain of KBIs that converge to the correct value in the thermodynamic limit, a sufficient number of molecules has to be simulated. 3. Finite–size effects related to the sizes of the subvolumes embedded in the system. 4. Finite–size effects related to the computed RDFs. KBIs should be com- puted from RDFs of open systems, while nearly always, RDFs are com- puted from closed systems. In this thesis, we develop a framework to accurately compute KBIs based on the method of Krüger and co–workers [74] . In chapters 2 and 3, the shape and size effects related to computing KBIs using small subvolumes are studied. In