Doctor of Philosophy / Department of Chemistry / Paul E. Smith / Kirkwood Buff (KB) theory is one of the most important theories of solutions. The theory can relate integrals over radial (pair) distribution functions (rdfs) in the grand canonical ensemble to common thermodynamic properties. An inversion of the KB theory has been proposed by Ben-Naim and this has led to the wide spread popularity of KB theory. The idea of the KB inversion procedure is to calculate KB integrals from available thermodynamic properties. The KB theory can be used to validate the force field (ff) parameters used in molecular dynamics simulations. We have tested a series of small molecule ff parameters using KB theory that consists of both atom centered partial atomic charges and extra charge sites. The results indicate that using extra charge sites, derived from QM calculations, does not necessarily provide a more accurate representation of condensed phase properties. A further study aimed at an ongoing project of deriving new biomolecular ff parameters based on KB theory, has developed ff parameters for esters in order to represent the ester conjugation of the phospholipid molecule. The models were further tested against experimental properties. Preferential solvation (PS) is an important concept of solution mixtures that can be described using KB theory. The difference between local composition and bulk composition in solution mixtures leads to the concept of PS. A generalized explanation based on local mole fractions was derived by Ben-Naim using KB theory. However, the original expressions have been modified over years. Here, we propose a new approach based on local volume fractions to explore PS in binary and ternary solution mixtures. Experimental and simulation data were used to examine different approaches to PS. A relationship between the rdf and the triplet distribution function can be obtained using the Kirkwood Superposition Approximation (KSA). A combination of Fluctuation Solution Theory and experimental rdfs are used to examine the KSA at a series of state points for pure water. The accuracy of several other approximate relationships between the pair and triplet correlation functions was also investigated and are in good agreement for regions of the phase diagram where the compressibility is small.

Doctor of Philosophy / Department of Chemistry / Paul E. Smith / The Kirkwood-Buff (KB) theory of solutions, published in 1951, established a route from integrals over radial (pair) distribution functions (RDFs) in the grand canonical ensemble to a set of thermodynamic quantities in an equivalent closed ensemble. These “KB integrals” (KBIs) can also be expressed in terms of the particle-particle (i.e., concentration or density) fluctuations within grand canonical ensemble regions. Contributions by Ben-Naim in 1977 provided the means to obtain the KBIs if one already knew the set of thermodynamic quantities for the mixture of interest; that is, he provided the inversion procedure. Thus, KB theory provides a two-way bridge between local (microscopic) and global (bulk/thermodynamic) properties. Due to its lack of approximations, its wide ranging applicability, and the absence of a competitive theory for rigorously understanding liquid mixtures, it has been used to understand solution microheterogeneity, solute solubility, cosolvent effects on biomolecules, preferential solvation, etc. Here, after using KB theory to test the accuracy of pair potentials, we present and illustrate two extensions of the theory, resulting in a general Fluctuation Solution Theory (FST). First, we generalize KB theory to include two-way relationships between the grand canonical ensemble’s particle-energy and energy-energy fluctuations and additional thermodynamic quantities. This extension allows for non-isothermal conditions to be considered, unlike traditional KB theory. We illustrate these new relationships using analyses of experimental data and molecular dynamics (MD) simulations for pure liquids and binary mixtures. Furthermore, we use it to obtain conformation-specific infinitely dilute partial molar volumes and compressibilities for proteins (other properties will follow) from MD simulations and compare the method to a non-FST method for obtaining the same properties. The second extension of KB theory involves moving beyond doublet particle fluctuations to additionally consider triplet and quadruplet particle fluctuations, which are related to derivatives of the thermodynamic properties involved in regular KB theory. We present these higher order fluctuations obtained from experiment and simulation for pure liquids and binary mixtures. Using the newfound experimental third and fourth cumulants of the distribution of particles in solution, which can be extracted from bulk thermodynamic data using this extension, we also probe particle distributions’ non-Gaussian nature.