From Structure to Thermodynamics with Local Molecular Field Theory

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A fundamental goal of statistical mechanics is to connect a description of the intermolecular interactions and the accompanying microscopic structural details of a molecular system to its macroscopic thermodynamic properties. When the interactions between molecular components are treated with sufficient simplicity, as in an ideal gas or a hard sphere fluid for example, the link between structure and thermodynamics can be apparent. In contrast, when both local and non-local interactions are present in the system, competition between the various short and long ranged forces can lead to surprising thermodynamic behaviors as exemplified by the complexities of liquid water. Local molecular field (LMF) theory provides a physically motivated formalism for systematically decomposing the structure and thermodynamics of molecular systems into portions arising from local and non-local interactions. In this thesis, LMF theory is employed to examine the structure and thermodynamics of molecular systems, with a focus on aqueous solutions.

LMF-motivated truncations of classical water models are first developed as

analysis tools to explore the roles of the local hydrogen bond network, dispersion interactions, and long ranged multipolar interactions in the determination of sev- eral anomalous thermodynamic properties of bulk water. This type of analysis is then extended to the study the relative importance of hydrogen bonding and inter- facial unbalancing potentials in hydrophobic effects. The underlying ideas of LMF theory are then utilized to study local and non-local interactions in ion solvation. Modifications to classical dielectric continuum theories are explored with a focus on determining the electrostatic potentials inside ionic cores. LMF ideas are then used to develop the concept of a Gaussian test charge. We then argue that this type of test charge is the appropriate generalization of a classical point test charge to probe the dielectric response of molecularly detailed systems and develop an accurate for- malism for the description of the dielectric response to such probes. Finally, a LMF theoretic foundation for performing free energy calculations is developed and tested before concluding the thesis with a discussion of future work involving LMF theory.