Statistical Mechanical Theory for and Simulations of Charged Fluids and Water

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Treatment of electrostatic interactions in simulations remains a topic of current research. These interactions are present in most biomolecular simulations, and they remain an expensive part of the simulation. Herein we explore the application of local molecular field (LMF) theory to this problem. Local molecular field theory splits the Coulomb potential $1/r$ into short-ranged and long-ranged components. The short-ranged component may be treated explicitly in simulations and the long-ranged component is contained in a mean-field-like average external electrostatic potential. In this thesis, the derivations and approximations inherent in using the previously developed LMF theory are explored, and connections to classical electrostatics are made. Further the approach is justified for molecular systems. The application of LMF theory to several systems is explored. First, a simple system of uniformly charged walls with neutralizing counterions is treated via simulations using LMF theory. We then explore systems involving molecular water at ambient conditions. A simple approximation to LMF theory using only the short-ranged component of $1/r$ is quite powerful for bulk water. A full treatment using LMF theory extends the validity of such spherical truncations to nonuniform systems. This thesis studies the successful treatment of water confined between hydrophobic walls with and without an applied electric field -- a system which is a classic example of the failings of spherical truncations in molecular simulations. Additional results exemplify the applicability of LMF simulations to more molecularly realistic simulations. Connection is also made between these simulations of confined water and a related theory of hydrophobicity due to Lum, Chandler, and Weeks (1999).