# Multi-scale Statistical Theory And Molecular Simulation Of Electrolyte Solutions

## Description

To clarify the role of ab initio molecular dynamics (AIMD) simulation, this study organizes the McMillan-Mayer (MM) theorem, the potential distribution theorem, and quasi-chemical approach to provide theory for the thermodynamic effects associated with long-length scales. This multi-scale statistical mechanical (MSSM) theory implements quasi-chemical theory after utilizing the MM theorem to integrate-out the solvent degrees of freedom. The MSSM theory treats composition fluctuations which would be accessed by larger-scale calculations, and also long-ranged interactions of special interest for electrolyte solutions. The theory is applied to a primitive electrolyte solution model proposed to investigate ion pairing in the context of tetraethyammonium tetrafluoroborate in propylene carbonate. A Gaussian statistical model is shown to be an effective physical approximation for outer-shell contributions, and they are conclusive for the free energies within the quasi-chemical formulation. Gaussian statistical theory can be more effective than the Bennett numerically exact method when exhaustive sampling is not available, i.e., for finite samples. These results lead to the analysis of the asymptotical behavior of a relative information entropy and thus a new formula for the ion excess free energies. This asymptotic perspective completely avoids the computationally limiting evaluation of the outer-shell contributions. In addition, we use AIMD to obtain the charges on tetramethylammonium and tetrafluoroborate ions contacting neutral and charge carbon nanotube electrodes, and also charges tetraethyammonium and tetrafluoroborate ions in propylene carbonate solution.