Theory of model electrolyte solutions: Assessing the short- and long-ranged contributions by molecular simulations

In this work, we conduct a comprehensive simulation study on Helmholtz energies for non-primitive model electrolyte solutions in order to assess fluid theories. Simulation data is obtained with two different methods. Using a new thermodynamic integration path, we calculate Helmholtz energy contributions arising from damped, short-ranged electrostatic pair potentials. The division of the potential into a damped, short-ranged and a long-ranged part using a complementary error function corresponds to the division of a standard Ewald sum. Additionally, we applied a standard thermodynamic integration method to obtain the full electrostatic contribution to the Helmholtz energy. We evaluate the analytical long-range contribution developed by Rodgers and Weeks [J. M. Rodgers and J. D. Weeks, J. Chem. Phys. 131, 244108 (2009)] and find excellent agreement to our simulation data for any damping parameter α*≥1.5 for liquid-like densities. Further, the simulation data is compared to a third order perturbation theory we recently presented. By analyzing the theory against results of molecular simulations we were able to introduce refinements to our theory, such as a rearranged Padé approximation. We show, however, that third order perturbation theory, despite these improvements, is only reliable for strongly damped potentials (α*<1) for ion-dipole as well as for purely dipolar fluids. This study shows that a perturbation theory of third order is insufficient for such systems.