Non-unique Lennard-Jones Parameter Problem with a Monatomic Cation

Abstract

In molecular mechanical force fields, a monatomic ion is represented as a charged van der Waals particle that interacts with all atoms of the molecular system. The Coulomb potential normally specifies the electrostatic interaction of the charge. The Lennard-Jones (LJ) potential expresses the pair-wise exchange-repulsion and dispersion interactions between atoms i and j with the well depth eij and the distance Rmin,ij at which the potential reaches the minimum. Following the Lorentz-Berthelot combination rule, the charge and the dispersion parameters, e and Rmin, define the force field of a monatomic ion. 1 The force field parameters are optimized to reproduce experimental findings through molecular simulations. Various experimental and theoretical data have been considered; a partial list includes the free energy of hydration, the entropy of hydration, the radial distribution function of water oxygen atoms around the ion, the lattice constant and the lattice energy of ionic crystals, osmotic coefficients, and geometric and energetic data from ab initio quantum mechanical calculations of monohydrates to water clusters of ions. 2-8 Unfortunately, it has been difficult to determine a