Polarization as a field variable from molecular dynamics simulations.

A theoretical and computational framework for systematically calculating the macroscopic polarization density as a field variable from molecular dynamics simulations is presented. This is done by extending the celebrated Irving and Kirkwood [J. Chem. Phys. 18, 817 (1950)] procedure, which expresses macroscopic stresses and heat fluxes in terms of the atomic variables, to the case of electrostatics. The resultant macroscopic polarization density contains molecular dipole, quadrupole, and higher-order moments, and can be calculated to a desired accuracy depending on the degree of the coarse-graining function used to connect the molecular and continuum scales. The theoretical and computational framework is verified by recovering the dielectric constant of bulk water. Finally, the theory is applied to calculate the spatial variation of the polarization vector in the electrical double layer of a 1:1 electrolyte solution. Here, an intermediate asymptotic length scale is revealed in a specific region, which validates the application of mean field Poisson-Boltzmann theory to describe this region. Also, using the existence of this asymptotic length scale, the lengths of the diffuse and condensed/Stern layers are identified accurately, demonstrating that this framework may be used to characterize electrical double layers over a wide range of concentrations of solutions and surface charges.