The reaction potential in anisotropic dense fluids

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Abstract
In Monte Carlo or molecular dynamics calculations for anisotropic dipolar fluids the long-range electrostatic interaction potential poses a serious problem because of the microscopic dimensions of the simulation cells. As in homogeneous bulk fluids these small system sizes necessitate a separation of the entire electrostatic potential into short- and long-range parts. Interactions due to the former are evaluated explicitly while the net effect of the latter can be taken into account via the reaction potential approach. Since short-range interactions are evaluated explicitly the range of these interactions is commonly associated with a cavity characterized by a dielectric constant ϵ = 1 which is embedded in a homogeneous dielectric of ϵ = ϵL. The total electrostatic potential Φ(r) caused by an assembly of molecular dipoles inside the cavity can be split formally into a ‘direct’ part Φ0(r) and a much smaller ‘reaction’ part R(r) due to the polarization of the surrounding dielectric by the molecular dipoles. Φ(r) can be obtained as a solution of the three-dimensional generalized Poisson equation. In this paper we discuss a method which allows for a computation of R(r) in anisotropic fluids. The anisotropic fluid is modelled as an infinite dielectric slab in the x, y plane of thickness d. Unfortunately, R(r) cannot be calculated analytically in an easy way because of the cavity embedded in the dielectric slab. Therefore, we approach a solution of the generalized Poisson equation numerically by the finite element method. However, if the cavity vanishes, i.e. the dielectric slab is continuous in the x, y plane an analytical solution of Poisson's equation can easily be obtained. In this special case a comparison between the analytical and the corresponding finite element result is used as a check on the accuracy of our computer program and the numerical stability of the results. In addition the analytical solution for the slab without a cavity provides suitable boundary values which help to reduce the amount of computer time required by the finite element calculation of R(r) for the system with a cavity.

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