The dielectric response of a simple model of a polar fluid near neutral interfaces is examined by a combination of linear response theory and extensive molecular dynamics simulations. Fluctuation expressions for a local permittivity tensor epsilon(r) are derived for planar and spherical geometries, based on the assumption of a purely local relationship between polarization and electric field. While the longitudinal component of epsilon exhibits strong oscillations on the molecular scale near interfaces, the transverse component becomes ill defined and unphysical, indicating nonlocality in the dielectric response. Both components go over to the correct bulk permittivity beyond a few molecular diameters. Upon approaching interfaces from the bulk, the permittivity tends to increase, rather than decrease as commonly assumed, and this behavior is confirmed for a simple model of water near a hydrophobic surface. An unexpected finding of the present analysis is the formation of "electrostatic double layers" signaled by a dramatic overscreening of an externally applied field inside the polar fluid close to an interface. The local electric field is of opposite sign to the external field and of significantly larger amplitude within the first layer of polar molecules.

An extension to the P(3)M algorithm for electrostatic interactions is presented that allows to efficiently compute dipolar interactions in periodic boundary conditions. Theoretical estimates for the root-mean-square error of the forces, torques, and the energy are derived. The applicability of the estimates is tested and confirmed in several numerical examples. A comparison of the computational performance of the new algorithm to a standard dipolar-Ewald summation methods shows a performance crossover from the Ewald method to the dipolar P(3)M method for as few as 300 dipolar particles. In larger systems, the new algorithm represents a substantial improvement in performance with respect to the dipolar standard Ewald method. Finally, a test comparing point-dipole-based and charged-pair based models shows that point-dipole-based models exhibit a better performance than charged-pair based models.

We introduce a regularization procedure to define electrostatic energies and forces in a slab system of thickness h that is periodic in two dimensions and carries a net charge. The regularization corresponds to a neutralization of the system by two charged walls and can be viewed as the extension to the two-dimensional (2D)+h geometry of the neutralization by a homogeneous background in the standard three-dimensional Ewald method. The energies and forces can be computed efficiently by using advanced methods for systems with 2D periodicity, such as MMM2D or P3M/ELC, or by introducing a simple background-charge correction to the Yeh-Berkowitz approach of slab systems. The results are checked against direct lattice sum calculations on simple systems. We show, in particular, that the Madelung energy of a 2D square charge lattice in a uniform compensating background is correctly reproduced to high accuracy. A molecular dynamics simulation of a sodium ion close to an air/water interface is performed to demonstrate that the method does indeed provide consistent long-range electrostatics. The mean force on the ion reduces at large distances to the image-charge interaction predicted by macroscopic electrostatics. This result is used to determine precisely the position of the macroscopic dielectric interface with respect to the true molecular surface.

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