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The accurate modeling of the dielectric properties of water is crucial for many applications in physics, computational chemistry and molecular biology. This becomes possible in the framework of nonlocal electrostatics, for which we propose a novel formulation allowing for numerical solutions for the nontrivial molecular geometries arising in the applications mentioned before. Our approach is based on the introduction of a secondary field, $psi$, which acts as the potential for the rotation free part of the dielectric displacement field ${bf D}$. For many relevant models, the dielectric function of the medium can be expressed as the Greens function of a local differential operator. In this case, the resulting coupled Poisson (-Boltzmann) equations for $psi$ and the electrostatic potential $phi$ reduce to a system of coupled PDEs. The approach is illustrated by its application to simple geometries.
Molecular dynamics simulations of biomolecules have been widely adopted in biomedical studies. As classical point-charge models continue to be used in routine biomolecular applications, there have been growing demands on developing polarizable force
A unified account, from a pedagogical perspective, is given of the longitudinal and transverse projective delta functions proposed by Belinfante and of their relation to the Helmholtz theorem for the decomposition of a three-vector field into its lon
By using fundamental units c, h, G as conversion factors one can easily transform the dimensions of all observables. In particular one can make them all ``geometrical, or dimensionless. However this has no impact on the fact that there are three fund
We present a new class of electrostatics problems that are exactly solvable by adding finitely many image charges. Given a charge at some location inside a cavity bounded by up to four conducting grounded segments of spheres: if the spheres have a sy
Solvation free energy is an important quantity in Computational Chemistry with a variety of applications, especially in drug discovery and design. The accurate prediction of solvation free energies of small molecules in water is still a largely unsol