Coulomb interactions via local dynamics:: a molecular-dynamics algorithm

We derive and describe in detail a recently proposed method for obtaining Coulomb interactions as the potential of mean force between charges which are dynamically coupled to a local electromagnetic field. We focus on the molecular dynamics version of the method and show that it is intimately related to the Car-Parrinello approach, while being equivalent to solving Maxwell's equations with a freely adjustable speed of light. Unphysical self-energies arise as a result of the lattice interpolation of charges, and are corrected by a subtraction scheme based on the exact lattice Green function. The method can be straightforwardly parallelized using standard domain decomposition. Some preliminary benchmark results are presented.