One of the two topics alluded to in the title deals with a new method for the parameterization of electrostatic interactions. The starting point is to rewrite regular charge equilibration models in terms of bond variables rather than as atomic variables. While the original charge equilibration method can be obtained as a limiting case, it is possible to introduce a new bond term, which effectively introduces a band gap. The band gap is present in nature but not in the original charge equilibration method. The hope is that a successful parameterization will allow us to tackle more problems with force fields than currently possible.

The other topic (provided there is time left) deals with ways how to efficiently solve for elastic deformation when an object is contact with a semi-infinite, elastic manifold, e.g., the situation of a soft, elastic solid (or membrane) pressed against a hard corrugated substrate. We worked out the details of a Green's function formulation, in which only the outermost atoms of the elastic solids need to be considered. The effects of all bulk atoms is encoded in the Green's functions. The method allows us to simulate systems with atomic resolution, whose linear length approaches 1 micron.