Integral equation methods for molecular scale calculations in the liquid phase

We report here a series of works^1-5 devoted to the modelling of the liquid phase for quantum chemistry calculations. The question under consideration is the computation of the electrostatic interaction between charge densities in the presence of a continuum dielectric medium. It consists of solving an elliptic problem of the form -div(ε(x)∇V) = ρ where the field ε(x) exhibits a discontinuity on a closed surface. We show how an enhanced use of integral equations methods has recently led to significant progress in this field: reduction of the computational cost in the standard cases, extension of existing methods to sophisticated cases out of reach so far, development of new possibilities. This work has a wide range of applications in chemistry and biology.