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 liqui d phase for quantum chemistry calculations. The question under consideratio n is the computation of the electrostatic interaction between charge densit ies in the presence of a continuum dielectric medium. It consists of solvin g an elliptic problem of the form -div(epsilon(x)del V) = rho where the fie ld epsilon(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 s o far, development of new possibilities. This work has a wide range of appl ications in chemistry and biology.