[1] 
L. Jager.
Fluid Density Approximation for an Implicit Solvent Model.
Dissertation, Institut für Numerische Simulation, Universität
Bonn, 2007. [ bib  .pdf 1 ] The microscopic simulation of molecules in solution is a highly challenging task. An explicit simulation of the entire solutesolvent system is often unfeasible due to the high number of degrees of freedom necessary in order to adequately simulate the solvent effects. Therefore, implicit solvent models should be employed that can consider the influence of the solvent by the socalled potential of mean force (PMF) without introducing new degrees of freedom to the system. An efficient approximation of the PMF then leads to an efficient simulation of the entire solutesolvent system. The liquid state integral equation theory for the computation of the mean density of fluids provides a promising tool for the approximation of the PMF. However, existing methods, which are nearly unexceptional based on the OrnsteinZernike equation, do not lead to efficient implicit solvent methods due to the computational costs and the approximation involved. Hence, we derive our new BGY3d model based on the YBGhierarchy from statistical physics. With this model, we are able to approximate the solvent density around an arbitrary solute with full threedimensional resolution. We employ the Kirkwood approximation as closure for the BGY3d equation. A special product approach leads to an efficient numerical solution of the BGY3d model. Compared to the 3dHNC method of Beglov and Roux, which is based on the OrnsteinZernike equation, the computational costs for our BGY3d method are considerably lower. Moreover, the Kirkwood approximation leads to an improved approximation of the main peak of the computed density distribution while providing the same overall accuracy. In order to consider more realistic fluids, we extend our model to molecular solvents. To this end, we employ the socalled normalized sitesite superposition approximation of Taylor and Lipson for the intramolecular interaction. With this molecular BGY3d (BGY3dM) model, we can compute the density for solvent molecules interacting by the shortrange LennardJones potential as well as the longrange Coulomb potential. A comparison between results computed with our BGY3dM model and results from a molecular dynamics simulation reveals that the modelling of the intramolecular bonds and the computed densities lead to good approximations. The computational effort for the BGY3dM method is two to three orders of magnitude smaller when compared to a molecular dynamics simulation. The application of our method to the approximation of the density of carbon disulfide around several solutes leads to realistic density and charge distributions.
