Research Group of Prof. Dr. M. Griebel
Institute for Numerical Simulation

  author = {L.~Jager},
  title = { Fluid Density Approximation for an Implicit Solvent
  school = {Institut f\"ur Numerische Simulation, Universit\"{a}t Bonn},
  year = {2007},
  annote = {INSdiss,thesis},
  type = {Dissertation},
  abstract = {The microscopic simulation of molecules in solution is a
		  highly challenging task. An explicit simulation of the
		  entire solute-solvent 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 so-called
		  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 solute-solvent 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 Ornstein-Zernike
		  equation, do not lead to efficient implicit solvent methods
		  due to the computational costs and the approximation
		  Hence, we derive our new BGY3d model based on the
		  YBG-hierarchy from statistical physics. With this model, we
		  are able to approximate the solvent density around an
		  arbitrary solute with full three-dimensional 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
		  3d-HNC method of Beglov and Roux, which is based on the
		  Ornstein-Zernike 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
		  so-called normalized site-site 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
		  short-range Lennard-Jones potential as well as the
		  long-range 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.},
  pdf = { 1}