An obvious dilemma in molecular computer modelling is the fact that as
the system is described in more details and more rigorously, the number of
atoms that can be included becomes smaller. While the quantum *ab-initio*
molecular dynamics may be based on a high quality, controllable approximation
of the fundamental quantum theory, in practical terms it can be applied only
to relatively small, typically a few dozens atoms, molecular systems, which
can be simulated during a few picosecond. Classical molecular dynamics simulations
can deal with tens of thousand atoms and cover a time scale of many nanosecond,
but they typically use empirical potential functions with many adjustable
parameters. When we go to mesoscale phenomena, the number of atoms and simulation
time becomes unaffordable even for the classical molecular dynamics, and
more simplified models becomes necessary. There is obvious need in developing
methods which use information, obtained at a more fundamental and more accurate
level for a small system, to construct an effective classical model
to be used in simulations of bigger systems on longer time scale.

Suggested recently inverse Monte Carlo approach may be used to link
together different levels of molecular modelling.

The inverse Monte Carlo method solves the inverse problem of the statistical
mechanics - reconstruct interaction potential between molecules if the distribution
function is known. If we know from some source the radial distribution
function between particles, we can calculate the corresponding pair interaction
potential. It is possible to prove that solution of the inverse problem is
unique, but until recently there were no practically realisable way to find
it.

The general scheme is the following. First, detailed simulation on
a more fundamental, "ab initio" level. Then, construction of a simplified
(coarse-grained) model. Next, using the inverse MC to compute effective interaction
potentials for the simplified model, based on distribution functions, calculated
during the first step. Finally, simulation of the simplified model on a longer
time- and length scale. Below is the list of papers describing applications
of the inverse Monte carlo method to different problems.

- Alexander P. Lyubartsev and Aatto Laaksonen "
*Calculation of Effective Interaction Potentials from Radial Distribution Functions: A Reverse Monte Carlo Approach*" Phys.Rev.E, v.52, p.3730 (1995). Abstract ; Paper (PostScript file) - Alexander P. Lyubartsev and Aatto Laaksonen.
*Osmotic and Activity Coefficients from effective potentials for Hydrated Ions.*Phys. Rev. E, v.55(5),p.5689 (1997). Abstract ; Paper (Postscript file) . - A.P.Lyubartsev, A.Laaksonen. "
*Reconstruction of pair interaction potentials from radial distribution functions."*Computer Physics Communucations, v. 121-122, p.57-59 (1999). Paper (postscript file) - A.P.Lyubartsev, A.Laaksonen. "
*Effective Potentials for Ion-DNA Interactions*" J. Chem. Phys., v.111, p.11207-11215 (1999). Abstract - R.Kjellander, A.P.Lyubartsev, and S.Marcelja,
*"McMillan Theory for Solvent Effects in Inhomogeneous Systems: Calculation of Interaction Pressure in Aqueous Electrical Double Layers"*J. Chem. Phys., 114(21), 9565-9577 (2001) Abstract and full text from the JCP Web site - A. P. Lyubartsev and S. Marcelja
*Evaluation of effective ion-ion potentials in aqueous electrolytes*Phys.Rev.E, v.65(4), 041203 (2002) Abstract and full text from the APS Web site

- A.P. Lyubartsev
*"Multiscale modeling of lipids and lipid bilayers"*Eur. Biophys. J., (2005) + Supplementary information

- A.P.Lyubartsev and A.Laaksonen,
*"Determination of pair potentials from ab-initio simulations: Application to liqid water"*Chem.Phys.Lett., v. 325, pp.15-21 (2000) Abstract - A.P Lyubartsev, K. Laasonen and A. Laaksonen "
*Hydration of Li+ ion. An ab-initio molecular Dynamics Simulation*" J. Chem. Phys., v. 114, p.3120-3126 (2001) Abstract and full text from the JCP Web site

- V. Lobaskin, A. Lyubartsev and P. Linse "
*Effective macroion-macroion potentials in asymmetric electrolytes*" Phys. Rev. E, v. 63, 020401 (2001) Abstract and full text from the PRE Web site

This project has been supported by the Swedish Natural Sciences Research Council (NFR)

A universal code to perform Inverse Monte Carlo calculation of effective potentials from results of more detailed ("atomistic") simulations.

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