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Prof. Aatto Laaksonen
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An approach for bridging various levels of description of matter from first principles to meso-scale in computer simulations II: Applications
A major dilemma in computer simulations is the fact that the more accurate and realistic a molecular model is, the smaller has to be the system size and shorter the covered time scale in order to make the simulations affordable in some reasonable computer time. Ab-initio molecular dynamics simulations, for example,with the forces calculated from Quantum Mechanics of electrons and atoms, are currently feasible only for an order of 100 atoms during a few dozens of picoseconds. Classical molecular dynamics simulations, relying on empirical atom-atom potentials, normally cover scales of $10^4$ atoms during several nanoseconds. However even this is not enough for description of many problems in soft-matter physics where even more simplified and coarse-grained models have to be used. The present two lectures will describe a general approach how to use results of a more fundamental, more accurate theory, to construct simplified, coarse-grained models to be used in large-scale simulations.Inverse Monte Carlo method
The key element of this recently suggested approach is the Inverse Monte Carlo (IMC) method[1] which allows us to reconstruct the effective pair potential from radial distribution functions (RDF). The general scheme of the approach is the following: First, detailed simulation on a more fundamental, for example first principles ab-initio level to obtain a set of RDFs. Then, construction of a simplified, coarse-grained model. Next, application of the inverse Monte Carlo method to compute effective interaction potentials for the simplified model, on the basis of the distribution functions calculated in the first step. Finally, simulation of the simplified model on a longer length- and time- scale.Calculation of Effective Potentials
Several examples of computations of effective potentials are shown. Our starting point is ab-initio level of simulation of liquid water[5] and ionic solution[6]. These simulations have been carried out using Car-Parrinello molecular dynamics scheme for 32 water molecules and dissolved ion. Effective water-water and water-ion potentials have been determined without any use of empirical parameters.On the next step of coarse-graining, the explicit description of water molecules may be removed and substituted by effective solvent-mediated ion-ion potentials. These potentials can be used in Monte-Carlo (MC), Brownian dynamics (BD). Langevin dynamics (LD) or dissipative particle dynamics (DPD) simulations on the scale of hundreds of Ångströms. This class of model can already describe behavior of macromolecules. A simulation of ionic environment of DNA[2,3,4] is shown as an example.
A few other application of effective potential methodology are shown, for example building of a coarse-grained model of lipid molecules forming a membrane bilayer, or reconstruction of effective potentials between charged colloid particles.
References:
[1] Lyubartsev, A.P.; Laaksonen, A. Phys.Rev.E, 52, 3730-3737 (1995).[2] Lyubartsev, A.P.; Laaksonen, A. J. Phys. Chem., 100, 16410 (1996).
[3] Lyubartsev, A.P.; Laaksonen, A. Phys.Rev.E, 55, 5689-5696 (1997).
[4] Lyubartsev, A.P.; Laaksonen, A. J. Chem. Phys., 111, 11207 (1999).
[5] Lyubartsev, A.P.; Laaksonen, A. Chem. Phys. Lett., 325, 15-21 (2000).
[6] Lyubartsev, A.P.; Laasonen, K.; and Laaksonen, A. J. Chem. Phys., 114, 3120 (2001).