Force Matching

System Distance (A) Mesh-Size (A) Unknowns per Set averaged 

3 For each studied system, the range of distances at which pair-forces are modeled as cubic splines is given, as well as mesh sizes and the number of resulting unknowns, the number of configurations included in a set to generate an over-determined system of equations, and the number of sets for which the least squared solution is averaged. 

At short distances, approximately equal to the excluded volume diameter, effective pair forces obtained from force matching exhibit unphysically large fluctuations. This is largely due to inadequate sampling of configurations at short distances in 

The fitting coefficients An for CC14, benzene, and water are listed in Table 8-4. The corresponding effective COM pair-potential, U(r), was obtained by integrating F(r) with the condition that the potential is zero at the outer cutoff  

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The best solvent for a molecular solid Is one whose Intermolecular forces match the forces holding the molecules in the crystal. For a solid held together by dispersion forces, good solvents are nonpolar liquids such as carbon tetrachloride (CCI4) and cyclohexane (Cg H12) For polar solids, a polar solvent such as acetone works well. Example provides some practice in recognizing solubility types. 

Abstract A force matching technique based on previous work by Voth and co-workers is devel-... 

Keywords Coarse-graining, Force-matching, Effective fragment potential method, Molecular... 

The aim of the force matching procedure is to obtain the effective pair-force between CG sites using the force data obtained from a detailed atomistic molecular dynamics (MD) trajectory. The current implementation of the force-matching method closely follows the formulation from Refs. [23, 24],... 

The reduction in the number of degrees of freedom can lead to an incorrect pressure in the simulation of the coarse-grained systems in NVT ensembles or to an incorrect density in NPT ensembles [24], The pressure depends linearly on the pair-forces in the system, hence the effect of the reduced number of degrees of freedom can be accounted for during the force matching procedure [24], If T is the temperature, V the volume, N the number of degrees of freedom of the system, and kb the Boltzmann constant then the pressure P of a system is given by... 

Here, pAt MD is the pressure in the system in detailed atomistic MD and VCG and Ncg are the volume and number of degrees of freedom of the coarse-grained system. The left side of this equation is evaluated for the coarse-grained system for each snapshot during force-matching. 

Figure 8-7. Coarse-graining of CCI4. (a) Black COM-COM RDF from EFP-MD, (b) red RDF from CG-MD, (c) orange circles the effective COM pair-force, (d) green polynomial fit of the force matching data, (e) blue the effective COM pair potential...

Favorable coarse-graining results for CCI4 are not surprising because this molecule is spherically symmetric. Planar benzene presents a more stringent test for the force-matching approach. Figure 8-8 shows the effective pair-force and pair-potential for the benzene COM. 

Water is a very important and widely used solvent. Many of the unique properties of water are the result of the complex interactions that occur among water molecules. A water molecule is planar and highly polar, so it is an important system to test with the force matching approach. The coarse-graining results for water are summarized... 

Site-site W-W radial distribution function obtained from CGMD simulation and compared with that of the atomistic MD simulation using the force-matching procedure. 

So far, CG approaches offer the most viable route to the molecular modeling of self-organization phenomena in hydrated ionomer membranes. Admittedly, the coarse-grained treatment implies simplifications in structural representation and in interactions, which can be systematically improved with advanced force-matching procedures however, it allows simulating systems with sufficient size and sufficient statishcal sampling. Structural correlations, thermodynamic properties, and transport parameters can be studied. 

Youngs, T.G.A., Del Popolo, M.G., and Kohanoff, J., Development of complex classical forcefields through force matching to ab initio data Application to a room-temperature ionic liquid, /. Phys. Chem. B, 110, 5697-5707, 2006. 

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