Iterative Boltzmann method

The Iterative Boltzmann Method (IBM) was developed to circumvent the problems encountered with the simplex technique. " It is designed to optimize coarse-graining parameters against the structure of an atomistic simulation, and it lifts the limitation of needing analytical potentials. 

Figure 3 The bond angle potential on the meso-scale for polystyrene obtained by the Iterative Boltzmann Method. The angle is defined by three consecutive super-atoms...

Figure 5 The approach of the RDF by the Iterative Boltzmann Method in the case of atactic polystyrene. Running averages were applied to the data for clarity. Not all iterations are shown.

Both the inverse Monte Carlo and iterative Boltzmann inversion methods are semi-automatic since the radial distribution function needs to be re-evaluated at... 

Concerning the secrnid option to generate numerically a tabulated potential that closely reproduces a given melt structure, the iterative Boltzmann inversion (IBl) method [29,41, 51, 52] has been developed. 

Iterative Boltzmann Inversion Coarse Graining (IBICG). IBICG method was introduced and successfully applied to macromolecules by Kremer et and Muller-Plathe et jjjg method consists of steps like... 

In structure matching methods, potentials between the CG sites are determined by fitting structural properties, typically radial distribution functions (RDF), obtained from MD employing the CG potential (CG-MD), to those of the original atomistic system. This is often achieved by either of two closely related methods, Inverse Monte Carlo [12-15] and Boltzmann Inversion [5, 16-22], Both of these methods refine the CG potentials iteratively such that the RDF obtained from the CG-MD approaches the corresponding RDF from an atomistic MD simulation. 

Consider a mixture of acoustic-mode (rL) and ionized-impurity (r,) scattering. For tL t, we would expect r 0 = 1.18 and for r, tl, rn0 = 1.93. But for intermediate mixtures, r 0 goes through a minimum value, dropping to about 1.05 at 15% ionized-impurity scattering (Nam, 1980). For this special case (sL = i, s, = — f), the integrals can be evaluated in terms of tabulated functions (Bube, 1974). For optical-mode scattering the relaxation-time approach is not valid, at least below the Debye temperature, but rn may still be obtained by such theoretical methods as a variational calculation (Ehrenreich, 1960 Nag, 1980) or an iterative solution of the Boltzmann equation (Rode, 1970), and typically varies between 1.0 and 1.4 as a function of temperature (Stillman et al., 1970 Debney and Jay, 1980). 

RDFs calculated from a CG simulation using these initial interaction potentials differ from those calculated from the atomistic simulation. An inverse Monte Carlo algorithm is therefore used to iteratively refine these interaction potentials by correcting them by the difference between the CG and atomistic RDFs. This is essentially the same method that was used by Shelley et al to derive the parameters between the CG lipid head group particles, and is also similar to the Boltzmann inversion method, " which also uses an iterative procedure that uses RDFs measured from atomistic simulations to derive CG interaction potentials. Lyubartsev has used this method to fully parameterize his own CG model of DMPC. 

Holst, M., R. E. Kozack, F. Saied and S. Subramaniam. (1994b). Treatment of electrostatic effects in proteins multigrid-based Newton iterative method for solution of the full nonlinear Poisson-Boltzmann equation. Proteins. 18 231-45. 

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