Monte Carlo methods reverse modelling

Particularly useful applications of the Monte Carlo method include modelling complex oscillatory reactions and studying enzyme catalysis [8,9]. As an example of the latter treatment, we will consider a system involving an initial reversible complex formation between the enzyme and the substrate, accompanied by a reversible step of inhibition of the catalyst... 

Instead of calculations, practical work can be done with scale models (33). In any case, calculations should be checked wherever possible by experimental methods. Using a Monte Carlo method, for example, on a shape that was not measured experimentaUy, the sample size in the computation was aUowed to degrade in such a way that the results of the computation were inaccurate (see Fig. 8) (30,31). Reversing the computation or augmenting the sample size as the calculation proceeds can reveal or eliminate this source of error. 

Random structure methods have proved useful in solving structures from X-ray powder diffraction patterns. The unit cell can usually be found from these patterns, but the normal single-crystal techniques for solving the structure cannot be used. A variation on this technique, the reverse Monte Carlo method, includes in the cost function the difference between the observed powder diffraction pattern and the powder pattern calculated from the model (McGreevy 1997). It is, however, always necessary to include some chemical information if the correct structure is to be found. Various constraints can be added to the cost function, such as target coordination numbers or the deviation between the bond valence sum and atomic valence (Adams and Swenson 2000b Swenson and Adams 2001). 

McGreevy, R. L. (1997). Reverse Monte Carlo methods for structure modelling. In C. R. A. Catlow (ed.), Computer Modelling in Inorganic Crystallography. San Diego and New York Academic Press, pp. 151-84. 

Swenson, J. and Adams, St. (2001). The application of the bond valence method to reverse Monte Carlo produced structural models of superionic glasses. Phys. Rev. B64, 024204. 

ARITVE Modelling the Silica Glass Structure by the Rietveld Method. A. Le Bail, J. Non Cryst. Solids, 1995, 183, 39 42, and Reverse Monte Carlo and Rietveld Modelling of the NaPbM2F9 (M = Fe, V) Fluoride Glass Structures, A. Le Bail, J. Non Cryst. Solids, 2000, 271, 249 259... 

Pikunic, J., Clinard, C., Cohaut, N., et al. (2003). Structural modeling of porous carbons constrained reverse Monte Carlo method. Langmuir, 19, 8565-82. 

Reverse Monte Carlo Methods for Structural Modelling... 

One example of the NMR reconstraction problem employs the reversible-jump Markov chain Monte-Carlo method [16]. It assumes that the model spectram S Fi,F2) is made up of a limited number m of two-dimensional Gaussian resonance lines. Then m, the linewidths, intensities, and frequency co-ordinates are varied until the Markov chain reaches convergence. The allowed transitions between the current map M and the new map M comprise movement, merging or splitting of resonance lines, and birth or death of component responses. Compatibility with the experimental traces is checked by projecting M at the appropriate angles. The procedure has been found to be stable and reproducible [16]. 

The Monte Carlo method, however, is prone to model risk. If the stochastic process chosen for the underlying variable is unrealistic, so will be the estimate of VaR. This is why the choice of the underlying model is particularly important. The geometric Brownian motion model described above adequately describes the behavior of some financial variables, but certainly not that of short-term fixed-income securities. In the Brownian motion, shocks on prices are never reversed. This does not represent the price process for default-free bonds, which must converge to their face value at expiration. 

STRUCTURAL MODELING OF POROUS CARBONS USING A HYBRID REVERSE MONTE CARLO METHOD... 

Ti02 itself does not form glass, but hydrated titania or the xerogel which is produced from titanium alkoxides or salts through the sol-gel reaction is usually amorphous. Petkov et al. (1998) reported a stmctural analysis on such titania xerogels. Reverse Monte Carlo method was employed to simulate the X-ray RDF curve. In the structure model proposed... 

In all these examples, the importance of good simulation and modeling cannot be stressed enough. A variety of methods have been used in this field to simulate the data in the cases studies described above. Blander et al. [4], for example, used a semi-empirical molecular orbital method, MNDO, to calculate the geometries of the free haloaluminate ions and used these as a basis for the modeling of the data by the RPSU model [12]. Badyal et al. [6] used reverse Monte Carlo simulations, whereas Bowron et al. [11] simulated the neutron data from [MMIM]C1 with the Empirical Potential Structure Refinement (EPSR) model [13]. 

The SM2/AM1 model was used to examine anomeric and reverse anomeric effects and allowed to state that aqueous solvation tends to reduce anomeric stabilization [58]. Moreover, SM2/AM1 and SM3/PM3 models were accounted for in calculations of the aqueous solvation effects on the anomeric and conformational equilibria of D-glucopy-ranose. The solvation models put the relative ordering of the hydroxymethyl conformers in line with the experimentally determined ordering of populations. The calculations indicated that the anomeric equilibrium is controlled primarily by effects that the gauche/trans 0-C6-C5-0 hydroxymethyl conformational equilibrium is dominated by favorable solute-solvent hydrogen bonding interactions, and that the rotameric equilibria were controlled mainly by dielectric polarization of the solvent [59]. On the other hand, Monte Carlo results for the effects of solvation on the anomeric equilibrium for 2-methoxy-tetrahydropyran indicated that the AM1/SM2 method tends to underestimate the hydration effects for this compound [60]. 

This paper does not intend to be a review rather comments and examples are given for some of the recent progress. The related literature is not searched exhaustively and the selection is rather arbitrary. Preliminary results of two new studies by the XD method are presented in order to demonstrate the capabilities of the method at new conditions. The reverse Monte Carlo (RMC) technique is also discussed in more detail to show a new perspective in the structural modelling of solutions. 

The main advance in recent years has been the development of methods to obtain models of structures that are consistent with the total diffraction pattern. One method is the Reverse Monte Carlo (RMC) method (McGreevy and Pusztai 1988, McGreevy 1995, Keen 1997, 1998). In this method, the Monte Carlo technique is used to modify a configuration of atoms in order to give the best agreement with the data. This can be carried out using either S Q) or T(r) data, or both simultaneously. We also impose a... 

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