Reverse Monte Carlo

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]. 

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. 

In general, Monte Carlo simulations are such calculations in which the values of some parameters are determined by the average of some randomly generated individuals.45-54 In chemistry applications, the most prevalent methods are the so called Metropolis Monte Carlo (MMC)55 and Reverse Monte Carlo (RMC) ones. The most important quantities in these methods are some kinds of U energy-type potentials (e.g. internal energy, enthalpy,... 

In the Reverse Monte Carlo (RMC) method [5], the pair correlation function or the structure factor is calculated after each random move (Ssim(<]) or gsimfr)) and compared to the respective target function obtained from experimental diffraction data (Sexp(q) or gexp(r)). It is possible to calculate Ssm(q) with full periodicity from the atomic positions. This method is best in principle [10], but the computational cost is much greater than for any of the other available methods. It is also possible to obtain Ssm(q) by first calculating gsm(r) from the atomic positions and then Fourier transform this function and calculate Ssim(q). The disadvantage of this approach is that there is an additional computational cost associated with the Fourier transform of gsm(r) after each move. 

Some recent developments in the research of the structure and dynamics of solvated ions are discussed. The solvate structure of lithium ion in dimethyl formamide and preliminary results on the structure of sodium chloride aqueous solutions under high pressures are presented to demonstrate the capabilities of the traditional X-ray diffiraction method at new conditions. Perspectives of solution chemistry studies by combined methods as e.g. diffraction results with reverse Monte Carlo simulations, are also shown. 

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. 

V. Reverse Monte Carlo simulation of molecular liquids... 

In spite of the great success of the computer simulation methods in the determination of the microscopic properties of the solutions, the capacity of the traditional MD and MC simulations is always limited by the choice of the suitable potential functions to describe the interatomic interactions. The potentials are most often checked by comparison of the structural properties calculated from the simulation with those determined experimentally. The reverse Monte Carlo (RMC) method, developed by McGreevy and Pusztai [41] does not rely upon knowledge of any interaction potential, instead it generates a large set of atomic configurations on the condition that the difference between the experimental and calculated structure functions (or pair-distribution functions) should be minimum. The same structural... 

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... 

Keen DA (1998) Reverse Monte Carlo refinement of disordered silica phases. In Thorpe MF, Billinge SJL (eds) Local Structure from Diffraction. Plennm, New York, p 101-119 Keen DA, Dove MT (1999) Comparing the local structures of amorphous and crystalline polymorphs of silica. JPhys Condensed Matter 11 9263-9273... 

Maxwell JC (1864) On the calculation of the eqnilibrium and stiffness of frames. Phil Mag 27 294-299 McGreevy RL, Pusztai L (1988) Reverse Monte Carlo simulation A new technique for the determination of disordered structures. Molec Simulations 1 359-367 McGreevy RL (1995) RMC - Progress, problems and prospects. Nuclear Instmments Methods A 354 1-16 Palmer DC, Finger LW (1994) Pressnre-induced phase transition in ciistobalite an x-ray powder diffraction study to 4.4 GPa. Am Mineral 79 1-8... 

Tucker MG, Squires MD, Dove MT, Keen DA (2000) Reverse Monte Carlo study of cristobahte. J Phys Condensed Matter (submitted)... 

Proffen T, Welbeny TR (1997) Analysis of diffuse scattering via the reverse Monte Carlo technique A systematic investigation. Acta Crystallogr Sect A 53 202-216 Proffen T, Welbeny TR (1998) Analysis of diffuse scattering of single ciystals using Monte Carlo methods. Phase Transit 67 373-397... 

INVESTIGATION OF THE STRUCTURAL DISORDER D4 ICE Ih USING NEUTRON DIFFRACTION AND REVERSE MONTE CARLO MODELLING... 

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... 

RMCPOW RMCA Version 3, R. L. McGreevy, M. A. Howe and J. D.Wicks, (1993), available at http // www.studsvik.uu.se/ and Reverse Monte Carlo modelling of neutron powder diffraction data, A. Mellergard and R. L. McGreevy, Acta Crystallogr., Sect. A, 1999, 55, 783 Direct Space for magnetic structures... 

RMC Reverse Monte Carlo modelling of neutron powder diffraction... 

RMC + + G. Evrard, L. Pusztai, Reverse Monte Carlo Modelling of the... 

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