Empirical Potential Structure Refinement

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]. 

Thompson, H. Soper. A.K. Buchanan, P. Aldiwan, N. Creek, J.L. Koh, C.A. (2006). Methane hydrate formation and decomposition Structural studies via neutron diffraction and empirical potential structure refinement. J. Chem. Phys., 124 (16), Art. No. 164508. 

Figure 2.3 Cation-anion (a) and cation-cation (b) center-of-mass radial distribution functions determined by empirical potential structure refinement from neutron diffraction studies of [C CjImlCl, [CiCjIm][PF ], and [CjCjIm][Tf2N]. (From Acc. Chem. Res., 40,1146-1155,2007. With permission.)...

Figure 1.7 (See color insert following page 414.) Probability densities determined by empirical potential structure refinement from neutron diffraction studies of [CjCiImllPF ]. Densities are for (a) [PF l and (b) [CiCiIm]+ around a central anion.

Figure 2.8 (See color insert following page 414.) Probability densities determined by empirical potential structure refinement from neutron diffraction studies of [CjCiIm][Pp5] containing 33 mol% benzene. Densities are for (a) [PF ]", (b) benzene, and (c) [CjCjIm]+ around a central cation. Surfaces are drawn to encompass the top 25% of ions within 8 A for the anion and benzene and 10 A for the cation. (From Dee-tlefs, M., Hardacre, C., Nieuwenhuyzen, M., Sheppard, O., and Soper, A. K., /. Phys. Chem. B, 109, 1593-1598,2005. With permission.)...

Soper, A.K., Tests of the empirical potential structure refinement method and a new method of application to neutron diffraction data on water, Mol. Phys., 99, 1503-1516,2001. 

Probably the most notable work on the structure in liquid water based upon experimental data has been that of Soper and co-workers [6,8,10,30,46,55]. He has considered water under both ambient and high temperature and pressure conditions. He has employed both the spherical harmonic reconstruction technique [8,46] and empirical potential structure refinement [6,10] to extract estimates for the pair distribution function for water from site-site radial distribution functions. Both approaches must deal with the fact that the three g p(r) available from neutron scattering experiments provide an incomplete set of information for determining the six-dimensional pair distribution function. Noise in the experimental data introduces further complications, particularly in the former technique. Nonetheless, Soper has been able to extract the principal features in the pair (spatial) distribution function. Of most significance here is the fact that his findings are in qualitative agreement with those discussed above. 

Using Monte Carlo, the model is then relaxed using the new potential, resulting in a new calculated g r). The process is then iterated until it reaches convergence. This approach, known as Empirical Potential Structure Refinement (EPSR) has proved very powerful in the study of complex liquids, and of the solvation states of molecules in solution. It is particularly successful when it has as target functions a number (though not necessarily the complete set) of DPDFs from the system in question. 

Special techniques, isotope substitution in neutron diffraction with empirical potential structure refinement, permit partial pair correlation functions to be obtained. The three partial pair correlation functions g(Ow-Ow, r), g(Ow-Hw, r), and g(Hw-Hw, r), provide more information on the molecular structure of water as discussed below. Those for water at ambient conditions are shown in Fig. 1.2 (Soper 2000). 

C. Landron, A. K. Soper, T. Jenkins, G. N. Greaves, L. Heima, and J. P. Coutures, Measuring neutron scattering structure factor for liquid alumina and analysing the radial distribution function by empirical potential structure refinement, J. Non-Ciyst Solids 293, 453-457 (2001). 

Landron C, Hennet L, Jenkins T, Greaves G, Coutures J-P, Soper A (2001) Liquid alumina detailed atomic coordination determined from neutron diffraction data using empirical potential structure refinement. Phys Rev Lett 86(21) 4839-4842... 

In order to extract microscopic quantities such as spatial probabilities and RDFs from collected differential cross scattering data, analysis is typically performed following reverse Monte Carlo (RMC) or empirical potential structure refinement (EPSR) procedures [7]. The latter procedure can be viewed as a Monte Carlo simulation of system utilising a model potential similar to a classical molecular mechanics force field. This model potential is modified in order to bring the total structure factor calculated from the model system as close as possible to the ejq)erimental data. From configurations generated with this refined potential, standard quantities (such as RDFs) may be calculated. 

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