First example of multi-scale reverse Monte Carlo modeling for small-angle scattering experimental data using reverse mapping from coarse-grained particles to atoms.

We propose a new method for multi-scale reverse Monte Carlo (RMC) modeling of small-angle scattering data using reverse mapping from coarse-grained particles to atoms in cases where scale separation cannot be assumed. For efficient RMC analysis for small-angle scattering data, it is important to determine a large scale structure with the lowest possible computing cost. In order to find this large scale structure, a method using coarse-grained particles instead of atoms is suitable. As our first example, we examine the structure of expanded fluid Hg near the critical point. For this system, small-angle x-ray scattering (SAXS) data and wide-angle x-ray diffraction data (XRD) are observed in the same thermodynamic state. First, RMC analysis using coarse-grained particles for SAXS data is performed. Second, RMC analysis for SAXS and XRD data is performed with the replacement of a coarse-grained particle by an ad hoc cluster of several Hg atoms. In the present study, we have determined that the size of one coarse-grained particle corresponds to ten Hg atoms. The number density for the coarse-grained particles is set to one-tenth the actual number density of atoms and the cutoff length is three times (6.9 Å) that of Hg atoms (2.3 Å). As a result, this approach is found to be successful and the computing cost of RMC analysis can be reduced.