Crystal Structure Solution from Neutron Powder Diffraction Data by a new Monte Carlo Approach Incorporating Restrained Relaxation of the Molecular Geometry

Abstract

We report the development of a new aspect of the Monte Carlo method for crystal structure solution from powder diffraction data and demonstrate the advantages of this new approach by applying it to solve the low‐temperature crystal structure (phase II) of perdeuterated pyrene from neutron powder diffraction data. In previous applications of our Monte Carlo technique, the structural fragment was constrained to have a standard geometry throughout the calculation, whereas in the new approach, restrained relaxation of the structural fragment from standard geometry is considered for each structure sampled during the calculation. The new approach gives rise to a substantially improved discrimination (in terms of the weighted profile R factor Rwp) between the correct structure solution and incorrect structures sampled during the Monte Carlo calculation [for the calculation with standard geometry of the structural fragment, Rwp ranged from circa 27.5–30% for `wrong' structures to 21.2% for the best structure solution (i.e. discrimination ~6.3%); for the calculation with relaxation of the geometry of the structural fragment, Rwp ranged from circa 24–26% for `wrong' structures to 11.6% for the best structure solution (i.e. discrimination ~12.4%)]. The work reported here represents the first application of the Monte Carlo method for structure solution using neutron powder diffraction data; the new methodology (applicable to both neutron and X‐ray powder diffraction data) represents a substantial enhancement of the scope and potential of the method, particularly for cases in which the discrimination in Rwp between the correct structure solution and incorrect structure solutions is expected to be inherently small.

The Genetic Algorithm: Foundations and Apllications in Structure Solution from Powder Diffraction Data

“…Initial work on direct-space structure solution focused on the development of Monte Carlo (Harris et al, 1994;Kariuki et al, 1996;Tremayne et al, 1996a,b;Ramprasad et al, 1995;Elizabe  et al, 1997;Tremayne, Kariuki, Harris, Shankland & Knight, 1997) and simulated annealing (Newsam et al, 1992;Andreev et al, 1996Andreev et al, , 1997 methods for exploring the R wp (X) hypersurface. In the present paper, we describe a method for`direct-space' structure solution based on the application of a genetic algorithm to explore the R wp (X) hypersurface.…”

Evolving Opportunities in Structure Solution from Powder Diffraction Data—Crystal Structure Determination of a Molecular System with Twelve Variable Torsion Angles

“…Because of these properties, films of block copolymers are ideal precursors for membranes with nanometersized channels or nanochannels. The nanochannels can be produced by full [11,12] or partial decomposition [13,14] of the cylindrical domains formed from one of the blocks, as was demonstrated for diblock films. [11±14] Here we report the first preparation of thin films with nanochannels from a triblock copolymer, polyisoprene-blockpoly(2-cinnamoylethyl methacrylate)-block-poly(tert-butyl acrylate) or PI-b-PCEMA-b-PtBA 1.…”

The Rietveld Refinement in the EXPO Software: A Powerful Tool at the End of the Elaborate Crystal Structure Solution Pathway

“…Simulated Annealing is an iterative metaheuristic algorithm widely used to address discrete and continuous optimization problems. Its main advantage is that during the explorative walk on the CF hypersurface via the Monte Carlo method [33,41,42], uphill moves are allowed, providing the trial model to escape from local minima in search of the global minimum. On the contrary, one shortage of SA is the high computational cost, strongly dependent above all on the chosen annealing schedule that regulates the temperature (T) parameter control.…”