On the efficient evaluation of Fourier patterns for nanoparticles and clusters

Journal of Computational Chemistry
Antonio CervellinoAntonietta Guagliardi

Abstract

Samples made of an isotropically oriented ensemble of atomic clusters or structures that are not large crystals (i.e. extended less than 10 periods in each direction) are at the frontier of today's material science and chemistry. Examples are nanoparticles, nanotubes, amorphous matter, polymers, and macromolecules in suspension. For such systems the computation of powder diffraction patterns (which may provide an efficient characterization) is to be performed the hard way, by summing contributions from each atom pair. This work deals with performing such computation in the most practical and efficient way. Three main points are developed: how to encode the enormous array of interatomic distances (which increase as the square or higher powers of the cluster diameter) to a much smaller array of equispaced values on a coarse grid (whose size increases linearly with the diameter); how to perform a fast computation of the diffraction pattern from this equispaced grid; how to optimize the grid step to obtain an arbitrarily small error on the computed diffraction pattern. Theory and examples are jointly developed and presented.

References

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Citations

Oct 21, 2011·Acta Crystallographica. Section A, Foundations of Crystallography·Noel William Thomas
Aug 10, 2010·Biomaterials·Antonietta GuagliardiMaddalena Mastrogiacomo
Apr 8, 2016·Chemical Reviews·Tao LiByeongdu Lee
Apr 11, 2017·ACS Nano·Federica BertolottiAntonietta Guagliardi
Sep 14, 2011·Angewandte Chemie·Giuseppe CernutoAntonietta Guagliardi
Nov 10, 2010·Physical Chemistry Chemical Physics : PCCP·Franziska NiederdraenkChristian Kumpf
Aug 31, 2013·Journal of Physics. Condensed Matter : an Institute of Physics Journal·Brian Richard Pauw
Sep 3, 2019·Acta Crystallographica. Section A, Foundations and Advances·Ran GuSimon J L Billinge
May 2, 2020·Acta Crystallographica. Section A, Foundations and Advances·Antonio Cervellino, Ruggero Frison
Nov 4, 2016·Acta Crystallographica. Section A, Foundations and Advances·Luca Gelisio, Paolo Scardi
Nov 4, 2016·Acta Crystallographica. Section A, Foundations and Advances·Federica BertolottiNorberto Masciocchi
Oct 22, 2013·Journal of Physics. Condensed Matter : an Institute of Physics Journal·Orsolya Gereben, Valeri Petkov
Nov 4, 2016·Acta Crystallographica. Section A, Foundations and Advances·Ann Christin DippelBo B Iversen
Jul 31, 2020·Scientific Reports·Fabio FerriNorberto Masciocchi
Jan 28, 2009·Journal of the American Chemical Society·Angela FioreLiberato Manna
Feb 18, 2011·Journal of the American Chemical Society·Giuseppe CernutoAntonietta Guagliardi
Aug 3, 2006·Journal of the American Chemical Society·Ludovico CademartiriGeoffrey A Ozin

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