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A benchmark method for global optimization problems in structure determination from powder diffraction data
Author(s) -
Shankland Kenneth,
Markvardsen Anders J.,
Rowlatt Christopher,
Shankland Norman,
David William I. F.
Publication year - 2010
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s0021889810008113
Subject(s) - maxima and minima , conjugate gradient method , minification , benchmark (surveying) , diffraction , famotidine , global optimization , conjugate , algorithm , materials science , physics , mathematics , mathematical analysis , mathematical optimization , optics , geology , medicine , geodesy
Quasi‐Newton–Raphson minimization and conjugate gradient minimization have been used to solve the crystal structures of famotidine form B and capsaicin from X‐ray powder diffraction data and characterize the χ 2 agreement surfaces. One million quasi‐Newton–Raphson minimizations found the famotidine global minimum with a frequency of ca 1 in 5000 and the capsaicin global minimum with a frequency of ca 1 in 10 000. These results, which are corroborated by conjugate gradient minimization, demonstrate the existence of numerous pathways from some of the highest points on these χ 2 agreement surfaces to the respective global minima, which are passable using only downhill moves. This important observation has significant ramifications for the development of improved structure determination algorithms.