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From a random to the correct structure: the VLD algorithm
Author(s) -
Burla Maria Cristina,
Giacovazzo Carmelo,
Polidori Giampiero
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/s0021889810018285
Subject(s) - fourier transform , algorithm , fourier series , representation (politics) , term (time) , probabilistic logic , set (abstract data type) , mathematics , phaser , fourier analysis , mathematical analysis , computer science , physics , optics , statistics , quantum mechanics , politics , political science , law , programming language
A recent probabilistic reformulation of the difference electron‐density Fourier synthesis [Burla, Caliandro, Giacovazzo & Polidori (2010). Acta Cryst. A 66 , 347–361] suggested that the most suitable Fourier coefficients are the sum of the classical difference term ( mF − DF p ) with a flipping term, depending on the model and on its quality. The flipping term is dominant when the model is poor and is negligible when the model is a good representation of the target structure. In the case of a random model the Fourier coefficient does not vanish and therefore could allow the recovery of the target structure from a random model. This paper describes a new phasing algorithm which does not require use of the concept of structure invariants or semi‐invariants: it is based only on the properties of the new difference electron density and of the observed Fourier synthesis. The algorithm is cyclic and very easy to implement. It has been applied to a large set of small‐molecule structures to verify the suitability of the approach.