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Direct phasing from Patterson syntheses by δ recycling.

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Title: Direct phasing from Patterson syntheses by δ recycling.
Authors: Rius, Jordi1
Source: Acta Crystallographica: Section A (Wiley-Blackwell). Jan2012, Vol. 68 Issue 1, p77-81. 5p. 2 Charts.
Subjects: Patterson function, Crystal structure, Fourier transforms, Scattering (Physics), Organic compounds
Abstract: The direct methods origin-free modulus sum function [Rius (1993). Acta Cryst. A 49, 406-409] includes in its definition the structure factor G(Φ) of the squared crystal structure expressed in terms of Φ, the set of ϕ phases of the normalized structure factors E's of the crystal structure of unit-cell volume V. Here the simpler sum function variant = ∑ H E− H∫ VδP,Δ(Φ)exp( i2π Hr)d V extended over all H reflections is introduced which involves no G's and in which the δP,Δ function corresponds to δP = FT−1{()exp[ iϕ H(Φ)]} (where FT = Fourier transform) with all values smaller than Δ = 2.5σP equated to zero ( is the variance of δP calculable from the experimental intensities). The new phase estimates are obtained by Fourier transforming δP,Δ. This iterative phasing method (δ recycling) only requires calculation of Fourier transforms at two stages. Since δM≃δP/2, similar arguments are valid for δM = FT−1[( E H−〈 E〉)exp( iϕ H)] from which the corresponding phasing function follows. [ABSTRACT FROM AUTHOR]
Copyright of Acta Crystallographica: Section A (Wiley-Blackwell) is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
An: 69870972
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  Data: Direct phasing from Patterson syntheses by δ recycling.
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  Data: <searchLink fieldCode="DE" term="%22Patterson+function%22">Patterson function</searchLink><br /><searchLink fieldCode="DE" term="%22Crystal+structure%22">Crystal structure</searchLink><br /><searchLink fieldCode="DE" term="%22Fourier+transforms%22">Fourier transforms</searchLink><br /><searchLink fieldCode="DE" term="%22Scattering+%28Physics%29%22">Scattering (Physics)</searchLink><br /><searchLink fieldCode="DE" term="%22Organic+compounds%22">Organic compounds</searchLink>
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  Data: The direct methods origin-free modulus sum function [Rius (1993). Acta Cryst. A 49, 406-409] includes in its definition the structure factor G(Φ) of the squared crystal structure expressed in terms of Φ, the set of ϕ phases of the normalized structure factors E's of the crystal structure of unit-cell volume V. Here the simpler sum function variant = ∑ H E− H∫ VδP,Δ(Φ)exp( i2π Hr)d V extended over all H reflections is introduced which involves no G's and in which the δP,Δ function corresponds to δP = FT−1{()exp[ iϕ H(Φ)]} (where FT = Fourier transform) with all values smaller than Δ = 2.5σP equated to zero ( is the variance of δP calculable from the experimental intensities). The new phase estimates are obtained by Fourier transforming δP,Δ. This iterative phasing method (δ recycling) only requires calculation of Fourier transforms at two stages. Since δM≃δP/2, similar arguments are valid for δM = FT−1[( E H−〈 E〉)exp( iϕ H)] from which the corresponding phasing function follows. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Acta Crystallographica: Section A (Wiley-Blackwell) is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1107/S0108767311043145
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      – Code: eng
        Text: English
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        PageCount: 5
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    Subjects:
      – SubjectFull: Patterson function
        Type: general
      – SubjectFull: Crystal structure
        Type: general
      – SubjectFull: Fourier transforms
        Type: general
      – SubjectFull: Scattering (Physics)
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      – SubjectFull: Organic compounds
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      – TitleFull: Direct phasing from Patterson syntheses by δ recycling.
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              Text: Jan2012
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