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Giacovazzo, Carmelo; Siliqi, Dritan; Altomare, Angela; Cascarano, Giovanni Luca; Rizzi, Rosanna; Spagna, Riccardo

The probability distribution function of structure factors with non-integral indices. III. The joint probability distribution in the P1¯ case

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  • Medientyp: E-Artikel
  • Titel: The probability distribution function of structure factors with non-integral indices. III. The joint probability distribution in the P1¯ case
  • Beteiligte: Giacovazzo, Carmelo; Siliqi, Dritan; Altomare, Angela; Cascarano, Giovanni Luca; Rizzi, Rosanna; Spagna, Riccardo
  • Erschienen: International Union of Crystallography (IUCr), 1999
  • Erschienen in: Acta Crystallographica Section A Foundations of Crystallography
  • Sprache: Nicht zu entscheiden
  • DOI: 10.1107/s0108767398009994
  • ISSN: 0108-7673
  • Schlagwörter: Structural Biology
  • Entstehung:
  • Anmerkungen:
  • Beschreibung: <jats:p>The joint probability distribution function method has been developed in <jats:italic>P</jats:italic>1¯ for reflections with rational indices. The positional atomic parameters are considered to be the primitive random variables, uniformly distributed in the interval (0, 1), while the reflection indices are kept fixed. Owing to the rationality of the indices, distributions like <jats:italic>P</jats:italic>(<jats:italic>F</jats:italic> <jats:sub> <jats:bold>p</jats:bold> <jats:sub>1</jats:sub> </jats:sub>, <jats:italic>F</jats:italic> <jats:sub> <jats:bold>p</jats:bold> <jats:sub>2</jats:sub> </jats:sub>) are found to be useful for phasing purposes, where <jats:bold>p</jats:bold> <jats:sub>1</jats:sub> and <jats:bold>p</jats:bold> <jats:sub>2</jats:sub> are any pair of vectorial indices. A variety of conditional distributions like <jats:italic>P</jats:italic>(|<jats:italic>F</jats:italic> <jats:sub> <jats:bold>p</jats:bold> <jats:sub>1</jats:sub> </jats:sub>| | |<jats:italic>F</jats:italic> <jats:sub> <jats:bold>p</jats:bold> <jats:sub>2</jats:sub> </jats:sub>|), <jats:italic>P</jats:italic>(|<jats:italic>F</jats:italic> <jats:sub> <jats:bold>p</jats:bold> <jats:sub>1</jats:sub> </jats:sub>| |<jats:italic>F</jats:italic> <jats:sub> <jats:bold>p</jats:bold> <jats:sub>2</jats:sub> </jats:sub>), P(\varphi_{{\bf p}_1}|\,|F_{{\bf p}_1}|, F_{{\bf p}_2}) are derived, which are able to estimate the modulus and phase of <jats:italic>F</jats:italic> <jats:sub> <jats:bold>p</jats:bold> <jats:sub>1</jats:sub> </jats:sub> given the modulus and/or phase of <jats:italic>F</jats:italic> <jats:sub> <jats:bold>p</jats:bold> <jats:sub>2</jats:sub> </jats:sub>. The method has been generalized to handle the joint probability distribution of any set of structure factors, <jats:italic>i.e.</jats:italic> the distributions <jats:italic>P</jats:italic>(<jats:italic>F</jats:italic> <jats:sub>1</jats:sub>, <jats:italic>F</jats:italic> <jats:sub>2</jats:sub>,…, <jats:italic>F</jats:italic> <jats:sub> <jats:italic>n</jats:italic>+1</jats:sub>), <jats:italic>P</jats:italic>(|<jats:italic>F</jats:italic> <jats:sub>1</jats:sub>| |<jats:italic>F</jats:italic> <jats:sub>2</jats:sub>,…, <jats:italic>F</jats:italic> <jats:sub> <jats:italic>n</jats:italic>+1</jats:sub>) and <jats:italic>P</jats:italic>(\varphi<jats:sub>1</jats:sub>| |<jats:italic>F</jats:italic>|<jats:sub>1</jats:sub>, <jats:italic>F</jats:italic> <jats:sub>2</jats:sub>,…, F_{n+1}) have been obtained. Some practical tests prove the efficiency of the method.</jats:p>