ISSN:
1600-5724
Source:
Crystallography Journals Online : IUCR Backfile Archive 1948-2001
Topics:
Chemistry and Pharmacology
,
Geosciences
,
Physics
Notes:
A crystal structure in P\bar 1 consisting of P heavy atoms and Q light atoms in the unit cell is considered, and the random variable vectors h and k, subject to well defined restrictions, are uniformly and independently distributed in reciprocal space. The linear combination of two phases ψ = φh+ φk is a structure seminvariant if and only if h + k = 0 (mod ω) where ω = (2, 2, 2). Eh and Ek are the two normalized structure factors associated with phases φh and φk and EPh and EPk are the contributions of the heavy atoms respectively. The first neighborhood of ψ consists of the four magnitudes |Eh|, |Ek|, |E(h + k)/2|, |E(h - k)/2|- The conditional probability distribution of ψ, given the four magnitudes |Eh|, |Ek|, |E(h + k)/2|, |E(h - k)/2| and the known contributions EPh, EPk from the heavy atoms, is derived to the approximation of 1/N. In favorable cases, i.e. when phase indications from the four-magnitude neighborhood of the seminvariant and the heavy-atom contributions coincide, a reliable estimate for ψ is obtained. The result obtained is applied to the structure of a derivative of β-lactam and its usefulness is demonstrated.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1107/S0108767385000472
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