The joint probability distribution function of structure factors with rational indices. IV. The <i>P</i>1 case

Giacovazzo, Carmelo; Siliqi, Dritan; Fernández-Castaño, Cristina

doi:10.1107/s0108767398014792

Cited by 3 publications

(1 citation statement)

References 10 publications

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“…The space group P1 was considered in the fourth paper of the series. 129 In a nutshell, calculations for all space groups have to be made with reference to the derivations for P1 and P1, the most general cases. The method can be used to provide reliable estimates of structure factors with rational indices provided there is a priori knowledge of other structure factors, also with rational indices.…”

Section: Direct Methodsmentioning

confidence: 99%

5 Molecular structure from X-ray diffraction

Powell

2000

Annu. Rep. Prog. Chem., Sect. C

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The last of these reports appeared four years ago; 1 a number of major advances in structure elucidation have appeared in laboratories in that period, mostly in the ¢eld of macromolecular structure determination. This is largely because sub-100 non-hydrogen atom structure solution has become almost routine, with extremely robust solution and re¢nement programs being complemented by rapid data collection from single crystal samples. In many cases, the role of the in-house crystallographer in chemistry departments is to provide a service to synthetic chemists in an analogous way to that of NMR spectroscopists ¢fteen or twenty years ago. Many chemical crystallographers have used this as an opportunity to study more dif¢cult structures, for example larger molecules from both single crystal and powder methods, using twin datasets, and looking more closely at structures in charge density studies.This increased ease has not removed the perils of being ``Marshed''; the well-known investigator into errors in space group determination has examined structures deposited into the Cambridge Structural Database (CSD) with space group P1, of which more than 20% are incorrect. 2 The majority of errors appear to be due to typographical errors in the original publication, but a signi¢cant minority are due to incorrect space group assignment (usually authors missing a centre of inversion, and assigning P1 rather than P1, or not recognizing higher symmetry, e.g., assigning P1 (triclinic) rather than C2 (monoclinic). However, the author notes that in some cases of true P1 structures, the deviation from centrosymmetry is as small as 0.1 Ð, and would be expected to lead to dif¢culties in re¢nement unless the problem had been recognized, as the following example illustrates.The solution and re¢nement of the antibiotics Emycin E and D provides a warning not to abide by conventional wisdom under all circumstances. 3 Both antibiotics crystallize in a triclinic space group with two molecules in the asymmetric unit (Z 2). The dataset for Emycin E was in accordance with the normal measure of centricity, a mean hjE 2 À 1ji value of 0.978 (the expected value for a centrosymmetric dataset is 0.968, and is 0.736 for acentric), while that for Emycin D was 0.829. Both can be re¢ned to low residual indices (R-factors) in space group

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Section: Direct Methodsmentioning

confidence: 99%

5 Molecular structure from X-ray diffraction

Powell

2000

Annu. Rep. Prog. Chem., Sect. C

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Confined structures: basic crystallographic aspects

Giacovazzo

Siliqi

2002

Acta Cryst Sect A

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The concept of a con®ned structure is introduced. The statistical properties of the structure factors for such structures are derived and the main features of the Patterson function are described. It is shown that the structure-factor distributions for the con®ned structures coincide with those derived for the rational index re¯ections of ordinary structures. Algorithms potentially useful for protein crystal structure solution are identi®ed and checked via experimental applications.

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The joint probability distribution function of structure factors with rational indices. VI. Cases with reduced dimensionality

et al. 1999

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The probabilistic formulas relating standard and mixed type reflections (these last show integral and half-integral indices) are derived. It is shown that probabilistic estimates can be obtained by using particular sections of the three-dimensional reciprocal space. The concept of structure invariant is extended to define the wider class of structure quasi-invariant. Their statistical behaviour is briefly discussed with the help of some practical tests.

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The joint probability distribution function of structure factors with rational indices. IV. The P1 case

Cited by 3 publications

References 10 publications

5 Molecular structure from X-ray diffraction

5 Molecular structure from X-ray diffraction

Confined structures: basic crystallographic aspects

The joint probability distribution function of structure factors with rational indices. VI. Cases with reduced dimensionality

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