A minimal principle in X-ray crystallography: starting in a small way

Hauptman, H.

doi:10.1098/rspa.1993.0086

Cited by 8 publications

(9 citation statements)

References 7 publications

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“…For objects with heavyatom constituents, it may be possible to identify subsets of intensity data that are close enough to the kinematical condition to permit ab initio analyses [e.g. the interesting use of higher-order Laue zone data for this purpose by a group at the University of Bristol (Vincent & Exelby, 1991, 1993Vincent & Midgley, 1994)]. As mentioned above, the collection of intensity data from polycrystalline samples may be useful in some cases.…”

Section: The Quasi-kinematical Scattering Conceptmentioning

confidence: 99%

“…More recently, Patterson maps have been used in a highly innovative way to solve alloy crystal structures (Vincent & Exelby, 1991, 1993. Since reflections within the higher-order Laue zones have extinction distances approaching the kinematical approximation, their intensities can be used to solve the crystal structures.…”

Section: Solution Of the Phase Problemmentioning

confidence: 99%

“…For example, the tangent formula (Karle & Hauptman, 1956) has been shown to be useful for many noncentrosymmetric data sets, even if more suitable figures of merit be found [e.g. the minimal principle (Hauptman, 1993)] that are least sensitive to multiple-scattering perturbations. The Sayre (1952) equation, in a multi-solution form, has also been shown to be a powerful tool for many problems.…”

Section: Solution Of the Phase Problemmentioning

confidence: 99%

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Electron crystallography

Dorset¹

1996

Acta Crystallogr B Struct Sci

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The idea of solving unknown crystal structures from experimental electron-diffraction intensities and high-resolution electron micrographs has remained a controversial topic in the 60 year history of electron crystallography. In this review it will be shown that the application of modern direct phasing techniques, familiar to X-ray crystallographers, has decisively proven that such ab initio determinations are, in fact, possible. This statement does not, by any means, refute the existence of the several significant scattering perturbations identified by diffraction physicists. Rather, it does affirm that experimental parameters can be controlled to ensure that a 'quasi-kinematical' data set can be collected from many types of specimens. Numerous applications have been made to various types of specimens, ranging from small organics to proteins, and also some inorganic materials. While electron crystallography may not be the optimal means for determining accurate bonding parameters, it is often the method of choice when only microcrystalline specimens are available.

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Section: The Quasi-kinematical Scattering Conceptmentioning

confidence: 99%

Section: Solution Of the Phase Problemmentioning

confidence: 99%

Section: Solution Of the Phase Problemmentioning

confidence: 99%

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Electron crystallography

Dorset¹

1996

Acta Crystallogr B Struct Sci

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“…In recent years, there has been increasing activity, exploring the possibilities of direct determination of crystallographic phases for diffraction data from proteins. Although the large number of atoms in the unit cell can severely limit the application of traditional probabilistic methods (Karle, 1989), there have been alternative approaches (Hauptman, 1993;Miller, DeTitta, Jones, Langs, Weeks & Hauptman, 1993), where a nearly correct phase solution in a multiple set can be identified to lie near a previously identified optimal figure of merit so that these phases can be improved by annealing to determine the correct crystal structure (Weeks, Hauptman, Smith, Blessing, Teeter & Miller, 1995). Thus, given experimental X-ray intensities from a protein (e.og.…”

Section: Introductionmentioning

confidence: 99%

The pseudo-atom approach to phase determination in protein electron crystallography – noncentrosymmetric projections. Erratum

Dorset¹

1998

Acta Cryst Sect A

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In the paper by Dorset [Acta Cryst. (1997), A53, 445-455], identical strictures were placed on the plane groups p3 and p31m for origin definition, i.e. it was stated that all hk0 reflections were structure seminvariants. While this general restriction is true for p3 l m, it applies in p3 only for reflections where h-k = 3n. Hence, additional origin information (one non-seminvariant phase term) might have been used for this plane group, an option that will be considered in future work with these data sets. Owing to a typographical error, the SayreHughes equation was incorrectly reproduced and should be written E h = Nl/2(EkEh_k)kr.

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“…When a figure of merit is chosen that also depends on this invariant, e.g. the minimal principle (Hauptman, 1993), there is no difficulty in finding the structure by completely automated procedures. This means that invariants that depend mostly on large amplitudes (also positive quartets) will remain reliable for predicting new phases.…”

mentioning

confidence: 99%

The Accurate Electron Crystallographic Refinement of Organic Structures Containing Heavy Atoms

Dorset

1997

Acta Cryst Sect A

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Prospects for the accurate structure determination of heavy-atom-containing organic crystals were evaluated with electron diffraction data from perchloro and perbromo derivatives of copper phthalocyanine. While the extensive overlap of experimental Patterson maps (from 1200kV intensities) with respective crystal autocorrelation functions explains the success of previous direct structure analyses, it is clear that multiple-scattering perturbations still evident at high voltage will frustrate the determination of accurate bond distances and angles. If, however, the result obtained after direct structure analysis and Fourier refinement is used to position an idealized molecular model (i.e. with chemically reasonable bonding parameters), the correct structure can then be justified by a rotational search coupled with a multislice dynamical calculation. Even though dynamical scattering is not the only major perturbation to such data sets, the resolution-limited correction is still sufficient to identify the correct molecular orientation in the unit cell. Alternatively, an acceptable unconstrained structure refinement can be carried out via a procedure proposed by Huang, Liu, Gu, Xiong, Fan & Li [Acta Cryst. (1996), A52, 152-157]. A phenomenological adjustment of observed intensities, based initially on the heavy-atom positions found in a high-resolution electron micrograph, will permit all light atoms to be observed near their ideal positions in the ensuing Fourier refinement.

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A minimal principle in X-ray crystallography: starting in a small way

Cited by 8 publications

References 7 publications

Electron crystallography

Electron crystallography

The pseudo-atom approach to phase determination in protein electron crystallography – noncentrosymmetric projections. Erratum

The Accurate Electron Crystallographic Refinement of Organic Structures Containing Heavy Atoms

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