Application of direct methods on difference Fourier coefficients for the solution of partially known structures

Beurskens, P. T.; Hark, T. E. M. van den; Beurskens, Gezina

doi:10.1107/s0567739476001666

Cited by 25 publications

(26 citation statements)

References 2 publications

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“…The agreement between a SSC calculation and the experimental XPD pattern was quantified using the reliability-factor RMP. 23 As a starting point in our analysis, the atomic coordinates of the M-enantiomer of heptahelicence as determined by x-ray diffraction from crystalline samples 24 were used. In other words, we assumed the molecule to retain its "shape" upon adsorption, and considered as an only degree of freedom the orientation of the molecule with respect to the substrate surface.…”

Section: Heptahelicene On Cu(111): Scati'ering Calculations and Discumentioning

confidence: 99%

Orientation of chiral heptahelicene C30H18 on copper surfaces: An x-ray photoelectron diffraction study

Fasel¹,

Cossy²,

Ernst³

et al. 2001

The Journal of Chemical Physics

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The orientation and the intramolecular relaxation due to adsorption of the chiral phenanthrene-derivative heptahelicene, C 30 H 18 , on Cu(lll) and Cu(332) smfaces have been investigated by means of angle-scanned full-hemispherical x-ray photoelectron diffraction. Although the C 1 s diffraction patterns of the adsorbed submonolayer coverage helicene films exhibit scattering anisotropies of less than two percent, a detailed analysis involving simple molecular mechanics calculations of the atomic coordinates, photoelectron diffraction single-scattering cluster calculations and an R-factor analysis permits the determination of the helicene molecular orientation. On Cu(lll), the molecules are found to bind to the substrate surface via their terminal phenanthrene group oriented parallel to the surface plane, while on Cu(332) the three terminal C-6 rings are oriented parallel to the (Ill) terrace plane. Six azimuthal molecular orientations are found to coexist on Cu(lll), on Cu(332), however, the step-molecule interaction leads to a unique azimuthal alignment of the heptahelicene molecules. The heptahelicene on Cu(332) system thus represents a chiral surface with single-phase orientational order.

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Section: Heptahelicene On Cu(111): Scati'ering Calculations and Discumentioning

confidence: 99%

Orientation of chiral heptahelicene C30H18 on copper surfaces: An x-ray photoelectron diffraction study

Fasel¹,

Cossy²,

Ernst³

et al. 2001

The Journal of Chemical Physics

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“…In the former structure one Hglz unit was found from the Patterson tures, where a fragment of the structure was found by direct methods, will be described in the following paper (Beurskens, van den Hark & Beurskens, 1976). Some numerical results for a test structure will be given in Tables 2-4 for 4,4-dichloro-2a-aza-A-homocholestan-3,on, C27H45NOC12, space group P212121, Z=4 (Mootz & Berking, 1970).…”

Section: Examplesmentioning

confidence: 99%

“…(II) Space group P21/c; Z=4; one molecule per asymmetric unit (van den Hark & Beurskens, 1976). We had troubles in solving this structure, partly because of the relatively small number of reflexions that could be measured.…”

Section: Examplesmentioning

confidence: 99%

“…In the former structure one Hglz unit was found from the Patterson THE APPLICATION OF DIRECT METHODS synthesis, and we assumed the space group to be Cc; application of the program DIRDIF.D revealed the unexpected presence of a second HgI2 unit (Beurskens, Enckevort, Menger & Bosman, 1976). The application of DIRDIF.D on the heptahelicene structures, where a fragment of the structure was found by direct methods, will be described in the following paper (Beurskens, van den Hark & Beurskens, 1976). Some numerical results for a test structure will be given in Tables 2-4 for 4,4-dichloro-2a-aza-A-homocholestan-3,on, C27H45NOC12, space group P212121, Z=4 (Mootz & Berking, 1970).…”

Section: Examplesmentioning

confidence: 99%

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The application of direct methods to non-centrosymmetric structures containing heavy atoms

Gould¹,

Hark²,

Beurskens³

1976

Acta Cryst Sect A

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Direct methods are applied to the difference structure factors for a structure containing one or more heavy atoms in known positions. The present procedure is initiated by subtracting the known heavyatom contribution from the observed structure factor (assuming that the observed and calculated structure factors have the same phase) to obtain the magnitude and phase of the light-atom contribution. The Y.2 phase relationship (tangent formula) is used to recalculate the phases of the light-atom contributions, and -consequently -to recalculate the magnitude of the light-atom contribution. An iterative procedure is used to optimize the phases and amplitudes before a difference Fourier map is calculated. The method is applicable also for the solution of partially known structures.

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“…Various procedures exist to expand the partial model to the complete structure. If, however, the initial application of direct methods yields a recognizable model which cannot be expanded, this model is usually correctly oriented but misplaced relative to the symmetry elements (see for instance Karle, 1972;Beurskens et al, 1976;Silva and Viterbo, 1980), and the model has to be shifted to the (unknown) correct position. The orientation of a rigid part of the structure can also be found by rotation searches (e.g.…”

Section: § 1 Introductionmentioning

confidence: 99%

Translation functions for the positioning of a well oriented molecular fragment

Beurskens¹,

Gould²,

Slot³

et al. 1987

Zeitschrift Für Kristallographie - Crystalline Materials

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The application of Patterson methods to the solution of molecular structures with approximately equal atoms is usually limited by the translation function. The literature on translation functions for the positioning of a correctly oriented molecular fragment is surveyed and summarized. Similarities and differences in the published functions are discussed. Variations of these functions have been tested, with the goal of finding the function that will give the best results for small search fragments and that can be used in routine X-ray analyses of small and medium sized structures. We find that well known reciprocal-space correlation functions (which are shown to be closely related to the residual R 2 ), which make use of Fast Fourier Transform techniques, are fast and reliable. Best results are obtained when all symmetry elements are used simultaneously, and geometrically unacceptable positions are rejected. Test results show that for small fragments (containing less than 10% of the scattering matter of the asymmetric unit) one should use all observed reflections (including weak reflections) and the correlation function to be used should take care of the reciprocal space equivalent of sharpening, origin removal, and subtraction of intramolecular vectors. A computer program for the automatic positioning of a correctly oriented molecular fragment is described. § 1. IntroductionIn structure determination processes using direct methods to solve the phase problem, it often occurs that the resulting structural information is

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Application of direct methods on difference Fourier coefficients for the solution of partially known structures

Cited by 25 publications

References 2 publications

Orientation of chiral heptahelicene C30H18 on copper surfaces: An x-ray photoelectron diffraction study

Orientation of chiral heptahelicene C30H18 on copper surfaces: An x-ray photoelectron diffraction study

The application of direct methods to non-centrosymmetric structures containing heavy atoms

Translation functions for the positioning of a well oriented molecular fragment

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