The structure factor

Coppens, Philip

doi:10.1107/97809553602060000550

Cited by 9 publications

(6 citation statements)

References 33 publications

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“…Eventually, high-order series may be considered; see for example, (2, 3, 5) and references therein. Tickle & Moss (28) noted that “ The harmonic model is applicable only if the motion is purely translational, but provided the libration amplitudes are not too large it is a good approximation ”.…”

Section: Description Of Motionmentioning

confidence: 99%

“…It has been pointed out in the literature (5, 19) that the linear combinations (7.28) of the T, L, S elements use only differences between S xx ,S yy ,S zz and not the values themselves. Knowledge of two of these differences defines the third one.…”

Section: Rotation Around An Axis In a General Positionmentioning

confidence: 99%

“…Larger displacements can be described by anharmonic models (2–5 and references therein) or by explicit parameterization of discrete atomic positions using alternative conformations ( locations ). Alternative conformations represent partially present atoms – same atoms occupying different positions across unit cells of the whole crystal.…”

Section: Introductionmentioning

confidence: 99%

“…The aims, scope and results of this review include: comprehensive derivation of TLS equations from basic principles, incrementally going from simple special cases to more general ones;detailed analysis of TLS equations both for simple and general cases;discussion of some practical aspects relevant to TLS modeling. We address these points, in spite of a very large amount of literature devoted to the TLS modeling (for example 3, 5, 13, 16, 19, 22–30 and references therein), because it is difficult to find corresponding derivations and formulae at a basic mathematical level permitting crystallographers with a non-mathematical background to understand and easily reproduce them. Apart from differences in notation and a few minor typographical errors found in the publications mentioned above, our resulting formulae are no different from those in the previous publications.…”

Section: Introductionmentioning

confidence: 99%

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TLSfrom fundamentals to practice

Urzhumtsev

Afonine

Adams

2013

Crystallography Reviews

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The Translation-Libration-Screw-rotation (TLS) model of rigid-body harmonic displacements introduced in crystallography by Schomaker & Trueblood (1968) is now a routine tool in macromolecular studies and is a feature of most modern crystallographic structure refinement packages. In this review we consider a number of simple examples that illustrate important features of the TLS model. Based on these examples simplified formulae are given for several special cases that may occur in structure modeling and refinement. The derivation of general TLS formulae from basic principles is also provided. This manuscript describes the principles of TLS modeling, as well as some select algorithmic details for practical application. An extensive list of applications references as examples of TLS in macromolecular crystallography refinement is provided.

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Section: Description Of Motionmentioning

confidence: 99%

Section: Rotation Around An Axis In a General Positionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

TLSfrom fundamentals to practice

Urzhumtsev

Afonine

Adams

2013

Crystallography Reviews

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“…In theory, intensity ( I ) of different diffraction peaks corresponding to each lattice plane is indicated by the square of the structure factor ( F ) in which N j is the site occupancy factor of each atom, f j is the scattering factor, and ( x j , y j , z j ) is the crystallographic coordinates.…”

Section: Resultsmentioning

confidence: 99%

Generation of Site-Selective Structural Vacancies in a Multinary Metal–Organic Framework for Enhanced Catalysis

Wang

Rao

et al. 2023

ACS Appl. Mater. Interfaces

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Generating structural vacancies in metal−organic frameworks (MOFs) by partially removing the inorganic and organic units from the scaffolds is an effective strategy to modulate the pore parameters of the extended structures. However, pore enlargement is accomplished at the cost of loss in the number of active sites in typical MOFs, since dissociations of coordination linkages to create vacancies are not site-selective. Here, we performed site-specific vacancy generation in a multinary MOF (FDM-6) by selectively hydrolyzing the weak Zn�carboxylate linkages and keeping the strong Cu�pyrazolate linkages untouched. Surface area and pore size range of the materials could be systematically tuned by adjusting the water content and hydrolysis time. More than 56% of the Zn(II) sites in FDM-6 could be vacant, as evidenced by the atom occupancy analysis using powder X-ray diffraction, while most of the redox-active Cu sites are held in the backbone. The vacancies create highly connected mesopores, thus guaranteeing facile transportation of the guest molecules toward the active sites. Compared with the pristine MOF, FDM-6 with site-selective vacancies shows enhanced catalytic activity in bulky aromatic alcohol oxidation. Overall, the multinary MOF provides a platform in which both pore size enhancement and full retainment of active sites could be delivered in one framework by simple vacancy engineering.

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1.6 Phasing of X-ray Data

Usón

2012

Comprehensive Biophysics

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The structure factor

Cited by 9 publications

References 33 publications

TLSfrom fundamentals to practice

TLSfrom fundamentals to practice

Generation of Site-Selective Structural Vacancies in a Multinary Metal–Organic Framework for Enhanced Catalysis

1.6 Phasing of X-ray Data

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