A Unified Approach to Electron Counting in Main-Group Clusters
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Abstract:
A unified approach to electron counting in main-group cluster chemistry is presented, wherein the different classes, electron-rich, electron-precise, and electron-deficient, are viewed simply as different regions of a continuum defined by two variables, vertex count and valence electron count. The diverse structural chemistry of all main-group clusters can then be reconciled by recognizing that, within the confines of a fixed vertex count, each reduction of two in the total electron count must be associated with a distortion that destabilizes a single molecular orbital. This simple tenet affords a consistent framework for correlating structure with electron count across the entire spectrum of clusters, including the recently discovered hypoelectronic class. The different ways in which structure responds to changes in electron count within the different domains emerges as a logical consequence of the nature (bonding or nonbonding) of the particular orbital that is destabilized.Keywords:
Electron counting
Valence electron
Electron crystallography
Electron pair
In the quantitative determination of new structures, micro-/nano-crystalline materials pose significant challenges. The different properties of materials are structure-dependent. Traditionally, X-ray crystallography has been used for the analysis of these materials. Electron diffraction is a technique that complements other techniques; for example, single crystal X-ray diffraction and powder X-ray diffraction for determination of structure. Electron diffraction plays a very important role when crystals are very small using single crystal X-ray diffraction or very complex for structure solution by powder X-ray diffraction. With the introduction of advanced methodologies, important methods for crystal structural analysis in the field of electron crystallography have been discovered, such as rotation electron diffraction (RED) and automated electron diffraction tomography (ADT). In recent years, large numbers of crystal structures have been solved using electron crystallography.
Electron crystallography
Gas electron diffraction
Powder Diffraction
Selected area diffraction
Crystal (programming language)
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Valence electron
Electron counting
Boranes
Lone pair
Main group element
Boranes
Electron pair
Polyhedron
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Structure determination of porous materials is important for understanding the materials properties and exploiting their applications. Compared to X-ray diffraction, electron crystallography has two unique advantages. Crystals that are too small to be studied by X-ray diffraction can be studied by electron crystallography. The structure factor phase information, which is lost in diffraction, can be obtained from high resolution transmission electron microscopy (HRTEM) images. Here we will present different techniques and applications of electron crystallography for structure determination of zeolites and ordered mesoporous materials, based on electron diffraction data and/or HRTEM images. Electron crystallography and X-ray diffraction are complementary in many aspects. Their combinations show great potentials for structure determination of complex porous materials.
Electron crystallography
Selected area diffraction
Powder Diffraction
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Electron crystallography
Gas electron diffraction
Precession
Selected area diffraction
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The equations calculating the number of valence electrons on the boranes and heteroboranes are different from other simple condensed clusters such as the condensed organometallics and transition metal clusters. The equations calculating the number of valence electrons greatly differ between the condensed boranes and heteroboranes with the non-condensed boranes and heteroboranes too. These equations calculating the number of valence electrons on simple condensed clusters are all derived from the noble gas rule and Wade’s rule in the theory. The noble gas rule and Wade’s rule could be also applied to the high-nuclearity transition metal clusters, the equation details calculating the number of valence electrons is studied. The application ranges of the noble gas rule, Wade’s rule, and 6m+2n electron rule are extended. The calculating results are satisfying comparing with actual facts.
Electron counting
Boranes
Valence electron
Noble gas
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Electron crystallography
Gas electron diffraction
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Electron crystallography
Protein crystallization
Gas electron diffraction
Selected area diffraction
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Electron diffraction is one of the basic techniques to study crystal structures. With the improvement of the transmission electron microscope hardware facilities and the development of structural analysis methods, electron diffraction plays an increasingly important role in exploring the relationship between the material structures and their physical properties. In this review, the progress of crystal structure determination using electron diffraction was mainly discussed. Our group has analyzed many complex crystal structures including inorganic functional materials, zeolites and covalent organic framework materials, utilizing selected area electron diffraction and three-dimensional electron diffraction technology combined with powder X-ray diffraction, single crystal X-ray diffraction, high-resolution electron microscopy and other characterization methods.
Electron crystallography
Selected area diffraction
Gas electron diffraction
Crystal (programming language)
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The study of crystals at atomic level by electrons – electron crystallography – is an important complement to X-ray crystallography. There are two main advantages of structure determinations by electron crystallography compared to X-ray diffraction: (i) crystals millions of times smaller than those needed for X-ray diffraction can be studied and (ii) the phases of the crystallographic structure factors, which are lost in X-ray diffraction, are present in transmission-electron-microscopy (TEM) images. In this paper, some recent developments of electron crystallography and its applications, mainly on inorganic crystals, are shown. Crystal structures can be solved to atomic resolution in two dimensions as well as in three dimensions from both TEM images and electron diffraction. Different techniques developed for electron crystallography, including three-dimensional reconstruction, the electron precession technique and ultrafast electron crystallography, are reviewed. Examples of electron-crystallography applications are given. There is in principle no limitation to the complexity of the structures that can be solved by electron crystallography.
Electron crystallography
Gas electron diffraction
Ultrafast electron diffraction
Selected area diffraction
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3D electron diffraction is an emerging technique for the structural analysis of nanocrystals. The challenges that 3D electron diffraction has to face for providing reliable data for structure solution and the different ways of overcoming these challenges are described. The route from zone axis patterns towards 3D electron diffraction techniques such as precession-assisted electron diffraction tomography, rotation electron diffraction and continuous rotation is also discussed. Finally, the advantages of the new hybrid detectors with high sensitivity and fast readout are demonstrated with a proof of concept experiment of continuous rotation electron diffraction on a natrolite nanocrystal.
Electron crystallography
Gas electron diffraction
Selected area diffraction
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