Shape Of Molecules Research Articles

ChemInform Abstract: Curly Arrows Meet Electron Density Transfers in Chemical Reaction Mechanisms: From Electron Localization Function (ELF) Analysis to Valence‐Shell Electron‐Pair Repulsion (VSEPR) Inspired Interpretation

AbstractReview: 173 refs.

A chemist's point of view: the noncylindrical symmetry of electron density means nothing but still means something

Some uncertainties of the ellipticity of electron density are discussed in terms of double-bonding and valence-shell electron pair repulsion.

Molecular geometry inspired positioning for aerial networks

The advances in unmanned aerial vehicle (UAV) and wireless sensor technology made it possible to deploy aerial networks and to collect information in three dimensional (3D) space. These aerial networks enable high quality observation of events as multiple UAVs coordinate and communicate for data collection. The positioning of UAVs in aerial networks is critical for effective coverage of the environment and data collection. UAV systems have their characteristic constraints for node positioning such as dynamic topology changes or heterogeneous network structure. The positioning methods for two dimensional (2D) scenarios cannot be used for aerial networks since these approaches become NP-hard in 3D space.In this paper, we propose a node positioning strategy for UAV networks. We propose a wireless sensor and actor network structure according to different capabilities of the nodes in the network. The positioning algorithm utilizes the Valence Shell Electron Pair Repulsion (VSEPR) theory of chemistry, which is based on the correlation between molecular geometry and the number of atoms in a molecule. By using the rules of VSEPR theory, the actor nodes in the proposed approach use a lightweight and distributed algorithm to form a self organizing network around a central UAV, which has the role of the sink. The limitations of the basic VSEPR theory are eliminated by extending the approach for multiple central data collectors. The simulation results demonstrate that the proposed system provides high connectivity and coverage for the aerial sensor and actor network.

Curly arrows meet electron density transfers in chemical reaction mechanisms: from electron localization function (ELF) analysis to valence-shell electron-pair repulsion (VSEPR) inspired interpretation.

Probing the electron density transfers during a chemical reaction can provide important insights, making possible to understand and control chemical reactions. This aim has required extensions of the relationships between the traditional chemical concepts and the quantum mechanical ones. The present work examines the detailed chemical insights that have been generated through 100 years of work worldwide on G. N. Lewis's ground breaking paper on The Atom and the Molecule (Lewis, G. N. The Atom and the Molecule, J. Am. Chem. Soc. 1916, 38, 762-785), with a focus on how the determination of reaction mechanisms can be reached applying the bonding evolution theory (BET), emphasizing how curly arrows meet electron density transfers in chemical reaction mechanisms and how the Lewis structure can be recovered. BET that combines the topological analysis of the electron localization function (ELF) and Thom's catastrophe theory (CT) provides a powerful tool providing insight into molecular mechanisms of chemical rearrangements. In agreement with physical laws and quantum theoretical insights, BET can be considered as an appropriate tool to tackle chemical reactivity with a wide range of possible applications. Likewise, the present approach retrieves the classical curly arrows used to describe the rearrangements of chemical bonds for a given reaction mechanism, providing detailed physical grounds for this type of representation. The ideas underlying the valence-shell-electron pair-repulsion (VSEPR) model applied to non-equilibrium geometries provide simple chemical explanations of density transfers. For a given geometry around a central atom, the arrangement of the electronic domain may comply or not with the VSEPR rules according with the valence shell population of the considered atom. A deformation yields arrangements which are either VSEPR defective (at least a domain is missing to match the VSEPR arrangement corresponding to the geometry of the ligands), VSEPR compliant or pseudo VSEPR when the position of bonding and non-bonding domains are interchanged. VSEPR defective arrangements increase the electrophilic character of the site whereas the VSEPR compliant arrangements anticipate the formation of a new covalent bond. The frequencies of the normal modes which account for the reaction coordinate provide additional information on the succession of the density transfers. This simple model is shown to yield results in very good agreement with those obtained by BET.

Teaching of chemical bonding: a study of Swedish and South African students' conceptions of bonding

Almost 700 Swedish and South African students from the upper secondary school and first-term chemistry university level responded to our survey on concepts of chemical bonding. The national secondary school curricula and most common textbooks for both countries were also surveyed and compared for their content on chemical bonding. Notable differences between the countries were found in textbooks and in the curriculum regarding the topics of ionic bonding, bond energetics and use of the VSEPR model, the latter being absent in the Swedish curriculum and ionic bonding not explicitly mentioned in the South African curriculum. To some extent these differences are reflected in the students’ responses to the survey. It is also clear that university teachers in both countries must prepare effective counter-measures against deep rooted misunderstandings. For the upper secondary school level it is suggested that the bond energetics and exothermic and endothermic reactions be clearly and carefully presented and separated as the study indicates that mixing of these two concepts is a major cause of confusion.

The Use of Molecular Modeling as “Pseudoexperimental” Data for Teaching VSEPR as a Hands-On General Chemistry Activity

A hands-on activity appropriate for first-semester general chemistry students is presented that combines traditional VSEPR methods of predicting molecular geometries with introductory use of molecular modeling. Students analyze a series of previously calculated output files consisting of several molecules each in various geometries. Each structure is analyzed with respect to the calculated relative energies and bond angles and then compared to the predicted geometry obtained using VSEPR theory. Therefore, students gain exposure to and an introductory experience in computational chemistry, while reinforcing the connection between VSEPR theory and “pseudoexperimental” results obtained from the calculations. This exercise can be completed by first-semester general chemistry students in a 3-h time period and without the need for students to learn how to actually perform the calculation themselves. The benefits of the exercise as well as the impact of such visualization activities on spatial orientation, parti...

Pentafluoro-oxotellurate(VI) anions of mercury(II); syntheses and structures of [Hg(OTeF5)4](2-), [Hg(OTeF5)5](3-), [Hg2(OTeF5)6](2-), [Hg(OTeF5)4](2-)·Hg(OTeF5)2, and [Hg2(OTeF5)7](3-)·Hg(OTeF5)2.

Mercury(II) anions derived from the F5TeO- (teflate) group were synthesized and structurally characterized. The salts, [N(CH2CH3)4]2[Hg(OTeF5)4], [N(CH3)4]3[Hg(OTeF5)5], [N(CH2CH3)4]3[Hg(OTeF5)5], [N(CH3)4]2[Hg2(OTeF5)6], Cs2[Hg(OTeF5)4]·Hg(OTeF5)2, and {Cs3[Hg2(OTeF5)7]·Hg(OTeF5)2}·4SO2ClF, were obtained by reaction of Hg(OTeF5)2 with [M][OTeF5] (M = [N(CH3)4](+), [N(CH2CH3)4](+), Cs(+)) and were characterized by low-temperature single-crystal X-ray diffraction and low-temperature Raman spectroscopy. Unlike in the extensively fluorine-bridged solid-state structures of [HgF3](-) and [HgF4](2-), the less basic and more sterically demanding teflate ligands of the Hg(II) anions show less tendency to bridge. The anions exhibit a variety of structural motifs, ranging from well-isolated tetrahedral [Hg(OTeF5)4](2-) and square-pyramidal [Hg(OTeF5)5](3-) to the chain structures, [Hg2(OTeF5)6](2-) and [Hg2(OTeF5)7](3-)·Hg(OTeF5)2. The geometrical parameters and vibrational frequencies of [Hg(OTeF5)4](2-) (S4), [Hg(OTeF5)5](3-) (C1), and [Hg2(OTeF5)6](2-) (D2) anions, as well as the hypothetical [Hg3(OTeF5)8](2-) (C1) anion, were calculated using density functional theory methods (PBE1PBE/def2-TZVPP), which aided in the assignment of the Raman spectra of [Hg(OTeF5)4](2-), [Hg(OTeF5)5](3-), [Hg2(OTeF5)6](2-), and Cs2[Hg(OTeF5)4]·Hg(OTeF5)2. The calculated geometries were used to assess the effects of solid-state interionic interactions on the anion geometries. For the most part, the gross gas-phase trigonal bipyramidal (tbp) geometry of [Hg(OTeF5)5](3-) adheres to the predicted VSEPR geometry but contrasts with the solid-state anion structures, which have square-pyramidal geometries or geometries that lie between square pyramidal- and tbp-geometries. However, the bond length order calculated for the Hg-O bonds of tbp-[Hg(OTeF5)5](3-), Hg-Oeq > Hg-Oax, is opposite to that predicted by the VSEPR model of molecular geometry. Natural bond orbital analyses provided the associated Mayer bond orders, Mayer valencies, and natural population analysis charges.

Entasis through hook-and-loop fastening in a glycoligand with cumulative weak forces stabilizing Cu(I).

The idea of a possible control of metal ion properties by constraining the coordination sphere geometry was introduced by Vallee and Williams with the concept of entasis, which is frequently postulated to be at stake in metallobiomolecules. However, the interactions controlling the geometry at metal centers remain often elusive. In this study, the coordination properties toward copper ions—Cu(II) or Cu(I)—of a geometrically constrained glycoligand centered on a sugar scaffold were compared with those of an analogous ligand built on an unconstrained alkyl chain. The sugar-centered ligand was shown to be more preorganized for Cu(II) coordination than its open-chain analogue, with an unusual additional stabilization of the Cu(I) redox state. This preference for Cu(I) was suggested to arise from geometric constraints favoring an optimized folding of the glycoligand minimizing steric repulsions. In other words, the Cu(I) d(10) species is stabilized by valence shell electron pair repulsion (VSEPR). This idea was rationalized by a theoretical noncovalent interactions (NCI) analysis. The cumulative effects of weak forces were shown to create an efficient buckle as in a hook-and-loop fastener, and fine structural features within the glycoligand reduce repulsive interactions for the Cu(I) state. This study emphasizes that monosaccharide platforms are appropriate ligand backbones for a delicate geometric control at the metal center, with a network of weak interactions within the ligand. This structuration availing in glycoligands makes them attractive for metallic entasis.

VSEPR Theory: A closer look at chlorine trifluoride, ClF3.

Valence shell electron pair repulsion theory is a simple way of rationalising the shapes of many compounds in which a main group element is surrounded by ligands. ClF3 is a good illustration of this theory. The standard application of VSEPR theory to this molecule is as follows: Central atom: chlorine Valence electrons on central atom: 7 Three fluorine atoms contribute: 1 each Total: 10 = five electron pairs. The highest repulsion is between any two “lone electron pairs”, resulting in these moving apart as far as possible the next highest is between one lone pair and a bond pair the lowest is between two bond pairs. As applied to chlorine trifluoride, it results in a trigonal bipyramidal geometry for the shape-determining five electron pairs. One of the trigonal positions is occupied by the pair deriving from a Cl-F bond (F=white, Cl=red below). The other two trigonal positions are occupied by two sets of electron lone pairs (yellow below) at ≥ 120° (rule 5, but much more and the repulsions between the lone pair and the trigonal Cl-F bond would become too great, rule 6 above). The remaining two Cl-F bond pairs occupy the di-axial positions (rule 7 above). The above at least is the standard “text-book” picture. Regular readers of this blog may have noted that I often like to question the text books. So here goes. My issue is with the above explanation, of five electron pairs all associated in some way with the central atom. An expanded octet in other words. Well, if you take a look at earlier blogs, you may have observed that this expanded octet is not real (IMHO). If it’s not real, then we cannot be dealing with five electron pairs. Can VSEPR work with only eight electrons in this instance? And what are the coordinates of the so-called two “lone pairs”: is the angle subtended at the Cl by them really trigonal (~120)? I start with computing an accurate wavefunction, using the DFT-based ωB97XD/6-311++G(d,p)[1]. The electron count and the coordinates of the localised basins will be obtained using ELF (Electron localisation function). Click for 3D The electron basins are shown here as red spheres; 8 and 9 are the “lone pairs”, as it happens a very reasonable description since the populations for these are 2.07e. The 8-2-9 angle of 154° results from rule 5 above; lone pairs repel greatly. Indeed, one might almost describe 8 and 9 as being di-axial. In which case, the geometry is not that of a trigonal bipyramid but is closer to that of a square pyramid. Basin 7 is a Cl-F bond, with a population of 0.87e, rather less than a “pair” (the Wiberg bond index is 0.82). Basins 11+19 and 10+15 (similar basin splitting is observed for F2[2]) each total 0.91e; again less than a pair (Wiberg index 0.63). So the three Cl-F bonds are Other features include eg the orientation of the “lone pairs” on fluorines 3 and 4, in which e.g. 16 is oriented anti-periplanar to the 2-1 bond. This is in fact an anomeric effect! An NBO analysis reveals E(2) between Lp16 and σ*2-1 to be 6.3 kcal/mol, a relatively weak but still a real anomeric interaction. The total electron count for the ELF basins surrounding the central Cl is 6.84, not 10 as was implied in the simple argument set out above. VSEPR theory is a highly simplified way of looking at the geometric origins of this odd little molecule; an ELF analysis likewise paints only a partial picture. Indeed, it seems doubtful that any simple way of regarding this species can ever be entirely adequate. But we should be mindful that the “EP” (electron pair) of VSEPR might itself be rather misleading in perpetuating the idea that such main group elements contain expanded octets. But the geometry of chlorine trifluoride makes sense without imposing 10 valence electrons on the chlorine after all! References Henry S. Rzepa., "Gaussian Job Archive for ClF3", 2013. http://dx.doi.org/10.6084/m9.figshare.757728 S. Shaik, D. Danovich, B. Silvi, D.L. Lauvergnat, and P.C. Hiberty, "Charge-Shift Bonding—A Class of Electron-Pair Bonds That Emerges from Valence Bond Theory and Is Supported by the Electron Localization Function Approach", Chemistry - A European Journal, vol. 11, pp. 6358-6371, 2005. http://dx.doi.org/10.1002/chem.200500265

Comment on “Rabbit-ears hybrids, VSEPR sterics, and other orbital anachronisms”. A reply to a criticism

The first page of this article is displayed as the abstract.

VSEPR Theory and Octet-rule in Structural Chemistry

VSEPR Theory and Octet-rule in Structural Chemistry

The Physical Origins of the Chemical Bond

The properties of the chemical bond are the same as those of the electrostatic flux that links the cores of two bonded atoms via their bonding electrons. Both the bond and the flux depend only on the number of electrons that form the bond, and significantly, neither depends on how the electron density is distributed. This allows the rules of chemical bonding to be developed using classical electrostatic theory without the need to know how the electron density is distributed. The magnitude of the flux is equal to the bond order (bond valence) and hence correlates with the bond length [1]. A network of bonds is equivalent to a capacitive electric circuit which allows one to predict the bond fluxes, hence also the bond lengths. Bond angles are determined by the spherical symmetry of the flux around each atom, and the resulting bonding geometry can be predicted using little more than a pocket calculator. The rules of all the predictive bond models: the VSEPR model, the ionic model, the covalent bond model and the bond valence model can be derived using classical electrostatics without introducing problematic concepts such as hypervalency, dative bonding, hybridization and the dichotomy between ionic and covalent bonding, thus eliminating the paradoxes created by the physically questionable Lewis and orbital models. Quantum effects are rarely important except in the transition metals where in some cases they perturb the bonding geometry.

The Kimball Free-Cloud Model: A Failed Innovation in Chemical Education?

This historical review traces the origins of the Kimball free-cloud model of the chemical bond, otherwise known as the charge-cloud or tangent-sphere model, and the central role it played in attempts to reform the introductory chemical curriculum at both the high school and college levels in the 1960s. It also critically evaluates the limitations of the model, its current implicit role in the teaching of VSEPR theory, and its pedagogical implications, as well as providing a resource paper for those chemical educators interested in exploring its present-day applications.

Rabbit-ears hybrids, VSEPR sterics, and other orbital anachronisms

We describe the logical flaws, experimental contradictions, and unfortunate educational repercussions of common student misconceptions regarding the shapes and properties of lone pairs, inspired by overemphasis on “valence shell electron pair repulsion” (VSEPR) rationalizations in current freshman-level chemistry textbooks. VSEPR-style representations of orbital shape and size are shown to be fundamentally inconsistent with numerous lines of experimental and theoretical evidence, including quantum mechanical “symmetry” principles that are sometimes invoked in their defense. VSEPR-style conceptions thereby detract from more accurate introductory-level teaching of orbital hybridization and bonding principles, while also requiring wasteful “unlearning” as the student progresses to higher levels. We include specific suggestions for how VSEPR-style rationalizations of molecular structure can be replaced with more accurate conceptions of hybridization and its relationship to electronegativity and molecular geometry, in accordance both with Bent's rule and the consistent features of modern wavefunctions as exhibited by natural bond orbital (NBO) analysis.

From Photosynthesis and Magnetoception to Psychopathology, Free Will and Consciousness: Advances in Quantum Biology and Questions for the Future

Over the ten years that NeuroQuantology has been operating , significant strides have been made in advancing our understanding of quantum processes in the biological world, but despite these advances, many questions remain unanswered, particularly when it comes to NeuroQuantology (NeuroScience + QuantumPhysics) and the hard problem of consciousness, leaving many mysteries to be explored over the next ten years. Ideas from the Last Decade of Quantum Biology The last decade has produced some significant work showing how quantum effects can occur in biological systems, with advances in three areas utilizing three of the key ideas from quantum physics having been particularly prominent in the media, although often with a certain amount of controversy: 1. Superposition in Photosynthesis The superposition of a particle, enabling it to exist in a number of different states or locations simultaneously, is an idea that has been used to study how photosynthesis operates. Photosynthesis is an exceptionally efficient process, and it seems that this efficiency is made possible by the fact that superpositioning and coherence allow photons striking light absorbing molecules such as chlorophyll to try all possible routes through to the reaction center simultaneously, before settling for the optimal path. 2. Entanglement in Magnetoreception Quantum entanglement is one of the ideas that has been used to help explain how birds manage to navigate over extraordinary distances using the earth's magnetic fields as a guide. It has been suggested that entanglement could be occurring within molecules in the birds' eyes, creating an image of the magnetic field that the birds can align themselves with as they fly. The entanglement is created when light striking the birds' eye splits the molecule into a pair of free radicals, each of which has an intrinsic spin that can be reoriented by the magnetic field, but that remains briefly correlated with the other half of the pair as they drift apart. 3. Tunneling in Smell Perception The idea that a particle can tunnel or pass through an energy barrier, apparently disappearing on one side and then reappearing on the other, has been applied to the problem of understanding how the sense of smell operates. Traditional theories have depended on the idea that a molecule's shape determines its interaction with the smell receptor and therefore its scent, but there are certain molecules that seem to disprove this theory. An alternative theory based on quantum physics suggests that the smell receptors do not detect the molecule's shape, but rather react to subtle energy changes experienced by electrons that disappear from one side of the receptor, tunnel through the molecule, and then reappear on the other side. Questions in Quantum Neuroscience for the Next Ten Years The last decade has also seen some significant advances in our understanding of the brain, from research into how quantum computation might create consciousness through coherence in microtubules, to calls for the emergence of a new field of quantum psychiatry to use our understanding of quantum effects in the brain to help tackle mental illness. The progress in this field was perhaps made most apparent by the bringing together of researchers who have been investigating different aspects of quantum neuroscience at the Quantum Paradigms of Psychopathology symposium , in March 2011. Discussions focused on the manner in which quantum effects might not just be occurring in the healthy brain, but also creating pathological symptoms, including mental illnesses such as depression and schizophrenia. Advances in understanding these processes might not just help to unravel the functioning of the brain, but also provide the greatly needed new methods for the diagnosis and treatment of these conditions that are also driving other efforts to map and understand the brain. How well these efforts will succeed may depend on how willing we are to integrate different approaches, since mapping the neuronal pathways in the brain might not reveal much about how it functions, particularly when it comes to major questions such as the generation of consciousness and the concept of free will. If the ideas of people like Roger Penrose prove to be correct, consciousness may arise not just from the complex arrangement of neural circuits, but from quantum effects produced in the brain tissue, and free will may only be made possible by the existence of quantum phenomena. Even believers in a more traditional neural explanation of the hard problem may still hold out hope that quantum physics will help provide an explanation for consciousness, since, it may require a quantum computer to simulate biological processes at the level of complexity that is occurring in the brain to produce consciousness. NeuroQuantology (NeuroScience + QuantumPhysics) could prove to be the key to some of the biggest science projects of the next decade. Melissa Bunting

Conformer-dependent reactivity

When a floppy molecule meets an ultracold atom, what happens next depends on the molecule's shape.

Charge Density Analysis and Bond Characterization of 3d‐Transition Metal Complexes

AbstractChemical bond, which makes molecules from independent atoms, is a very important concept in understanding the molecular behavior. Bond characterization is therefore becoming ever needed for predicting the physical and chemical properties of the molecule and the material. Combined experimental and molecular orbital calculation studies have been used for such purpose in terms of deformation density distribution, natural bond orbital analysis and the topological analysis on the total electron density. These analyses provide not only the distribution of density accumulation and density depletion, but also the information such as bond order, bond type etc. Atom domain in molecule or compound can be defined uniquely. Therefore the combined quantum mechanical calculation and high resolution X‐ray crystallography studies will be extremely useful for characterizing the chemical bond precisely. Bonding in 3d‐transition metal complexes is a major topic in coordination chemistry. The complexity of the 3d orbital splittings subjected in the ligand field is well known and this makes the bonding characterization more interesting and challenging. Charge density analysis on a series of Cr compounds, which contain a Cr‐L multiple bond, will be presented. Detail characterization of Cr‐nitrido, ‐oxo, ‐imido, ‐carbyne and ‐carbene bonds will be described. Metal squarates of late 3d transition elements have been investigated systematically. The valence shell charge concentration (VSCC) around metal ion will be demonstrated by the Laplacian topology, which provides the physical basis for the Lewis structure and valence shell electron pair repulsion (VSEPR). The metal‐metal bond is extremely important for metal clusters; the metal‐metal quintuple bond is rare and a detail analysis will be described. Electronic configurations of the 3d metal ion play important role in coordination chemistry; taking the advantage of the x‐ray absorption spectroscopy available in synchrotron radiation facility, the exact electronic configuration can be monitored. The great recent improvements on both experiment and theory have made the charge density analysis more accessible to even more complicated system, for example, the excited state or the meta‐stable states.

Novel Silver Cobaltacarborane Complexes with a Linearly Bridging Halide

Great attention has been paid to halide coordination chemistry, not only because it constitutes the fundamentals of inorganic chemistry, but because the versatile coordination abilities of halides can be used to construct many interesting polynuclear complexes, which include halidebridged inorganic polymers, halide-capped metal clusters, halide-templated polynuclear assemblies, and anionic guests. The structural versatility of halides mainly originates from their coordinating abilities of adopting a bridging bond between two or more metal atoms, as well as a terminal bond. Moreover, a halide bridging bond angle is so flexible that thermodynamic stability can be endowed with proper geometry, which conceptually varies from acute to right, obtuse, and linear. In spite of innumerable reports on molecular metal halides, examples of the linearly bridging fashion are very scarce. The reason for the rarity of the linear M–X–M arrangement can be easily explained by the VSEPR (Valence Shell Electron Pair Repulsion) concept. The linear M–X–M formation has only been achieved by adopting a macrocyclic chelate ligand, which is structurally demanding, so that the VSEPR repulsions among lone-pair electrons on the halide atom could be overcome. In the synthetic exploration of new cobaltacarboranes, we found an unexpected ionic product comprising a cation with a linear Ag–X–Ag arrangement. At first, we attempted a reaction between Tl2C2B9H11 and CoCl2(PPh3)2, mimicking the previously reported preparation of a nickellacarborane, [3,3-(PPh3)2–3,1,2–NiC2B9H11]. We found that a new cobalt complex of dicarbollide was generated, but no more information could be obtained. Treatment of the product mixture with AgBr(PPh3)3 afforded a cationic [L3Ag–X–AgL3] (L = triphenylphosphine) with CoSAN as a counterion (CoSAN = [3,3-commo-3,1,2-Co(C2B9H11)2]). Although linear Ag–X–Ag could be achieved, the reaction result was not well reproducible, nor was its mechanism reasonable. Hence, we directed the preparation of the linear complexes in a rationalized synthetic manner, as depicted in the following reaction equation:

The low-symmetry lanthanum(III) oxotellurate(IV), La10Te12O39

Single crystals of deca­lanthanum(III) dodeca­oxotellurate(IV), La10Te12O39, were obtained by reacting La2O3 and TeO2 in a CsCl flux. Its crystal structure can be viewed as a three-dimensional network of corner- and edge-sharing LaO8 polyhedra with TeIV atoms filling the inter­stitial sites. The TeIV atoms with their 5s 2 electron lone pairs distort the LaO8 polyhedra through variable Te—O bonds. Among the six unique Te sites, four of them define empty channels extending parallel to the a axis. The formation of these channels is a result of the stereochemically active electron lone pairs on the TeIV atoms. The atomic arrangement of the Te—O units can be understood on the basis of the valence shell electron pair repulsion (VSEPR) model. A certain degree of disorder is observed in the crystal structure. As a result, one of the five different La sites is split into two positions with an occupancy ratio of 0.875 (2):0.125 (2). Also, one of the oxygen sites is split into two positions in a 0.559 (13):0.441 (13) ratio, and one O site is half-occupied. Such disorder was observed in all measured La10Te12O39 crystals.

Electronic structure effects in the vectorial bond-valence model

The vectorial bond-valence model (VBVM) describes the spatial distribution of bonds to each atom in a system in terms of the vector sum of the incident bond valences. It has been applied in the past to cations not subject to electronic structure effects (e.g., lone-pair or Jahn-Teller effects) in which case the expectation is that the vector sum will be approximately zero. Here we analyze 178 simpleoxide crystal structures and show that the vectorial bond-valence sum is a predictable function of the atomic valence (oxidation state) of each atom and the valence of the strongest bond to atoms for which second-order Jahn-Teller and lone-pair effects play a role in determining molecular geometry. Outliers are uniformly metastable or unstable under ambient conditions, suggesting that deviation from ideal vectorial bond-valence sums might be used as a proxy for some aspect of structural potential energy. These results are all strictly in harmony with the VSEPR model of molecular geometry, but may allow for more quantitative prediction.