The crystal orbital bond index (COBI) is a new and intuitive method for quantifying covalent bonding in solid-state materials. COBI is based on the bond index by Wiberg and Mayer and extends their ...ideas to the case of translationally invariant objects, that is, crystalline matter. COBI’s qualitative interpretation resembles the well-established crystal orbital overlap population and crystal orbital Hamilton population methods but should be more familiar to chemists since it directly relates to the classical bond order. In contrast to the aforementioned descriptors, COBI also allows for examining multicenter interactions within a local-orbital framework. As an additional bonding indicator, we refer to the Ewald sum for electrostatic lattice potentials, thereby enabling the calculation of electrostatic lattice energies as well as site potentials from quantum-mechanical charges as directly derived from the wave function, not from the density.
Covalent chemical bonding beyond the two-center two-electron (2c–2e) bond is well-known for (inter)halogenic compounds, in particular, electron-rich multicenter (or hypervalent) bonding of the ...three-center four-electron (3c–4e) type to explain both their structure and stability. In the present work, we examine different solid-state polyiodides by combining both local orbital wave function and projected force constant analysis in order to numerically quantify the influence of multicenter (hypervalent) bonding based on periodic density functional theory (DFT) calculations. After linking our findings to established qualitative theories on multicenter bonding, particularly, Alcock’s “secondary” bonding, we relate the bonding behavior in polyiodides to industrially relevant phase-change materials of the Ge–Sb–Te class, finding further evidence for the same underlying cause as regards chemical bonding in both material classes.
Layered phase‐change materials in the Ge−Sb−Te system are widely used in data storage and are the subject of intense research to understand the quantum‐chemical origin of their unique properties. To ...uncover the nature of the underlying periodic wavefunction, we have studied the interacting atomic orbitals including their phases by means of crystal orbital bond index and fragment crystal orbital analysis. In full accord with findings based on projected force constants, we demonstrate the role of multicenter bonding along straight atomic connectivities. While the resulting multicenter bonding resembles three‐center‐four‐electron bonding in molecules, its solid‐state manifestation leads to distinct long‐range consequences, thus serving to contextualize the material properties usually termed “metavalent”. Eventually we suggest multicenter bonding to be the origin of their astonishing bond‐breaking and phase‐change behavior, as well as the too small “van‐der‐Waals” gaps between individual layers.
Wavefunction analysis of phase‐change materials in terms of interacting atomic orbitals reveals the decisive role of electron‐rich multicenter interactions, similar yet different from the molecular case. The rather uncommon properties of these phases such as bond‐breaking behavior and other structural peculiarities arise as a natural consequence of electron‐rich multicenter bonding in condensed matter.
This paper addresses the global asymptotic regulation of robot manipulators under input constraints, both with and without velocity measurements. It is proven that robot systems subject to bounded ...inputs can be globally asymptotically stabilized via a saturated proportional-integral-derivative (PID) control in agreement with Lyapunov's direct method and LaSalle's invariance principle. Advantages of the proposed controller include an absence of modeling parameters in the control law formulation and an ability to ensure actuator constraints are not breached. This is accomplished by selecting control gains a priori, removing the possibility of actuator failure due to excessive torque input levels. The effectiveness of the proposed approach is illustrated via simulations.
The design of solids with tailored material properties requires a thorough understanding of their electronic structures. Examining the latter typically includes chemical-bonding analyses, which can ...reveal interatomic interactions and, thereby, explain remarkable structural and compositional features. Over the years, the nature of bonding was also considered to account for certain electronic peculiarities; yet, a direct connection between bonding and material properties such as electrical transport remains elusive due to fundamental reasons. To elucidate this problem, we carried out bonding analyses for a series of intermetallics chosen to reflect widely diverse bonding situations and analyzed by both wave function-based Löwdin charges and Crystal Orbital Bond Indices (COBI). In doing so, we established a library of integrated COBI values (ICOBI = quantum-chemical bond orders) as a guide for future analyses, whereas the outcome of our explorations clearly shows that the attempt to relate phenomena in the electronic band structure to the nature of bonding can be misleading.
Decomposing extended structures into smaller, molecular, even functional groups or simple fragments has a long tradition in chemistry because it allows for understanding certain electronic ...peculiarities in truly chemical terms. By doing so, invaluable property information is chemically accessible, for example, needed to rationalize catalytic or magnetic or optical nature. In order to also follow that train of thought for periodic materials, we have developed a tool which in a straightforward manner derives fragment molecular orbitals from plane-wave electronic-structure data of whatever kind of solid-state material. We here report on the mathematical apparatus of the method dubbed linear combination of fragment orbitals (LCFO) used for that purpose, implemented within the LOBSTER code. The method is illustrated from various sorts of molecular entities contained in such crystalline materials, together with an assessment of both accuracy and robustness of the new tool.
Chemical bonding in main‐group IV chalcogenides is an intensely discussed topic, easily understandable because of their remarkable physical properties that predestine these solid‐state materials for ...their widespread use in, for instance, thermoelectrics and phase‐change memory applications. The atomistic origin of their unusual property portfolio remains somewhat unclear, however, even though different and sometimes conflicting chemical‐bonding concepts have been introduced in the recent years. Here, it is proposed that projecting phononic force‐constant tensors for pairs of atoms along differing directions and ranges provide a suitable and quantitative descriptor of the bonding nature for these materials. In combination with orbital‐based quantitative measures of covalency such as crystal orbital Hamilton populations (COHP), it is concluded that the well‐established many‐center and even n‐center bonding is an appropriate picture of the underlying quantum‐chemical bonding mechanism, supporting the recent proposal of hyperbonded phase‐change materials.
Examining the chemical bonding in rock‐salt‐type IV–VI functional materials by projected force constants as derived from ab initio thermochemistry yields unusually strong long‐range forces along the cubic lattice vectors, impossible to account for by either two‐center covalent or ionic bonding. The full analysis, including orbital‐based bonding descriptors, points toward hyperbonding, thereby explaining certain unique properties of this material class.
We present a first-principles study based on plane-wave-derived Löwdin population analysis and other local bonding descriptors to investigate cathode and anode materials for lithium- and sodium-ion ...batteries, with a special emphasis on complex nitrogen chemistry. By comparing the Löwdin charges of commonly used electrode materials to other phases such as salts of dicyanamide and nanoporous carbon-based compounds, new conclusions of an improved intercalation behavior of the latter are derived. In addition, we explore the stability of the dicyanamide salts upon Li and Na removal, some of them resulting in dimerized structures. In particular, having a look at the different kinds of bonds and the corresponding covalency indicators reveals insights into the bonding changes during dimerization. Considering the astonishing thermal stability of metal dicyanamide salts, which are solid at room temperature, their electrochemical activity, and non-toxicity of alkali metal-based compounds, these materials are potential alternatives to commercially available electrodes, particularly as they show some flexibility in exhibiting anodic and cathodic behavior and allow for transition metal-free cathode materials.
Unbalances in rotating machinery cause vibration, noise and wear. Active bearings allow the use of specialized control algorithms which eliminate the bearing forces caused by unbalances. Most ...algorithms suffer from drawbacks, namely their lack of general stability, the need for exact rotor models, or their unclear rotordynamic interactions.
In this work, we found a closed-form analytical solution for the elimination of unbalance-induced bearing forces on arbitrary, gyroscopic rotors. We demonstrate that the force-free condition is met for any unbalance distribution. Furthermore, we proved that up to two resonances can be fully eliminated. We found a new Lyapunov stability theorem to prove the controller’s superior stability properties. The advantage of our approach is that different active bearing technologies are unified in a single, generalized theory. Our theory is not only limited to rotors, but applies to all systems with harmonic excitation that share the same general matrix structure. Finally, we provide evidence that our theoretic assumptions are also satisfied in reality: In an experiment we demonstrate that unbalance-induced bearing forces and rotor resonances can not only be eliminated in theory, but also in practice.
•Force and Resonance elimination with active bearings for general rotors.•Closed-form solution and proven stability.•Generalized approach, suitable for force and displacement actuators.•Comprehensive explanation.•No model required.
Abstract
Schichtartige Phasenwechselmaterialien des Typs Ge−Sb−Te werden industriell zur Datenspeicherung verwendet und sind auch heute noch Gegenstand intensiver Forschung, um den quantenchemischen ...Ursprung ihrer Eigenschaften zu verstehen. Zur Analyse der zugrundeliegenden periodischen Wellenfunktion untersuchen wir die wechselwirkenden Atomorbitale einschließlich ihrer Phaseninformation mit Hilfe des Kristallorbitalbindungsindex und der Fragmentkristallorbitalanalyse. In voller Übereinstimmung mit Ergebnissen aus langreichweitigen projizierten Kraftkonstanten untermauern wir die besondere Rolle von Mehrzentrenbindungen entlang geradliniger atomarer Anordnungen. Ebendiese Mehrzentrenbindung ähnelt der bekannten Dreizentren‐Vierelektronenbindung in Molekülen, hat aber im festen Zustand weitreichende Auswirkungen für die üblicherweise als “metavalent” bezeichneten Materialeigenschaften und verdeutlicht die Zusammenhänge. Es liegt nahe, daß diese Mehrzentrenbindung die Ursache für das erstaunliche Bindungsbruch‐ und Phasenwechselverhalten sowie für die zu kleinen “van‐der‐Waals”‐Lücken zwischen den einzelnen Schichten ist.
PDF
