Metavalent or Hypervalent Bonding: Is There a Chance for Reconciliation?

A family of solids including crystalline phase change materials such as GeTe and Sb2 Te3 , topological insulators like Bi2 Se3, and halide perovskites such as CsPbI3 possesses an unconventional property portfolio that seems incompatible with ionic, metallic, or covalent bonding. Instead, evidence is found for a bonding mechanism characterized by half-filled p-bands and a competition between electron localization and delocalization. Different bonding concepts have recently been suggested based on quantum chemical bonding descriptors which either define the bonds in these solids as electron-deficient (metavalent) or electron-rich (hypervalent). This disagreement raises concerns about the accuracy of quantum-chemical bonding descriptors is showed. Here independent of the approach chosen, electron-deficient bonds govern the materials mentioned above is showed. A detailed analysis of bonding in electron-rich XeF2 and electron-deficient GeTe shows that in both cases p-electrons govern bonding, while s-electrons only play a minor role. Yet, the properties of the electron-deficient crystals are very different from molecular crystals of electron-rich XeF2 or electron-deficient B2 H6 . The unique properties of phase change materials and related solids can be attributed to an extended system of half-filled bonds, providing further arguments as to why a distinct nomenclature such as metavalent bonding is adequate and appropriate for these solids.

Role of Spin Polarization and Dynamic Correlation in Singlet-Triplet Gap Inversion of Heptazine Derivatives.

The new generation of proposed light-emitting molecules for organic light-emitting diodes (OLEDs) has raised considerable research interest due to its exceptional feature─a negative singlet-triplet (ST) gap violating Hund's multiplicity rule in the excited S1 and T1 states. We investigate the role of spin polarization in the mechanism of ST gap inversion. Spin polarization is associated with doubly excited determinants of certain types, whose presence in the wave function expansion favors the energy of the singlet state more than that of the triplet. Using a perturbation theory-based model for spin polarization, we propose a simple descriptor for prescreening of candidate molecules with negative ST gaps and prove its usefulness for heptazine-type molecules. Numerical results show that the quantitative effect of spin polarization decreases linearly with the increasing highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) exchange integral. Comparison of single- and multireference coupled-cluster predictions of ST gaps shows that the former methods provide good accuracy by correctly balancing the effects of doubly excited determinants and dynamic correlation. We also show that accurate ST gaps may be obtained using a complete active space model supplemented with dynamic correlation from multireference adiabatic connection theory.

Revisiting the Nature of Chemical Bonding in Chalcogenides to Explain and Design their Properties.

Quantum chemical bonding descriptors have recently been utilized to design materials with tailored properties. Their usage to facilitate a quantitative description of bonding in chalcogenides as well as the transition between different bonding mechanisms is reviewed. More importantly, these descriptors can also be employed as property predictors for several important material characteristics, including optical and transport properties. Hence, these quantum chemical bonding descriptors can be utilized to tailor material properties of chalcogenides relevant for thermoelectrics, photovoltaics, and phase-change memories. Relating material properties to bonding mechanisms also shows that there is a class of materials, which are characterized by unconventional properties such as a pronounced anharmonicity, a large chemical bond polarizability, and strong optical absorption. This unusual property portfolio is attributed to a novel bonding mechanism, fundamentally different from ionic, metallic, and covalent bonding, which is called "metavalent." In the concluding section, a number of promising research directions are sketched, which explore the nature of the property changes upon changing bonding mechanism and extend the concept of quantum chemical property predictors to more complex compounds.

Machine Learning-Assisted Selection of Active Spaces for Strongly Correlated Transition Metal Systems.

Active space quantum chemical methods could provide very accurate description of strongly correlated electronic systems, which is of tremendous value for natural sciences. The proper choice of the active space is crucial but a nontrivial task. In this article, we present a neural network-based approach for automatic selection of active spaces, focused on transition metal systems. The training set has been formed from artificial systems composed of one transition metal and various ligands, on which we have performed the density matrix renormalization group and calculated the single-site entropy. On the selected set of systems, ranging from small benchmark molecules up to larger challenging systems involving two metallic centers, we demonstrate that our machine learning models could predict the active space orbitals with reasonable accuracy. We also tested the transferability on out-of-the-model systems, including bimetallic complexes and complexes with ligands, which were not involved in the training set. Also, we tested the correctness of the automatically selected active spaces on a Fe(II)-porphyrin model, where we studied the lowest states at the DMRG level and compared the energy difference between spin states or the energy difference between conformations of ferrocene with recent studies.

On-Surface Synthesis and Characterization of [7]Triangulene Quantum Ring.

The ability to engineer geometrically well-defined antidots in large triangulene homologues allows for creating an entire family of triangulene quantum rings (TQRs) with tunable high-spin ground state, crucial for next-generation molecular spintronic devices. Herein, we report the synthesis of an open-shell [7]triangulene quantum ring ([7]TQR) molecule on Au(111) through the surface-assisted cyclodehydrogenation of a rationally designed kekulene derivative. Bond-resolved scanning tunneling microscopy (BR-STM) unambiguously imaged the molecular backbone of a single [7]TQR with a triangular zigzag edge topology, which can be viewed as [7]triangulene decorated with a coronene-like antidot in the center. Additionally, dI/dV mapping reveals that both inner and outer zigzag edges contribute to the edge-localized and spin-polarized electronic states of [7]TQR. Both experimental results and spin-polarized density functional theory calculations indicate that [7]TQR retains its open-shell septuple ground state (S = 3) on Au(111). This work demonstrates a new route for the design of high-spin graphene quantum rings for future quantum devices.

Discovering Electron-Transfer-Driven Changes in Chemical Bonding in Lead Chalcogenides (PbX, where X = Te, Se, S, O).

Understanding the nature of chemical bonding in solids is crucial to comprehend the physical and chemical properties of a given compound. To explore changes in chemical bonding in lead chalcogenides (PbX, where X = Te, Se, S, O), a combination of property-, bond-breaking-, and quantum-mechanical bonding descriptors are applied. The outcome of the explorations reveals an electron-transfer-driven transition from metavalent bonding in PbX (X = Te, Se, S) to iono-covalent bonding in ß-PbO. Metavalent bonding is characterized by adjacent atoms being held together by sharing about a single electron (ES ≈ 1) and small electron transfer (ET). The transition from metavalent to iono-covalent bonding manifests itself in clear changes in these quantum-mechanical descriptors (ES and ET), as well as in property-based descriptors (i.e., Born effective charge (Z*), dielectric function ε(ω), effective coordination number (ECoN), and mode-specific Grüneisen parameter (γTO )), and in bond-breaking descriptors. Metavalent bonding collapses if significant charge localization occurs at the ion cores (ET) and/or in the interatomic region (ES). Predominantly changing the degree of electron transfer opens possibilities to tailor material properties such as the chemical bond (Z*) and electronic (ε∞ ) polarizability, optical bandgap, and optical interband transitions characterized by ε2 (ω). Hence, the insights gained from this study highlight the technological relevance of the concept of metavalent bonding and its potential for materials design.

Data-driven kinetic energy density fitting for orbital-free DFT: Linear vs Gaussian process regression.

We study the dependence of kinetic energy densities (KEDs) on density-dependent variables that have been suggested in previous works on kinetic energy functionals for orbital-free density functional theory. We focus on the role of data distribution and on data and regressor selection. We compare unweighted and weighted linear and Gaussian process regressions of KEDs for light metals and a semiconductor. We find that good quality linear regression resulting in good energy-volume dependence is possible over density-dependent variables suggested in previous literature studies. This is achieved with weighted fitting based on the KED histogram. With Gaussian process regressions, excellent KED fit quality well exceeding that of linear regressions is obtained as well as a good energy-volume dependence, which was somewhat better than that of best linear regressions. We find that while the use of the effective potential as a descriptor improves linear KED fitting, it does not improve the quality of the energy-volume dependence with linear regressions but substantially improves it with Gaussian process regression. Gaussian process regression is also able to perform well without data weighting.

Reply to the 'Comment on "Revisiting π backbonding: the influence of d orbitals on metal-CO bonds and ligand red shifts"' by G. Frenking and S. Pan, Phys. Chem. Chem. Phys., 2019, 22, DOI.

We respond to the comment by Pan and Frenking with regard to our investigation on transition and alkaline earth metal d orbital influence on their bonding to carbonyl ligands to clarify misconceptions. We do not consider the points raised in the comment as affecting our conclusions.

Reply to the 'Comment on "Revisiting π backbonding: the influence of d orbitals on metal-CO bonds and ligand red shifts"' by G. Frenking and S. Pan, Phys. Chem. Chem. Phys., 2019, 22, DOI: 10.1039/C9CP05951B.

We respond to the comment by Pan and Frenking with regard to our investigation on transition and alkaline earth metal d orbital influence on their bonding to carbonyl ligands to clarify misconceptions. We do not consider the points raised in the comment as affecting our conclusions.

Revisiting π backbonding: the influence of d orbitals on metal-CO bonds and ligand red shifts.

The concept of π backbonding is widely used to explain the complex stabilities and CO stretch frequency red shifts of transition metal carbonyls. We theoretically investigate a non-transition metal 18-electron carbonyl complex (Mg(CO)8) and find a pronounced CO red shift without metal-carbon π bonds. Moreover, we use truncated basis sets on the "honorary" and true transition metals Ca and Ti in Ca(CO)8 and [Ti(CO)8]2+ complexes to probe the influence of d functions on carbonyl complex stability, C-O bond strength, metal-to-ligand charge transfer and bond order compared to hypothetical complexes without metal-d contributions. We find that the occurrence of metal-ligand π bonds through metal d functions greatly enhances the complex stabilities on one hand but only slightly affects the CO red shift on the other hand, compared to metal carbonyl systems with no d contributions. We also highlight the discrepancy between the formal oxidation state of 0 of Mg and Ca despite them carrying a significant positive charge.

Understanding the Structure and Properties of Sesqui-Chalcogenides (i.e., V2 VI3 or Pn2 Ch3 (Pn = Pnictogen, Ch = Chalcogen) Compounds) from a Bonding Perspective.

A number of sesqui-chalcogenides show remarkable properties, which make them attractive for applications as thermoelectrics, topological insulators, and phase-change materials. To see if these properties can be related to a special bonding mechanism, seven sesqui-chalcogenides (Bi2 Te3 , Bi2 Se3 , Bi2 S3 , Sb2 Te3 , Sb2 Se3 , Sb2 S3 , and ß-As2 Te3 ) and GaSe are investigated. Atom probe tomography studies reveal that four of the seven sesqui-chalcogenides (Bi2 Te3 , Bi2 Se3 , Sb2 Te3 , and ß-As2 Te3 ) show an unconventional bond-breaking mechanism. The same four compounds evidence a remarkable property portfolio in density functional theory calculations including large Born effective charges, high optical dielectric constants, low Debye temperatures and an almost metal-like electrical conductivity. These results are indicative for unconventional bonding leading to physical properties distinctively different from those caused by covalent, metallic, or ionic bonding. The experiments reveal that this bonding mechanism prevails in four sesqui-chalcogenides, characterized by rather short interlayer distances at the van der Waals like gaps, suggestive of significant interlayer coupling. These conclusions are further supported by a subsequent quantum-chemistry-based bonding analysis employing charge partitioning, which reveals that the four sesqui-chalcogenides with unconventional properties are characterized by modest levels of charge transfer and sharing of about one electron between adjacent atoms. Finally, the 3D maps for different properties reveal discernible property trends and enable material design.

A Quantum-Mechanical Map for Bonding and Properties in Solids.

A 2D map is created for solid-state materials based on a quantum-mechanical description of electron sharing and electron transfer. This map intuitively identifies the fundamental nature of ionic, metallic, and covalent bonding in a range of elements and binary compounds; furthermore, it highlights a distinct region for a mechanism recently termed "metavalent" bonding. Then, it is shown how this materials map can be extended in the third dimension by including physical properties of application interest. Finally, it is shown how the map coordinates yield new insight into the nature of the Peierls distortion in phase-change materials and thermoelectrics. These findings and conceptual approaches provide a novel avenue to tailor material properties.

Kinetic energy densities based on the fourth order gradient expansion: performance in different classes of materials and improvement via machine learning.

We study the performance of fourth-order gradient expansions of the kinetic energy density (KED) in semi-local kinetic energy functionals depending on the density-dependent variables. The formal fourth-order expansion is convergent for periodic systems and small molecules but does not improve over the second-order expansion (the Thomas-Fermi term plus one-ninth of the von Weizsäcker term). Linear fitting of the expansion coefficients somewhat improves on the formal expansion. The tuning of the fourth order expansion coefficients allows for better reproducibility of the Kohn-Sham kinetic energy density than the tuning of the second-order expansion coefficients alone. The possibility of a much more accurate match with the Kohn-Sham kinetic energy density by using neural networks (NN) trained using the terms of the 4th order expansion as density-dependent variables is demonstrated. We obtain ultra-low fitting errors without overfitting of NN parameters. Small single hidden layer neural networks can provide good accuracy in separate KED fits of each compound, while for joint fitting of KEDs of multiple compounds multiple hidden layers were required to achieve good fit quality. The critical issue of data distribution is highlighted. We also show the critical role of pseudopotentials in the performance of the expansion, where in the case of a too rapid decay of the valence density at the nucleus with some pseudopotentials, numeric instabilities can arise.

Synthesis of a Cu-Filled Rh17S15 Framework: Microwave Polyol Process Versus High-Temperature Route.

Metal-rich, mixed copper-rhodium sulfide Cu3-δRh34S30 that represents a new Cu-filled variant of the Rh17S15 structure has been synthesized and structurally characterized. Copper content in the [CuRh8] cubic cluster was found to vary notably dependent on the chosen synthetic route. Full site occupancy was achieved only in nanoscaled Cu3Rh34S30 obtained by a rapid, microwave-assisted reaction of CuCl, Rh2(CH3CO2)4 and thiosemicarbazide at 300 °C in just 30 min; whereas merely Cu-deficient Cu3-δRh34S30 (2.0 ≥ δ ≥ 0.9) compositions were realized via conventional high-temperature ceramic synthesis from the elements at 950 °C. Although Cu3-δRh34S30 is metallic just like Rh17S15, the slightly enhanced metal content has a dramatic effect on the electronic properties. Whereas the Rh17S15 host undergoes a superconducting transition at 5.4 K, no signs of the latter were found for the Cu-derivatives at least down to 1.8 K. This finding is corroborated by the strongly reduced density of states at the Fermi level of the ternary sulfide and the disruption of long-range Rh-Rh interactions in favor of Cu-Rh interactions as revealed by quantum-chemical calculations.

Domain overlap matrices from plane-wave-based methods of electronic structure calculation.

Plane waves are one of the most popular and efficient basis sets for electronic structure calculations of solids; however, their delocalized nature makes it difficult to employ for them classical orbital-based methods of chemical bonding analysis. The quantum chemical topology approach, introducing chemical concepts via partitioning of real space into chemically meaningful domains, has no difficulties with plane-wave-based basis sets. Many popular tools employed within this approach, for instance delocalization indices, need overlap integrals over these domains-the elements of the so called domain overlap matrices. This article reports an efficient algorithm for evaluation of domain overlap matrix elements for plane-wave-based calculations as well as evaluation of its implementation for one of the most popular projector augmented wave (PAW) methods on the small set of simple and complex solids. The stability of the obtained results with respect to PAW calculation parameters has been investigated, and the comparison of the results with the results from other calculation methods has also been made.