A Piece of the Picture-Misunderstanding of Chemical Concepts

Oxidation States: Intrinsically Ambiguous?

The oxidation state ( OS ) formalism is a much-appreciated good in chemistry, receiving wide application. However, like all formalisms, limitations are inescapable, some of which have been recently explored. Providing a broader context, we discuss the OS and its interpretation from a computational perspective for transition metal (TM) complexes. We define a broadly applicable and easy-to-use procedure to derive OS s based on quantum chemical calculations, via the use of localized orbitals, dubbed the Intrinsic OS . Applying this approach to a cobalt complex in five OS s, isolated by Hunter and co-workers (Inorg. Chem.2021, 60, 17445), we find that the calculated Intrinsic OS matches the formal OS , consistent with the experimental characterization. Through analysis of the delocalized orbitals, the ligand field of the Co(III) complex is found to be "inverted", despite every cobalt-ligand bond being classically dative from the localized perspective-a bonding scenario very similar to that of [Cu(CF3)4]-. This is not atypical but rather a natural consequence of these metals bonding in the high-valent region, and we propose a more restrictive definition of (locally) inverted bonding. Additionally, two bonding descriptors within the Intrinsic Bonding Orbital (IBO) framework (σ-gain and π-loss) are introduced, which enable facile quantification of electron-sharing covalency across a broad range of TM complexes.

Constrained iterative Hirshfeld charges: A variational approach

We develop a variational procedure for the iterative Hirshfeld (HI) partitioning scheme. The main practical advantage of having a variational framework is that it provides a formal and straightforward approach for imposing constraints (e.g., fixed charges on certain atoms or molecular fragments) when computing HI atoms and their properties. Unlike many other variants of the Hirshfeld partitioning scheme, HI charges do not arise naturally from the information-theoretic framework, but only as a reverse-engineered construction of the objective function. However, the procedure we use is quite general and could be applied to other problems as well. We also prove that there is always at least one solution to the HI equations, but we could not prove that its self-consistent equations would always converge for any given initial pro-atom charges. Our numerical assessment of the constrained iterative Hirshfeld method shows that it satisfies many desirable traits of atoms in molecules and has the potential to surpass existing approaches for adding constraints when computing atomic properties.

ab initio study of Mn-based systems for oxidative degradation

Organic contaminants can be removed from water/wastewater by oxidative degradation using oxidants such as manganese oxides and/or aqueous manganese ions. The Mn species show a wide range of activity, which is related to the oxidation state of Mn. Here, we use ab initio molecular dynamics simulations to address Mn oxidation states in these systems. We first develop a correlation between Mn partial atomic charge and the oxidation state based on results of 31 simulations on known Mn aqueous complexes. The results collapse to a master curve; the dependence of partial atomic charge on oxidation state weakens with increasing oxidation state, which concurs with a previously proposed feedback effect. This correlation is then used to address oxidation states in Mn systems used as oxidants. Simulations of MnO₂ polymorphs immersed in water give average oxidation states (AOS) in excellent agreement with experimental results, in that β-MnO₂ has the highest AOS, α-MnO₂ has an intermediate AOS, and δ-MnO₂ has the lowest AOS. Furthermore, the oxidation state varies substantially with the atom's environment, and these structures include Mn(III) and Mn(V) species that are expected to be active. In regard to the MnO₄^-/HSO₃^-/O₂ system that has been shown to be a highly effective oxidant, we propose a novel Mn complex that could give rise to the oxidative activity, where Mn(III) is stabilized by sulfite and dissolved O₂ ligands. Our simulations also show that the O₂ would be activated to O₂^2- in this complex under acidic conditions, and could lead to the formation of OH radicals that serve as oxidants.

Activation of Molecular O2 on CoFe2 O4 (001) Surfaces: An Embedded Cluster Study

Dioxygen activation pathways on the (001) surfaces of cobalt ferrite, CoFe2 O4 , were investigated computationally using density functional theory and the hybrid Perdew-Burke-Ernzerhof exchange-correlation functional (PBE0) within the periodic electrostatic embedded cluster model. We considered two terminations: the A-layer exposing Fe2+ and Co2+ metal sites in tetrahedral and octahedral positions, respectively, and the B-layer exposing octahedrally coordinated Co3+ . On the A-layer, molecular oxygen is chemisorbed as a superoxide on the Fe monocenter or bridging a Fe-Co cation pair, whereas on the B-layer it is adsorbed at the most stable anionic vacancy. Activation is promoted by transfer of electrons provided by the d metal centers onto the adsorbed oxygen. The subsequent dissociation of dioxygen into monoatomic species and surface reoxidation have been identified as the most critical steps that may limit the rate of the oxidation processes. Of the reactive metal-O species, [FeIII -O]2+ is thermodynamically most stable, while the oxygen of the Co-O species may easily migrate across the A-layer with barriers smaller than the associative desorption.

In defence of oxidation states

In this Perspective, some of the criticisms which have been made concerning the use of oxidation states are addressed, particularly in the context of the teaching of inorganic chemistry. The Oxidation State method and the Covalent Bond Classification method are compared and contrasted, and it is concluded that while each method has its strengths and weaknesses, both are important in teaching and it should be recognized that no single model or method is appropriate in all circumstances.

Combined Role of Biaxial Strain and Nonstoichiometry for the Electronic, Magnetic, and Redox Properties of Lithiated Metal-Oxide Films: The LiMn2O4 Case

Understanding the interplay between strain and nonstoichiometry for the electronic, magnetic, and redox properties of LiMn₂O₄ films is essential for their development as Li-ion battery (LIB) cathodes, photoelectrodes, and systems for sustainable spintronics applications as well as for emerging applications that combine these technologies. Here, density functional theory (DFT) simulations suggest that compressive strain increases the reduction drive of (111) LiMn₂O₄ films by inducing >1 eV upshift of the valence band edge. The DFT results indicate that, regardless of the crystallographic orientation for the LiMn₂O₄ film, biaxial expansion increases the magnetic moments of the Mn atoms. Conversely, biaxial compression reduces them. For ferromagnetic films, these changes can be substantial and as large as over 4 Bohr magnetons per unit cell over the simulated range of strain (from -6 to +3%). The DFT simulations also uncover a compensation mechanism whereby strain induces opposite changes in the magnetic moment of the Mn and O atoms, leading to an overall constant magnetic moment for the ferromagnetic films. The calculated strain-induced changes in atomic magnetic moments reflect modifications in the local electronic hybridization of both the Mn and O atoms, which in turn suggests strain-tunable, local chemical, and electrochemical reactivity. Several energy-favored (110) and (111) ferromagnetic surfaces turn out to be half-metallic with minority-spin band gaps as large as 3.2 eV and compatible with spin-dependent electron-transport and possible spin-dependent electrochemical and electrocatalytic properties. The resilience of the ferromagnetic, half-metallic states to surface nonstoichiometry and compositional changes invites exploration of the potential of LiMn₂O₄ thin films for sustainable spintronic applications beyond state-of-the-art, rare-earth metal-based, ferromagnetic half-metallic oxides.

Comment on "Uncommon structural and bonding properties in Ag16B4O10" by A. Kovalevskiy, C. Yin, J. Nuss, U. Wedig, and M. Jansen, Chem. Sci., 2020, , 962

A thorough systematic study of the Electron Localization Function (ELF) in fcc silver metal, the deficient vacant-type Ag₁₆□₄ structure, and the Ag₁₆B₄O₁₀ title compound of the Chem. Sci., 2020, 11, 962 edge article leads to a further understanding of the sub-valent characteristics of silver in the silver borate compound. By visualizing the process in three consecutive steps, (fcc)_eq-Ag → (fcc)_ex-Ag → Ag₁₆□₄ → Ag₁₆B₄O₁₀, the electron reduction of Ag atoms can be traced to be due to (i) the expansion (ex) of the host metallic array from its equilibrium (eq) geometry and (ii) the vacancy creation and subsequent insertion of guest borate clusters. Our ELF analysis also allows us to identify to what extent metallic features remain in the title compound, providing an alternative explanation of why Ag₁₆B₄O₁₀ is not a conductor whereas pure silver is.

ELF superbasins (dark-yellow stick and ball circuits) reveal how borate clusters (green and red spheres) play the role of crystal defects interrupting the electric conductivity of metallic silver (grey spheres).

Using collective knowledge to assign oxidation states of metal cations in metal-organic frameworks

Knowledge of the oxidation state of metal centres in compounds and materials helps in the understanding of their chemical bonding and properties. Chemists have developed theories to predict oxidation states based on electron-counting rules, but these can fail to describe oxidation states in extended crystalline systems such as metal-organic frameworks. Here we propose the use of a machine-learning model, trained on assignments by chemists encoded in the chemical names in the Cambridge Structural Database, to automatically assign oxidation states to the metal ions in metal-organic frameworks. In our approach, only the immediate local environment around a metal centre is considered. We show that the strategy is robust to experimental uncertainties such as incorrect protonation, unbound solvents or changes in bond length. This method gives good accuracy and we show that it can be used to detect incorrect assignments in the Cambridge Structural Database, illustrating how collective knowledge can be captured by machine learning and converted into a useful tool.

Matrix Isolation Spectroscopic and Relativistic Quantum Chemical Study of Molecular Platinum Fluorides PtFn (n=1-6) Reveals Magnetic Bistability of PtF4

Molecular platinum fluorides PtF_n, n=1–6, are prepared by two different routes, photo‐initiated fluorine elimination from PtF₆ embedded in solid noble‐gas matrices, and the reaction of elemental fluorine with laser‐ablated platinum atoms. IR spectra of the reaction products isolated in rare‐gas matrices under cryogenic conditions provide, for the first time, experimental vibrational frequencies of molecular PtF₃, PtF₄ and PtF₅. Photolysis of PtF₆ enabled a highly efficient and almost quantitative formation of molecular PtF₄, whereas both PtF₅ and PtF₃ were formed simultaneously by subsequent UV irradiation of PtF₄. The vibrational spectra of these molecular platinum fluorides were assigned with the help of one‐ and two‐component quasirelativistic DFT computation to account for scalar relativistic and spin–orbit coupling effects. Competing Jahn‐Teller and spin–orbit coupling effects result in a magnetic bistability of PtF₄, for which a spin‐triplet (³B_2g, D_2h) coexists with an electronic singlet state (¹A_1g, D_4h) in solid neon matrices.

Na9 Bi5 Os3 O24 : A Diamagnetic Oxide Featuring a Pronouncedly Jahn-Teller-Compressed Octahedral Coordination of Osmium(VI)

The Jahn-Teller (JT) theorem constitutes one of the most fundamental concepts in chemistry. In transition-element chemistry, the 3d4 and 3d9 configurations in octahedral complexes are particularly illustrative, where a distortion in local geometry is associated with a reduction of the electronic energy. However, there has been a lasting debate about the fact that the octahedra are found to exclusively elongate. In contrast, for Na9 Bi5 Os3 O24 , the octahedron around Os6+ (5d2 ) is heavily compressed, lifting the degeneracy of the t2g set of 5d orbitals such that in the sense of a JT compression a diamagnetic ground state results. This effect is not forced by structural constraints, the structure offers sufficient space for osmium to shift the apical oxygen atoms to a standard distance. The relevance of these findings is far reaching, since they provide new insights in the hierarchy of perturbations defining ground states of open shell electronic systems.

Electronic Structure and Spectroscopic Properties of Group-7 Tri-Oxo-Halides MO3X (M = Mn-Bh, X = F-Ts)

The 24 trioxide halide molecules MO₃X of the manganese group (M = Mn-Bh; X = F-Ts), which are iso-valence-electronic with the famous MnO_4^- ion, have been quantum-chemically investigated by quasi-relativistic density-functional and ab initio correlated approaches. Geometric and electronic structures, valence and oxidation numbers, vibrational and electronic spectral properties, energetic stabilities of the monomers in the gas phase, and the decay mode of MnO₃F have been investigated. The light Mn-3d species are most strongly electron-correlated, indicating that the concept of a closed-shell Lewis-type single-configurational structure [Mn⁺⁷(d⁰) O^-2(p⁶)₃ F^-(p⁶)] reaches its limits. The concept of real-valued spin orbitals φ(r)·α and φ(r)·β breaks down for the heavy Bh-6d, At-6p and Ts-7p elements because of the dominating spin-orbit coupling. The vigorous decomposition of MnO₃F at ambient conditions starts by the autocatalyzed release of n O₂ and the formation of Mn_mO_3m-2nF_m clusters, triggered by the electron-depleted "oxylic" character of the oxide ligands in MnO₃X.

Reply to the ‘Comment on “Uncommon structural and bonding properties in Ag16B4O10” by A. Lobato, Miguel Á. Salvadó, and J. Manuel Recio, Chem. Sci., 2021, 12, DOI: 10.1039/D1SC02152D

Where are the excess electrons in Ag₁₆B₄O₁₀?

Understanding the Uniqueness of 2p Elements in Periodic Tables

The Periodic Table, and the unique chemical behavior of the first element in a column (group), were discovered simultaneously one and a half centuries ago. Half a century ago, this unique chemistry of the light homologs was correlated to the then available atomic orbital (AO) radii. The radially nodeless 1s, 2p, 3d, 4f valence AOs are particularly compact. The similarity of r(2s)≈r(2p) leads to pronounced sp-hybrid bonding of the light p-block elements, whereas the heavier p elements with n≥3 exhibit r(ns) ≪ r(np) of approximately -20 to -30 %. Herein, a comprehensive physical explanation is presented in terms of kinetic radial and angular, as well as potential nuclear-attraction and electron-screening effects. For hydrogen-like atoms and all inner shells of the heavy atoms, r(2s) ≫ r(2p) by +20 to +30 %, whereas r(3s)≳r(3p)≳r(3d), since in Coulomb potentials radial motion is more radial orbital expanding than angular motion. However, the screening of nuclear attraction by inner core shells is more efficient for s than for p valence shells. The uniqueness of the 2p AO is explained by this differential shielding. Thereby, the present work paves the way for future physical explanations of the 3d, 4f, and 5g cases.

Unraveling the mechanism of biomimetic hydrogen fuel production – a first principles molecular dynamics study

The Fe₂(bdt)(CO)₆ [bdt = benzenedithiolato] complex, a synthetic mimic of the [FeFe] hydrogenase enzyme can electrochemically convert protons into molecular hydrogen. The free energy landscape reveals a different mechanism for the biomimetic cycle.

Oxidation-State Constrained Density Functional Theory for the Study of Electron-Transfer Reactions

We propose a new constrained density functional theory (CDFT) approach which directly controls the oxidation state of the target atoms. In this new approach called oxidation-state constrained density functional theory (OS-CDFT), the eigenvalues of the occupation matrix obtained from projecting the Kohn-Sham wave functions onto the valence orbitals are constrained to obtain the desired oxidation states. This approach is particularly useful to study electron transfer problems in transition metal-containing systems due to the multivalent nature of the transition metal ions. The calculation of the forces on the ions and of the coupling constant was implemented under the OS-CDFT scheme to allow efficient and accurate study of electron transfer reactions. We demonstrated the application of this method in the study of different electron transfer reactions including the aqueous ferrous-ferric self-exchange reaction, polaron hopping in the TiO₂ anatase and bismuth vanadate, and photoexcited electron transfer in the sapphire.

Nine questions on energy decomposition analysis

The paper collects the answers of the authors to the following questions: Is the lack of precision in the definition of many chemical concepts one of the reasons for the coexistence of many partition schemes? Does the adoption of a given partition scheme imply a set of more precise definitions of the underlying chemical concepts? How can one use the results of a partition scheme to improve the clarity of definitions of concepts? Are partition schemes subject to scientific Darwinism? If so, what is the influence of a community's sociological pressure in the "natural selection" process? To what extent does/can/should investigated systems influence the choice of a particular partition scheme? Do we need more focused chemical validation of Energy Decomposition Analysis (EDA) methodology and descriptors/terms in general? Is there any interest in developing common benchmarks and test sets for cross-validation of methods? Is it possible to contemplate a unified partition scheme (let us call it the "standard model" of partitioning), that is proper for all applications in chemistry, in the foreseeable future or even in principle? In the end, science is about experiments and the real world. Can one, therefore, use any experiment or experimental data be used to favor one partition scheme over another? © 2019 Wiley Periodicals, Inc.

Oxidation states and ionicity

The concepts of oxidation state and atomic charge are entangled in modern materials science. We distinguish between these quantities and consider their fundamental limitations and utility for understanding material properties. We discuss the nature of bonding between atoms and the techniques that have been developed for partitioning electron density. While formal oxidation states help us count electrons (in ions, bonds, lone pairs), variously defined atomic charges are usefully employed in the description of physical processes including dielectric response and electronic spectroscopies. Such partial charges are introduced as quantitative measures in simple mechanistic models of a more complex reality, and therefore may not be comparable or transferable. In contrast, oxidation states are defined to be universal, with deviations constituting exciting challenges as evidenced in mixed-valence compounds, electrides and highly correlated systems. This Perspective covers how these concepts have evolved in recent years, our current understanding and their significance.

The Pentagonal-Pyramidal Hexamethylbenzene Dication: Many Shades of Coordination Chemistry at Carbon

A recent report on the crystal structure of the pentagonal-pyramidal hexamethylbenzene dication C6 (CH3 )62+ by Malischewski and Seppelt [Angew. Chem. Int. Ed. 2017, 56, 368] confirmed the structural proposal made in the first report of this compound in 1973 by Hogeveen and Kwant [Tetrahedron Lett. 1973, 14, 1665]. The widespread attention that this compound quickly gained led us to reinvestigate its electronic structure. On the basis of intrinsic bond orbital analysis, effective oxidation state analysis, ring current analysis, and comparison with well-established coordination complexes, it is demonstrated that the central carbon atom behaves like a transition metal. The central (apical) carbon atom, although best described as a highly Lewis-acidic carbon atom coordinated with an anionic cyclopentadienyl ligand, is also capable of acting as an electron-pair donor to a formal CH3+ group. The different roles of coordination chemistry are discussed.

An Objective Alternative to IUPAC's Approach To Assign Oxidation States

The IUPAC has recently clarified the term oxidation state (OS), and provided algorithms for its determination based on the ionic approximation (IA) of the bonds supported by atomic electronegativities (EN). Unfortunately, there are a number of exceptions and ambiguities in IUPAC's algorithms when it comes to practical applications. Our comprehensive study reveals the critical role of the chemical environment on establishing the OS, which cannot always be properly predicted using fix atomic EN values. By identifying what we define here as subsystems of enhanced stability within the molecular system, the OS can be safely assigned in many cases without invoking exceptions. New insights about the effect of local aromaticity upon OS are revealed. Moreover, we prove that there are intrinsic limitations of the IA that cannot be overcome. In this context, the effective oxidation state (EOS) analysis arises as a robust and general scheme to derive an OS without any external guidance.

Core Electron Topologies in Chemical Compounds: Case Study of Carbon versus Silicon

The similarities and differences between carbon and silicon have attracted the curiosity of chemists for centuries. Similarities and analogies can be found in their saturated compounds, but carbon exhibits a cornucopia of unsaturated compounds that silicon (and most other elements) cannot replicate. While this qualitative difference is empirically well known, quantum chemistry has previously only described quantitative differences related to orbital overlap, steric effects, or orbital energies. We study C₂ and Si₂ and their hydrides X₂ H_2n (X=C, Si; n=1, 2, 3) by first-principles quantum chemical calculation, and find a qualitative difference in the topologies of the core electrons: carbon has the propensity to alter its core electron topology when forming unsaturated compounds, and silicon has not. We draw a connection between the core electron topologies and ionization energies, and identify other elements we expect to have similarly flexible core topologies as carbon.

Analyzing Fluxional Molecules Using DORI

The Density Overlap Region Indicator (DORI) is a density-based scalar field that reveals covalent bonding patterns and noncovalent interactions in the same value range. This work goes beyond the traditional static quantum chemistry use of scalar fields and illustrates the suitability of DORI for analyzing geometrical and electronic signatures in highly fluxional molecular systems. Examples include a dithiocyclophane, which possesses multiple local minima with differing extents of π-stacking interactions and a temperature dependent rotation of a molecular rotor, where the descriptor is employed to capture fingerprints of CH-π and π-π interactions. Finally, DORI serves to examine the fluctuating π-conjugation pathway of a photochromic torsional switch (PTS). Attention is also placed on postprocessing the large amount of generated data and juxtaposing DORI with a data-driven low-dimensional representation of the structural landscape.

Curly arrows, electron flow, and reaction mechanisms from the perspective of the bonding evolution theory

Despite the usefulness of curly arrows in chemistry, their relationship with real electron density flows is still imprecise, and even their direct connection to quantum chemistry is still controversial. The paradigmatic description - from first principles - of the mechanistic aspects of a given chemical process is based mainly on the relative energies and geometrical changes at the stationary points of the potential energy surface along the reaction pathway; however, it is not sufficient to describe chemical systems in terms of bonding aspects. Probing the electron density distribution during a chemical reaction can provide important insights, enabling us to understand and control chemical reactions. This aim has required an extension of the relationships between the concepts of traditional chemistry and those of quantum mechanics. Bonding evolution theory (BET), which combines the topological analysis of the electron localization function (ELF) and Thom's catastrophe theory (CT), provides a powerful method that offers insight into the molecular mechanism of chemical rearrangements. In agreement with the laws of physical and aspects of quantum theory, BET can be considered an appropriate tool to tackle chemical reactivity with a wide range of possible applications. In this work, BET is applied to address a long-standing problem: the ability to monitor the flow of electron density. BET analysis shows a connection between quantum mechanics and bond making/forming processes. Likewise, the present approach retrieves the classical curly arrows used to describe the rearrangements of chemical bonds and provides detailed physical grounds for this type of representation. We demonstrate this procedure using the test set of prototypical examples of thermal ring apertures, and the degenerated Cope rearrangement of semibullvalene.

Materials discovery by chemical analogy: role of oxidation states in structure prediction

The likelihood of an element to adopt a specific oxidation state in a solid, given a certain set of neighbours, might often be obvious to a trained chemist. However, encoding this information for use in high-throughput searches presents a significant challenge. We carry out a statistical analysis of the occurrence of oxidation states in 16 735 ordered, inorganic compounds and show that a large number of cations are only likely to exhibit certain oxidation states in combination with particular anions. We use this data to build a model that ascribes probabilities to the formation of hypothetical compounds, given the proposed oxidation states of their constituent species. The model is then used as part of a high-throughput materials design process, which significantly narrows down the vast compositional search space for new ternary metal halide compounds. Finally, we employ a machine learning analysis of existing compounds to suggest likely structures for a small subset of the candidate compositions. We predict two new compounds, MnZnBr4 and YSnF7, that are thermodynamically stable according to density functional theory, as well as four compounds, MnCdBr4, MnRu2Br8, ScZnF5 and ZnCoBr4, which lie within the window of metastability.

Electronic Structural Analysis of Copper(II)-TEMPO/ABNO Complexes Provides Evidence for Copper(I)-Oxoammonium Character

Copper/aminoxyl species are proposed as key intermediates in aerobic alcohol oxidation. Several possible electronic structural descriptions of these species are possible, and the present study probes this issue by examining four crystallographically characterized Cu/aminoxyl halide complexes by Cu K-edge, Cu L_2,3-edge, and Cl K-edge X-ray absorption spectroscopy. The mixing coefficients between Cu, aminoxyl, and halide orbitals are determined via these techniques with support from density functional theory. The emergent electronic structure picture reveals that Cu coordination confers appreciable oxoammonium character to the aminoxyl ligand. The computational methodology is extended to one of the putative intermediates invoked in catalytic Cu/aminoxyl-driven alcohol oxidation reactions, with similar findings. Collectively, the results have important implications for the mechanism of alcohol oxidation and the underlying basis for cooperativity in this co-catalyst system.

VTST/MT studies of the catalytic mechanism of C-H activation by transition metal complexes with [Cu2(μ-O2)], [Fe2(μ-O2)] and Fe(IV)-O cores based on DFT potential energy surfaces

High-valent Cu and Fe species, which are generated from dioxygen activation in metalloenzymes, carry out the functionalization of strong C-H bonds. Understanding the atomic details of the catalytic mechanism has long been one of the main objectives of bioinorganic chemistry. Large H/D kinetic isotope effects (KIEs) were observed in the C-H activation by high-valent non-heme Cu or Fe complexes in enzymes and their synthetic models. The H/D KIE depends significantly on the transition state properties, such as structure, energies, frequencies, and shape of the potential energy surface, when the tunneling effect is large. Therefore, theoretical predictions of kinetic parameters such as rate constants and KIEs can provide a reliable link between atomic-level quantum mechanical mechanisms and experiments. The accurate prediction of the tunneling effect is essential to reproduce the kinetic parameters. The rate constants and HD/KIE have been calculated using the variational transition-state theory including multidimensional tunneling based on DFT potential energy surfaces along the reaction coordinate. Excellent agreement was observed between the predicted and experimental results, which assures the validity of the DFT potential energy surfaces and, therefore, the proposed atomic-level mechanisms. The [Cu₂(μ-O)₂], [Fe₂(μ-O)₂], and Fe(IV)-oxo species were employed for C-H activation, and their role as catalysts was discussed at an atomic level.

Charge transfer induced energy storage in CaZnOS:Mn – insight from experimental and computational spectroscopy

A spectroscopic study shows that energy storage prior to mechanoluminescence and thermoluminescence in CaZnOS:Mn can be effectuated by a ligand-to-Mn charge transfer.

Defect Tolerance to Intolerance in the Vacancy-Ordered Double Perovskite Semiconductors Cs2SnI6 and Cs2TeI6

Vacancy-ordered double perovskites of the general formula A2BX6 are a family of perovskite derivatives composed of a face-centered lattice of nearly isolated [BX6] units with A-site cations occupying the cuboctahedral voids. Despite the presence of isolated octahedral units, the close-packed iodide lattice provides significant electronic dispersion, such that Cs2SnI6 has recently been explored for applications in photovoltaic devices. To elucidate the structure-property relationships of these materials, we have synthesized solid-solution Cs2Sn1-xTexI6. However, even though tellurium substitution increases electronic dispersion via closer I-I contact distances, the substitution experimentally yields insulating behavior from a significant decrease in carrier concentration and mobility. Density functional calculations of native defects in Cs2SnI6 reveal that iodine vacancies exhibit a low enthalpy of formation, and that the defect energy level is a shallow donor to the conduction band rendering the material tolerant to these defect states. The increased covalency of Te-I bonding renders the formation of iodine vacancy states unfavorable and is responsible for the reduction in conductivity upon Te substitution. Additionally, Cs2TeI6 is intolerant to the formation of these defects, because the defect level occurs deep within the band gap and thus localizes potential mobile charge carriers. In these vacancy-ordered double perovskites, the close-packed lattice of iodine provides significant electronic dispersion, while the interaction of the B- and X-site ions dictates the properties as they pertain to electronic structure and defect tolerance. This simplified perspective based on extensive experimental and theoretical analysis provides a platform from which to understand structure-property relationships in functional perovskite halides.

Unique molecular geometries of reduced 4- and 5-coordinate zinc complexes stabilised by diiminopyridine ligand

Stepwise reduction of the diiminopyridine complex dimpyrZnCl₂ by KC₈ leads to compounds dimpyrZnCl (2), dimpyrZnCl(DMAP) (3) and dimpyrZn(DMAP)₂ (4) having unusual square-planar and see-saw geometries.

Principles of Chemical Bonding and Band Gap Engineering in Hybrid Organic-Inorganic Halide Perovskites

The performance of solar cells based on hybrid halide perovskites has seen an unparalleled rate of progress, while our understanding of the underlying physical chemistry of these materials trails behind. Superficially, CH₃NH₃PbI₃ is similar to other thin-film photovoltaic materials: a semiconductor with an optical band gap in the optimal region of the electromagnetic spectrum. Microscopically, the material is more unconventional. Progress in our understanding of the local and long-range chemical bonding of hybrid perovskites is discussed here, drawing from a series of computational studies involving electronic structure, molecular dynamics, and Monte Carlo simulation techniques. The orientational freedom of the dipolar methylammonium ion gives rise to temperature-dependent dielectric screening and the possibility for the formation of polar (ferroelectric) domains. The ability to independently substitute on the A, B, and X lattice sites provides the means to tune the optoelectronic properties. Finally, ten critical challenges and opportunities for physical chemists are highlighted.

Theoretical oxidation state analysis of Ru-(bpy)3: influence of water solvation and Hubbard correction in first-principles calculations

Oxidation state is a powerful concept that is widely used in chemistry and materials physics, although the concept itself is arguably ill-defined quantum mechanically. In this work, we present impartial comparison of four, well-recognized theoretical approaches based on Lowdin atomic orbital projection, Bader decomposition, maximally localized Wannier function, and occupation matrix diagonalization, for assessing how well transition metal oxidation states can be characterized. Here, we study a representative molecular complex, tris(bipyridine)ruthenium. We also consider the influence of water solvation through first-principles molecular dynamics as well as the improved electronic structure description for strongly correlated d-electrons by including Hubbard correction in density functional theory calculations.

Charge states of ions, and mechanisms of charge ordering transitions

To gain insight into the mechanism of charge ordering transitions, which conventionally are pictured as a disproportionation of an ion M as 2M(n+)→M((n+1)+) + M((n-1)+), we (1) review and reconsider the charge state (or oxidation number) picture itself, (2) introduce new results for the putative charge ordering compound AgNiO2 and the dual charge state insulator AgO, and (3) analyze the cationic occupations of the actual (not formal) charge, and work to reconcile the conundrums that arise. We establish that several of the clearest cases of charge ordering transitions involve no disproportion (no charge transfer between the cations, and hence no charge ordering), and that the experimental data used to support charge ordering can be accounted for within density functional-based calculations that contain no charge transfer between cations. We propose that the charge state picture retains meaning and importance, at least in many cases, if one focuses on Wannier functions rather than atomic orbitals. The challenge of modeling charge ordering transitions with model Hamiltonians isdiscussed.

Toward a comprehensive definition of oxidation state (IUPAC Technical Report)

A generic definition of oxidation state (OS) is formulated: “The OS of a bonded atom equals its charge after ionic approximation”. In the ionic approximation, the atom that contributes more to the bonding molecular orbital (MO) becomes negative. This sign can also be estimated by comparing Allen electronegativities of the two bonded atoms, but this simplification carries an exception when the more electronegative atom is bonded as a Lewis acid. Two principal algorithms are outlined for OS determination of an atom in a compound; one based on composition, the other on topology. Both provide the same generic OS because both the ionic approximation and structural formula obey rules of stable electron configurations. A sufficiently simple empirical formula yields OS via the algorithm of direct ionic approximation (DIA) by these rules. The topological algorithm works on a Lewis formula (for a molecule) or a bond graph (for an extended solid) and has two variants. One assigns bonding electrons to more electronegative bond partners, the other sums an atom’s formal charge with bond orders (or bond valences) of sign defined by the ionic approximation of each particular bond at the atom. A glossary of terms and auxiliary rules needed for determination of OS are provided, illustrated with examples, and the origins of ambiguous OS values are pointed out. An electrochemical OS is suggested with a nominal value equal to the average OS for atoms of the same element in a moiety that is charged or otherwise electrochemically relevant.

Prediction of electron energies in metal oxides

The ability to predict energy levels in metal oxides is paramount to developinguseful materials, such as in the development of water photolysis catalysts and efficient photovoltaic cells. The binding energy of electrons in materials encompasses a wealth of information concerning their physicochemistry. The energies control the optical and electrical properties, dictating for which kinds of chemistry and physics a particular material is useful. Scientists have developed theories and models for electron energies in a variety of chemical systems over the past century. However, the prediction of quantitative energy levels in new materials remains a major challenge. This issue is of particular importance in metal oxide research, where novel chemistries have opened the possibility of a wide range of tailored systems with applications in important fields including light-emitting diodes, energy efficient glasses, and solar cells. In this Account, we discuss the application of atomistic modeling techniques, covering the spectrum from classical to quantum descriptions, to explore the alignment of electron energies between materials. We present a number of paradigmatic examples, including a series of oxides (ZnO, In2O3, and Cu2O). Such calculations allow the determination of a "band alignment diagram" between different materials and can facilitate the prediction of the optimal chemical composition of an oxide for use in a given application. Throughout this Account, we consider direct computational solutions in the context of heuristic models, which are used to relate the fundamental theory to experimental observations. We review a number of techniques that have been commonly applied in the study of electron energies in solids. These models have arisen from different answers to the same basic question, coming from solid-state chemistry and physics perspectives. We highlight common factors, as well as providing a critical appraisal of the strengths and weaknesses of each, emphasizing the difficulties in translating concepts from molecular to solid-state systems. Finally, we stress the need for a universal description of the alignment of band energies for materials design from first-principles. By demonstrating the applicability and challenges of using theory to calculate the relevant quantities, as well as impressing the necessity of a clarification and unification of the descriptions, we hope to provide a stimulus for the continued development of this field.

Intrinsic Atomic Orbitals: An Unbiased Bridge between Quantum Theory and Chemical Concepts

Modern quantum chemistry can make quantitative predictions on an immense array of chemical systems. However, the interpretation of those predictions is often complicated by the complex wave function expansions used. Here we show that an exceptionally simple algebraic construction allows for defining atomic core and valence orbitals, polarized by the molecular environment, which can exactly represent self-consistent field wave functions. This construction provides an unbiased and direct connection between quantum chemistry and empirical chemical concepts, and can be used, for example, to calculate the nature of bonding in molecules, in chemical terms, from first principles. In particular, we find consistency with electronegativities (χ), C 1s core-level shifts, resonance substituent parameters (σR), Lewis structures, and oxidation states of transition-metal complexes.