Determination of the Bonding and Valence Distribution in Inorganic Solids by the Maximum Entropy Method

Comprehensive definition of oxidation state (IUPAC Recommendations 2016)

Oxidation state (OS) is defined using ionic approximation of bonds. Two principal algorithms are outlined for OS determination in a chemical compound described by a Lewis formula or bond graph. Typical origins of ambiguous OS values are pointed out, and the relationship between OS and the dn electron configuration of transition metals is commented on.

Classification ofABO3perovskite solids: a machine learning study

We explored the use of machine learning methods for classifying whether a particularABO3chemistry forms a perovskite or non-perovskite structured solid. Starting with three sets of feature pairs (the tolerance and octahedral factors, theAandBionic radii relative to the radius of O, and the bond valence distances between theAandBions from the O atoms), we used machine learning to create a hyper-dimensional partial dependency structure plot using all three feature pairs or any two of them. Doing so increased the accuracy of our predictions by 2–3 percentage points over using any one pair. We also included the Mendeleev numbers of theAandBatoms to this set of feature pairs. Doing this and using the capabilities of our machine learning algorithm, the gradient tree boosting classifier, enabled us to generate a new type of structure plot that has the simplicity of one based on using just the Mendeleev numbers, but with the added advantages of having a higher accuracy and providing a measure of likelihood of the predicted structure.

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.

Bond-valence model for metal cluster compounds. II. Matrix effect

The bond-valence model was commonly considered as inappropriate to metal cluster compounds, but recently it was shown that the model provides unique information on the lattice strains and stabilization mechanisms in (TM)6-chalcohalides, Mx(TM)6Ly (TM = transition metal, L = the chalcogen and/or halogen ligands; M = counter-cation). The previous study was mainly devoted to the non-uniform distribution of the anion valences (bond-valence sums) around clusters. This and the previous paper are focused on two additional phenomena: (i) a steric conflict between counter-cations and the cluster-ligand framework resulting in `common' lattice strains [previous paper: Levi et al. (2013). Acta Cryst. B69, 419-425], and (ii) steric conflict between the small (TM)6-cluster and the large coordination polyhedron around the cluster or so-called matrix effect (this paper). It was shown that both phenomena can be well described by changes in the bond-valence parameters. This paper demonstrates that the matrix effect results in high strains in the TM-L bonds in most of the (TM)6-chalcohalides (TM = Nb, Mo, W and Re). In spite of this, the violations for the total TM valence are minimal, because the cluster stretching is fully or partially compensated by compression of the TM-L bonds. As a result, the influence of the matrix effect on the material stability is rather positive: it decreases the volume of the structural units and in many cases ensures a more favorable distribution of the bond valences around TM atoms, stabilizing the cluster compound.

Structure and bonding in SnWO4, PbWO4, and BiVO4: lone pairs vs inert pairs

Three ternary oxides, SnWO4, PbWO4, and BiVO4, containing p-block cations with ns2np0 electron configurations, so-called lone pair cations, have been studied theoretically using density functional theory and UV-visible diffuse reflectance spectroscopy. The computations reveal significant differences in the underlying electronic structures that are responsible for the varied crystal chemistry of the lone pair cations. The filled 5s orbitals of the Sn2+ ion interact strongly with the 2p orbitals of oxygen, which leads to a significant destabilization of symmetric structures (scheelite and zircon) favored by electrostatic forces. The destabilizing effect of this interaction can be significantly reduced by lowering the symmetry of the Sn2+ site to enable the antibonding Sn 5s-O 2p states to mix with the unfilled Sn 5p orbitals. This interaction produces a localized, nonbonding state at the top of the valence band that corresponds closely with the classical notion of a stereoactive electron lone pair. In compounds containing Pb2+ and Bi3+ the relativistic contraction of the 6s orbital reduces its interaction with oxygen, effectively diminishing its role in shaping the crystal chemical preferences of these ions. In PbWO4 this leads to a stabilization of the symmetric scheelite structure. In the case of BiVO4 the energy of the Bi 6s orbital is further stabilized. Despite this stabilization, the driving force for a stereoactive lone pair distortion appears to be enhanced. The energies of structures exhibiting distorted Bi3+ environments are competitive with structures that possess symmetric Bi3+ environments. Nevertheless, the "lone pair" that results associated with a distorted Bi3+ environment in BiVO4 is more diffuse than the Sn2+ lone pair in beta-SnWO4. Furthermore, the distortion has a much smaller impact on the electronic structure near the Fermi level.