In defence of oxidation states

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.

Chemdex: quantification and distributions of valence numbers, oxidation numbers, coordination numbers, electron numbers, and covalent bond classes for the elements

The paper introduces Chemdex, a freely accessible web-based database of over 70 000 compounds characterised by crystallography from across the periodic table. Its software calculates for an atom of interest within each compound classifications including valence number, oxidation number, coordination number, electron number, several covalent bond classifications, and the attached atom set. Users may explore distributions of these classifications by percentages and heat map displays for individual elements or sets of elements, or in several cases for one classification plotted against a second. These properties often display clear periodicity. Based upon distributions across the periodic table of valence numbers, electron numbers, coordination numbers, and attached atom data suggestions are made regarding the placement of hydrogen in the periodic table, membership of group 3 in the periodic table, locations of the early actinoids in the periodic table, and assignments of certain elements as metalloids.

Local Oxidation States in {FeNO}6-8 Porphyrins: Insights from DMRG/CASSCF-CASPT2 Calculations

A first DMRG/CASSCF-CASPT2 study of a series of paradigmatic {FeNO}6, {FeNO}7, and {FeNO}8 heme-nitrosyl complexes has led to substantial new insight as well as uncovered key shortcomings of the DFT approach. By virtue of its balanced treatment of static and dynamic correlation, the calculations have provided some of the most authoritative information available to date on the energetics of low- versus high-spin states of different classes of heme-nitrosyl complexes. Thus, the calculations indicate low doublet-quartet gaps of 1-4 kcal/mol for {FeNO}7 complexes and high singlet-triplet gaps of ≳20 kcal/mol for both {FeNO}6 and {FeNO}8 complexes. In contrast, DFT calculations yield widely divergent spin state gaps as a function of the exchange-correlation functional. DMRG-CASSCF calculations also help calibrate DFT spin densities for {FeNO}7 complexes, pointing to those obtained from classic pure functionals as the most accurate. The general picture appears to be that nearly all the spin density of Fe[P](NO) is localized on the Fe, while the axial ligand imidazole (ImH) in Fe[P](NO)(ImH) pushes a part of the spin density onto the NO moiety. An analysis of the DMRG-CASSCF wave function in terms of localized orbitals and of the resulting configuration state functions in terms of resonance forms with varying NO(π*) occupancies has allowed us to address the longstanding question of local oxidation states in heme-nitrosyl complexes. The analysis indicates NO(neutral) resonance forms [i.e., Fe(II)-NO0 and Fe(III)-NO0] as the major contributors to both {FeNO}6 and {FeNO}7 complexes. This finding is at variance with the common formulation of {FeNO}6 hemes as Fe(II)-NO+ species but is consonant with an Fe L-edge XAS analysis by Solomon and co-workers. For the {FeNO}8 complex {Fe[P](NO)}-, our analysis suggests a resonance hybrid description: Fe(I)-NO0 ↔ Fe(II)-NO-, in agreement with earlier DFT studies. Vibrational analyses of the compounds studied indicate an imperfect but fair correlation between the NO stretching frequency and NO(π*) occupancy, highlighting the usefulness of vibrational data as a preliminary indicator of the NO oxidation state.

Hypervalence: A Useful Concept or One That Should Be Gracefully Retired?

In this essay the origins of the term hypervalence and its application in p-block element chemistry are considered and it is argued that the term should now be consigned to the graveyard of concepts that no longer afford any discernible value or insight, certainly from an educational perspective. In contrast, the educational merits of the octet rule are also examined where it is concluded that this rule does have significant pedagogical value, albeit mostly within the ambit of introductory level explanations. For a few of the chosen exemplar compounds, a selection of orbital-based analyses, at different levels of sophistication, are also considered, and their values appraised together with a brief survey of some of the more general computational studies which have been employed in relation to this topic.

Metal-Metal Bond Umpolung in Heterometallic Extended Metal Atom Chains

Understanding the fundamental properties governing metal–metal interactions is crucial to understanding the electronic structure and thereby applications of multimetallic systems in catalysis, material science, and magnetism. One such property that is relatively underexplored within multimetallic systems is metal–metal bond polarity, parameterized by the electronegativities (χ) of the metal atoms involved in the bond. In heterobimetallic systems, metal–metal bond polarity is a function of the donor–acceptor (Δχ) interactions of the two bonded metal atoms, with electropositive early transition metals acting as electron acceptors and electronegative late transition metals acting as electron donors. We show in this work, through the preparation and systematic study of a series of Mo₂M(dpa)₄(OTf)₂ (M = Cr, Mn, Fe, Co, and Ni; dpa = 2,2′-dipyridylamide; OTf = trifluoromethanesulfonate) heterometallic extended metal atom chain (HEMAC) complexes that this expected trend in χ can be reversed. Physical characterization via single-crystal X-ray diffraction, magnetometry, and spectroscopic methods as well as electronic structure calculations supports the presence of a σ symmetry 3c/3e^– bond that is delocalized across the entire metal-atom chain and forms the basis of the heterometallic Mo₂–M interaction. The delocalized 3c/3e^– interaction is discussed within the context of the analogous 3c/3e^– π bonding in the vinoxy radical, CH₂CHO. The vinoxy comparison establishes three predictions for the σ symmetry 3c/3e^– bond in HEMACS: (1) an umpolung effect that causes the Mo–M interactions to become more covalent as Δχ increases, (2) distortion of the σ bonding and non-bonding orbitals to emphasize Mo–M bonding and de-emphasize Mo–Mo bonding, and (3) an increase in Mo spin population with increasing Mo–M covalency. In agreement with these predictions, we find that the Mo₂···M covalency increases with increasing Δχ of the Mo and M atoms (Δχ_Mo–M increases as M = Cr < Mn < Fe < Co < Ni), an umpolung of the trend predicted in the absence of σ delocalization. We attribute the observed trend in covalency to the decreased energic differential (ΔE) between the heterometal orbital and the σ bonding molecular orbital of the Mo₂ quadruple bond, which serves as an energetically stable, “ligand”-like electron-pair donor to the heterometal ion acceptor. As M is changed from Cr to Ni, the σ bonding and nonbonding orbitals do indeed distort as anticipated, and the spin population of the outer Mo group is increased by at least a factor of 2. These findings provide a predictive framework for multimetallic compounds and advance the current understanding of the electronic structures of molecular heteromultimetallic systems, which can be extrapolated to applications in the context of mixed-metal surface catalysis and multimetallic proteins.

This work describes how use of a metal−metal quadruply bonded metalloligand can reverse expected trends in metal−metal bond polarity through the preparation and systematic study of a novel series of Mo₂M(dpa)₄(OTf)₂ (M = Cr, Mn, Fe, Co, and Ni) heterotrimetallic extended metal atom chain (HEMAC) complexes. These complexes feature a 3c/3e⁻ metal−metal bond that is delocalized across the entire metal atom chain and is compared to the 3c/3e⁻ π bonding in the vinoxyl radical.

Comment on "In Defence of Oxidation States" by N. C. Norman and P. G. Pringle, Dalton Transactions, 2022, 51, DOI: 10.1039/D0DT03914D

The evolution of the Covalent Bond Classification as a pedagogical tool for classifying an element's chemistry is described.

Reply to the 'Comment on "In Defence of Oxidation States"' by J. C. Green, Dalton Transactions, 2022, 51, DOI: 10.1039/D1DT02930D

We reiterate and reinforce some of the points concerning oxidation states and the Covalent Bond Classification method we made in the Perspective article entitled 'In Defence of Oxidation States' including a brief discussion of the relative merits of the terms 'metathesis' and 'redox' when considering addition across a metal-metal bond.