Can We Safely Obtain Formal Oxidation States from Centroids of Localized Orbitals?

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.

Reply to the 'Comment on "The oxidation state in low-valent beryllium and magnesium compounds"' by S. Pan and G. Frenking, Chem. Sci., 2022, , DOI: 10.1039/D2SC04231B

A recent article by Pan and Frenking challenges our assignment of the oxidation state of low valent group 2 compounds. With this reply, we show that our assignment of Be(+2) and Mg(+2) oxidation states in Be(cAACDip)2 and Mg(cAACDip)2 is fully consistent with our data. Some of the arguments exposed by Pan and Frenking were based on visual inspection of our figures, rather than a thorough numerical analysis. We discuss with numerical proof that some of the statements made by the authors concerning our reported data are erroneous. In addition, we provide further evidence that the criterion of the lowest orbital interaction energy in the energy decomposition analysis (EDA) method is unsuitable as a general tool to assess the valence state of the fragments. Other indicators based on natural orbitals for chemical valence (NOCV) deliver a more reliable bonding picture. We also emphasize the importance of using stable wavefunctions for any kind of analysis, including EDA.

How reduced are nucleophilic gold complexes?

Nucleophilic formal gold(-I) and gold(I) complexes are investigated via Intrinsic Bond Orbital analysis and Energy Decomposition Analysis, based on density functional theory calculations. The results indicate gold(0) centres engaging in electron-sharing bonding with Al- and B- based ligands. Multiconfigurational (CASSCF) calculations corroborate the findings, highlighting the gap between the electonic structures and the oxidation state formalism.

Bis(imidazolium)-1,3-diphosphete-diide: A Building Block for FeC2 P2 Complexes and Clusters

Reaction of the 6π-electron aromatic four-membered heterocycle (IPr)₂ C₂ P₂ (1) (IPr=1,3-bis(2,6-diisopropylphenyl)-1,3-dihydro-2H-imidazol-2-ylidene) with [Fe₂ CO₉ ] gives the neutral iron tricarbonyl complex [Fe(CO)₃ -η³ -{(IPr)₂ C₂ P₂ }] (2). Oxidation with two equivalents of the ferrocenium salt, [Fe(Cp)₂ ](BArF₂₄ ), affords the dicationic tricarbonyl complex [Fe(CO)₃ -η⁴ -{(IPr)₂ C₂ P₂ }](BArF₂₄ )₂ (4). The one-electron oxidation proceeds under concomitant loss of one CO ligand to give the paramagnetic dicarbonyl radical cation complex [Fe(CO)₂ -η⁴ -{(IPr)₂ C₂ P₂ }](BArF₂₄ ) (5). Reduction of 5 allows the preparation of the neutral dicarbonyl complex [Fe(CO)₂ -η⁴ -{(IPr)₂ C₂ P₂ }] (6). An analysis by various spectroscopic techniques (⁵⁷ Fe Mössbauer, EPR) combined with DFT calculations gives insight into differences of the electronic structure within the members of this unique series of iron carbonyl complexes, which can be either described as electron precise or Wade-Mingos clusters.

Oxidation State Localized Orbitals: A Method for Assigning Oxidation States Using Optimally Fragment-Localized Orbitals and a Fragment Orbital Localization Index

Oxidation states represent the ionic distribution of charge in a molecule and are significant in tracking redox reactions and understanding chemical bonding. While effective algorithms already exist based on formal Lewis structures as well as using localized orbitals, they exhibit differences in challenging cases where effects such as redox noninnocence are at play. Given a density functional theory (DFT) calculation with chosen total charge and spin multiplicity, this work reports a new approach to obtaining fragment-localized orbitals that is termed oxidation state localized orbitals (OSLO), together with an algorithm for assigning the oxidation state using the OSLOs and an associated fragment orbital localization index (FOLI). Evaluating the FOLI requires fragment populations, and for this purpose a new version of the intrinsic atomic orbital (IAO) scheme is introduced in which the IAOs are evaluated using a reference minimal basis formed from on-the-fly superposition of atomic density (IAO-AutoSAD) calculations in the target basis set and at the target level of theory. The OSLO algorithm is applied to a range of challenging cases including high valent metal oxide complexes, redox noninnocent NO and dithiolate transition metal complexes, a range of carbene-containing TM complexes, and other examples including the potentially inverted ligand field in [Cu(CF₃)₄]^-. Across this range of cases, OSLO produces generally satisfactory results. Furthermore, in borderline cases, the OSLOs and associated FOLI values provide direct evidence of the emergence of covalent interactions between fragments that nicely complements existing approaches.

Unveiling the Electronic Structure of the Bi(+1)/Bi(+3) Redox Couple on NCN and NNN Pincer Complexes

Low-valent group 15 compounds stabilized by pincer ligands have gained particular interest, given their direct access to fine-tune their reactivity by the coordination pattern. Recently, bismuth has been employed in a variety of catalytic transformations by taking advantage of the (+1/+3) redox couple. In this work, we present a detailed quantum–chemical study on the electronic structure of bismuth pincer complexes from two different families, namely, bis(ketimine)phenyl (NCN) and triamide bismuthinidene (NNN). The use of the so-called effective oxidation state analysis allows the unambiguous assignation of the bismuth oxidation state. In contrast to previous studies, our calculations suggest a Bi(+1) assignation for NCN pincer ligands, while Bi(+3) character is found for NNN pincer complexes. Notably, regardless of its oxidation state, the central bismuth atom disposes of up to two lone pairs for coordinating Lewis acids, as indicated by very high first and second proton affinity values. Besides, the Bi–NNN systems can also accommodate two Lewis base ligands, indicating also ambiphilic behavior. The effective fragment orbital analysis of Bi and the ligand allows monitoring of the intricate electron flow of these processes, revealing the noninnocent nature of the NNN ligand, in contrast with the NCN one. By the dissection of the electron density into effective fragment orbitals, we are able to quantify and rationalize the Lewis base/acid character.

Effective oxidation state analysis sheds light on the electronic structure of chemical systems. The oxidation state of bismuthinidene pincer complexes can be assigned as Bi(+1) or Bi(+3) depending on the nature of the ligands. Despite this assignation, the reactivity pattern as Lewis base or acid is similar. The occupation of the effective fragment orbitals gives a straightforward method to quantify the reactivity.

Bent and Linear {CoNO}8 Entities: Structure and Bonding in a Prototypic Class of Nitrosyls

Among the isoelectronic ligands CN^-, CO, and NO⁺, an oblique bonding to the metal is well-established for the nitrosyl ligand, with M-N-O angles down to ≈120°. In the last decades, the nitrosyl community got into the habit of addressing a bent-bonded nitrosyl ligand as ¹NO^-. Thus, because various redox forms of a nitrosyl ligand seem to exist, the ligand is considered to be "noninnocent" because of the obvious ambiguity of an oxidation state (OS) assignment of the ligand and metal. Among the bent-bonded species, the low-spin {CoNO}⁸ class is prototypic. From this class, some 20 new nitrosyl compounds, the X-ray structure determinations of which comply with strict quality criteria, were analyzed with respect to the OS issue. As a result, the effective OS method shows a low-spin d⁸ Co^I-NO⁺ couple instead of a negative OS of the ligand at the BP86/def2-TZVP (+D3, +CPCM with infinite permittivity) level of theory. The same holds for some new members of the linear subclass of {CoNO}⁸ compounds. For all compounds, a largely invariable "real" charge of ≈ -0.3 e was obtained from population analyses. All of these electron-rich d⁸ species strive to manage Pauli repulsion between the metal electrons and the lone pair at the nitrosyl's nitrogen atom, with the bending of the CoNO unit as the most frequent escape.

A Crystalline Iron Terminal Methylidene

Iron methylidene species are alleged intermediates in the Fischer-Tropsch process and in olefin cyclopropanation, yet iron methylidene complexes with unambiguously established molecular and electronic structures remain elusive. In this study, we characterize an iron terminal methylidene complex by single-crystal X-ray diffractometry (scXRD), CHN combustion elemental analysis, ¹H/¹³C/³¹P/¹H-¹³C NMR, and zero-field ⁵⁷Fe Mössbauer spectroscopy and study its reactivity. A series of closely related complexes in different oxidation states were synthesized, isolated and characterized in order to validate the electronic structure of the title methylidene complex. The computational analysis substantiates the proposed Fischer-type electronic description while emphasizing high Fe═CH₂ bond covalency, considerable double bond order, and thus, substantial alkylidene character.

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.