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

Ligand field theory, Pauli shields and ultra-covalency in organometallic chemistry

This paper explores the ligand field picture applied to organometallic compounds. Given the dearth of experimental data, the high-level ab initio ligand field theory (aiLFT) method is deployed as a surrogate for experiment and the necessary d orbital sequences and relative energies are obtained computationally. These are fitted to local cellular ligand field (CLF) σ, π and δ bonding parameters. Results are reported for planar [Cu(CR3)4]-, (R = F, H), octahedral M(CO)6n (M = Fe, Mn, Cr, V, Ti; n = +2, +1, 0, -1, -2), and the sandwich compounds M(Cp)2 (Cp = cyclopentadienyl, M = Fe, Ni, V), [Ni(Cp)2]2+ and Cr(C6H6)2. With respect to the aiLFT framework, these organometallic systems behave just like coordination complexes and most maintain the integrity of their formal dn configurations. Both [Cu(CR3)4]- compounds are formulated as low-spin d8 CuIII species and have normal ligand fields consistent with their planar geometries. The metal carbonyls reveal a new way of counting valence electrons which only requires the CLF d orbital energy level diagram to rationalise the 18-electron rule as well as its many exceptions. The bonding in sandwich compounds shows a remarkable variation. In ferrocene, Cp- behaves as a strong field ligand, comparable to [CN]- in [Fe(CN)6]4-. Fe(Cp)2 is low spin as is Cr(C6H6)2. Cp- in Fe(Cp)2 is a weak σ donor, strong π donor and weak δ acceptor while benzene in Cr(C6H6)2 is also a weak σ and strong π donor but is a much better δ acceptor. In contrast, Cp- is weak field in high spin, 20-electron Ni(Cp)2 but 'ultra-covalent' in [Ni(Cp)2]2+. The formal IV oxidation state is too high for the ligand set and the integrity of the d6 configuration is lost. Similarly, [V(CO)6]- and [Ti(CO)6]2- are ultra-covalent except now the formal metal oxidation states are too negative. Both mechanisms relate to the breaching of the metal's 3s23p6 'Pauli shield' and these ultra-covalent systems lie outside the ab initio ligand field regime. However, within the ligand field regime, the bonding in 'coordination complexes' and 'organometallic compounds' has the same conceptual footing and the nature of the local σ, π and δ interactions can be extracted from analysing the ligand field d orbitals.

Catalytically Relevant Organocopper(III) Complexes Formed through Aryl-Radical-Enabled Oxidative Addition

Stepwise oxidative addition of copper(I) complexes to form copper(III) species via single electron transfer (SET) events has been widely proposed in copper catalysis. However, direct observation and detailed investigation of these fundamental steps remain elusive owing largely to the typically slow oxidative addition rate of copper(I) complexes and the instability of the copper(III) species. We report herein a novel aryl-radical-enabled stepwise oxidative addition pathway that allows for the formation of well-defined alkyl-CuIII species from CuI complexes. The process is enabled by the SET from a CuI species to an aryl diazonium salt to form a CuII species and an aryl radical. Subsequent iodine abstraction from an alkyl iodide by the aryl radical affords an alkyl radical, which then reacts with the CuII species to form the alkyl-CuIII complex. The structure of resultant [(bpy)CuIII(CF3)2(alkyl)] complexes has been characterized by NMR spectroscopy and X-ray crystallography. Competition experiments have revealed that the rate at which different alkyl iodides undergo oxidative addition is consistent with the rate of iodine abstraction by carbon-centered radicals. The CuII intermediate formed during the SET process has been identified as a four-coordinate complex, [CuII(CH3CN)2(CF3)2], through electronic paramagnetic resonance (EPR) studies. The catalytic relevance of the high-valent organo-CuIII has been demonstrated by the C-C bond-forming reductive elimination reactivity. Finally, localized orbital bonding analysis of these formal CuIII complexes indicates inverted ligand fields in σ(Cu-CH2) bonds. These results demonstrate the stepwise oxidative addition in copper catalysis and provide a general strategy to investigate the elusive formal CuIII complexes.

Mechanistic Insights into the Origins of Selectivity in a Cu-Catalyzed C-H Amidation Reaction

The catalytic transformation of C-H to C-N bonds offers rapid access to fine chemicals and high-performance materials, but achieving high selectivity from undirected aminations of unactivated C(sp3)-H bonds remains an outstanding challenge. We report the origins of the reactivity and selectivity of a Cu-catalyzed C-H amidation of simple alkanes. Using a combination of experimental and computational mechanistic studies and energy decomposition techniques, we uncover a switch in mechanism from inner-sphere to outer-sphere coupling between alkyl radicals and the active Cu(II) catalyst with increasing substitution of the alkyl radical. The combination of computational predictions and detailed experimental validation shows that simultaneous minimization of both Cu-C covalency and alkyl radical size increases the rate of reductive elimination and that both strongly electron-donating and electron-withdrawing substituents on the catalyst accelerate the selectivity-determining C-N bond formation process as a result of a change in mechanism. These findings offer design principles for the development of improved catalyst scaffolds for radical C-H functionalization reactions.

Cooperative and Orthogonal Switching in the Solid State Enabled by Metal-Organic Framework Confinement Leading to a Thermo-Photochromic Platform

Cooperative behavior and orthogonal responses of two classes of coordinatively integrated photochromic molecules towards distinct external stimuli were demonstrated on the first example of a photo-thermo-responsive hierarchical platform. Synergetic and orthogonal responses to temperature and excitation wavelength are achieved by confining the stimuli-responsive moieties within a metal-organic framework (MOF), leading to the preparation of a novel photo-thermo-responsive spiropyran-diarylethene based material. Synergistic behavior of two photoswitches enables the study of stimuli-responsive resonance energy transfer as well as control of the photoinduced charge transfer processes, milestones required to advance optoelectronics development. Spectroscopic studies in combination with theoretical modeling revealed a nonlinear effect on the material electronic structure arising from the coordinative integration of photoresponsive molecules with distinct photoisomerization mechanisms. Thus, the reported work covers multivariable facets of not only fundamental aspects of photoswitch cooperativity, but also provides a pathway to modulate photophysics and electronics of multidimensional functional materials exhibiting thermo-photochromism.

Computational Studies of Rubber Ozonation Explain the Effectiveness of 6PPD as an Antidegradant and the Mechanism of Its Quinone Formation

The discovery that the commercial rubber antidegradant 6PPD reacts with ozone (O₃) to produce a highly toxic quinone (6PPDQ) spurred a significant research effort into nontoxic alternatives. This work has been hampered by lack of a detailed understanding of the mechanism of protection that 6PPD affords rubber compounds against ozone. Herein, we report high-level density functional theory studies into early steps of rubber and PPD (p-phenylenediamine) ozonation, identifying key steps that contribute to the antiozonant activity of PPDs. In this, we establish that our density functional theory approach can achieve chemical accuracy for many ozonation reactions, which are notoriously difficult to model. Using adiabatic energy decomposition analysis, we examine and dispel the notion that one-electron charge transfer initiates ozonation in these systems, as is sometimes argued. Instead, we find direct interaction between O₃ and the PPD aromatic ring is kinetically accessible and that this motif is more significant than interactions with PPD nitrogens. The former pathway results in a hydroxylated PPD intermediate, which reacts further with O₃ to afford 6PPD hydroquinone and, ultimately, 6PPDQ. This mechanism directly links the toxicity of 6PPDQ to the antiozonant function of 6PPD. These results have significant implications for development of alternative antiozonants, which are discussed.

On the highest oxidation states of the actinoids in AnO4 molecules (An = Ac - Cm): A DMRG-CASSCF study

Actinoid tetroxide molecules AnO₄ (An = Ac - Cm) are investigated with the ab initio density matrix renormalization group (DMRG) approach. Natural orbital shapes are used to read out the oxidation state (OS) of the f-elements, and the atomic orbital energies and radii are used to explain the trends. The highest OSs reveal a "volcano"-type variation: For An = Ac - Np, the OSs are equal to the number of available valence electrons, that is, Ac^III , Th^IV , Pa^V , U^VI , and Np^VII . Starting with plutonium as the turning point, the highest OSs in the most stable AnO₄ isomers then decrease as Pu^V , Am^V , and Cm^III , indicating that the 5f-electrons are hard to be fully oxidized off from Pu onward. The variations are related to the actinoid contraction and to the 5f-covalency characteristics. Combined with previous work on OSs, we review their general trends throughout the periodic table, providing fundamental understanding of OS-relevant phenomena.

Redox-active ligands as a challenge for electronic structure methods

To improve the catalytic activity of 3d transition metal catalysts, redox-active ligands are a promising tool. These ligands influence the oxidation state of the metal center as well as the ground spin-state and make the experimental determination of both properties challenging. Therefore, first-principles calculations, in particular employing density functional theory with a proper choice of exchange-correlation (xc) functional, are crucial. Common xc functionals were tested on a simple class of metal complexes: homoleptic, octahedral tris(diimine) iron(II) complexes. The spin-state energy splittings for most of these complexes showed the expected linear dependence on the amount of exact exchange included in the xc functionals. Even though varying redox-activity affects the electronic structure of the complexes considerably, the sensitivity of the spin-state energetics to the exact exchange admixture is surprisingly small. For iron(II) complexes with highly redox-active ligands and for a broad range of ligands in the reduced tris(diimine) iron(I) complexes, self-consistent field convergence to local minima was observed, which differ from the global minimum in the redox state of the ligand. This may also result in convergence to a molecular structure that corresponds to an energetically higher-lying local minimum. One criterion to detect such behavior is a change in the sign of the slope for the dependence of the spin-state energy splittings on the amount of exact exchange. We discuss possible protocols for dealing with such artifacts in cases in which a large number of calculations makes checking by hand unfeasible.

Spectroscopic Manifestations and Implications for Catalysis of Quasi-d10 Configurations in Formal Gold(III) Complexes

Several gold +I and +III complexes are investigated computationally and spectroscopically, focusing on the d-configuration and physical oxidation state of the metal center. Density functional theory calculations reveal the non-negligible electron-sharing covalent character of the metal-to-ligand σ-bonding framework. The bonding of gold(III) is shown to be isoelectronic to the formal Cu^III complex [Cu(CF₃ )₄ ]^1- , in which the metal center tries to populate its formally unoccupied 3d_x2-y2 orbital via σ-bonding, leading to a reduced d¹⁰ Cu^I description. However, Au L₃ -edge X-ray absorption spectroscopy reveals excitation into the d-orbital of the Au^III species is still possible, showing that a genuine d¹⁰ configuration is not achieved. We also find an increased electron-sharing nature of the σ-bonds in the Au^I species, relative to their Ag^I and Cu^I analogues, due to the low-lying 6s orbital. We propose that gold +I and +III complexes form similar bonds with substrates, owing primarily to participation of the 5d_x2-y2 or 6s orbital, respectively, in bonding, indicating why Au^I and Au^III complexes often have similar reactivity.

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(cAAC^Dip)₂ and Mg(cAAC^Dip)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.

Revisiting Formal Copper(III) Complexes: Bridging Perspectives with Quasi-d 10 Configurations

The formal Cu(III) complex [Cu(CF₃)₄]^1- has often served as a paradigmatic example of challenging oxidation state assignment - with many reports proposing conflicting descriptions. Here we report a computational analysis of this compound, employing Energy Decomposition Analysis and Intrinsic Bond Orbital Analysis. We present a quasi-d ¹⁰ perspective of the metal centre, resulting from ambiguities in d-electron counting. The implications for describing reactions which undergo oxidation state changes, such as the formal reductive elimination from the analogous [Cu(CF₃)₃(CH₂Ph)]^1- complex (Paeth et al. J. Am. Chem. Soc. 2019, 141, 3153), are probed. Electron flow analysis finds that the changes in electronic structure may be understood as a quasi-d ¹⁰ to d ¹⁰ transition at the metal centre, rendering this process essentially redox neutral. This is reminiscent of a previously studied formal Ni(IV) complex (Steen et al., Angew. Chem. Int. Ed. 2019, 58, 13133-13139), and indicates that our description of electronic structure has implications for the understanding of elementary organometallic reaction steps.