The interplay of covalency, cooperativity, and coupling strength in governing C-H bond activation in Ni2E2 (E = O, S, Se, Te) complexes

Dinickel dichalcogenide complexes hold vital multifaceted significance across catalysis, electron transfer, magnetism, materials science, and energy conversion. Understanding their structure, bonding, and reactivity is crucial for all aforementioned applications. These complexes are classified as dichalcogenide, subchalcogenide, or chalcogenide based on metal oxidation and coordinated chalcogen, and due to the associated complex electronic structure, ambiguity often lingers about their classification. In this work, using DFT, CASSCF/NEVPT2, and DLPNO-CCSD(T) methods, we have studied in detail [(NiL)2(E2)] (L = 1,4,7,10-tetramethyl-1,4,7,10-tetraazacyclododecane; E = O, S, Se and Te) complexes and explored their reactivity towards C-H bond activation for the first time. Through a comprehensive analysis of the structure, bonding, and reactivity of a series of [(NiL)2(E2)] complexes with E = O, S, Se, and Te, our computational findings suggest that {Ni2O2} and {Ni2S2} are best categorised as dichalcogenide-type complexes. In contrast, {Ni2Se2} and {Ni2Te2} display tendencies consistent with the subchalcogenide classification, and this aligns with the earlier structural correlation proposed (Berry and co-workers, J. Am. Chem. Soc. 2015, 137, 4993) reports on the importance of the E-E bond strength. Our study suggests the reactivity order of {Ni2O2} > {Ni2S2} > {Ni2Se2} > {Ni2Te2} for C-H bond activation, and the origin of the difference in reactivity was attributed to the difference in the Ni-E bond covalency, and electronic cooperativity between two Ni centres that switch among the classification during the reaction. Further non-adiabatic analysis at the C-H bond activation step demonstrates a decrease in coupling strength as we progress down the group, indicating a correlation with metal-ligand covalency. Notably, the reactivity trend is found to be correlated to the strength of the antiferromagnetic exchange coupling constant J via developing a magneto-structural-barrier map - offering a hitherto unknown route to fine-tune the reactivity of this important class of compound.

Predicting spin states of iron porphyrins with DFT methods including crystal packing effects and thermodynamic corrections

Accurate computational treatment of spin states for transition metal complexes, exemplified by iron porphyrins, lies at the heart of quantum bioinorganic chemistry, but at the same time represents a great challenge for approximate density functional theory (DFT) methods, which are predominantly used. Here, the accuracy of DFT methods for spin-state splittings in iron porphyrin is assessed by probing the ability to correctly predict the ground states for six FeIII or FeII complexes experimentally characterized in solid state. For each case, molecular and periodic DFT calculations are employed to quantify the effect of porphyrin side substituents and the crystal packing effect (CPE) on the spin-state splitting. It is proposed to partition the total CPE into additive components, the direct and structural one, the importance of which is shown to significantly vary from case to case. By knowing the substituent effect, the CPE, and the Gibbs free energy thermodynamic correction from calculations, one can employ the experimental ground-state information in order to derive a quantitative constraint on the electronic energy difference for a simplified (porphin) model of the experimentally characterized metalloporphyrin. The constraints derived in such a way-in the form of single or double inequalities-are used to assess the accuracy of dispersion-corrected DFT methods for 6 spin-state splittings of [FeIII(P)(2-MeIm)2]+, [FeIII(P)(2-MeIm)]+, [FeII(P)(THF)2] and [FeII(P)] models (where P is porphin, 2-MeIm is 2-methylimidazole, THF is tetrahydrofuran). These data constitute the new benchmark set of spin states for crystalline iron porphyrins (SSCIP6). The highest accuracy is obtained in the case of double-hybrid functionals (B2PLYP-D3, DSD-PBEB95-D3), whereas hybrid functionals, especially those with reduced admixture of the exact exchange (B3LYP*-D3, TPSSh-D3), are found to considerably overstabilize the intermediate spin state, leading to incorrect ground-state prediction in FeIII porphyrins. The present approach, which can be generalized to other transition metal complexes, is not only useful in method benchmarking, but also sheds light on the interpretations of experimental data for metalloporphyrins, which are important models to understand the electronic properties of heme proteins.

DFT Struggles to Predict the Energy Landscape for Iron Pyridine Diimine-Catalyzed [2 + 2] Cycloaddition of Alkenes: Insights into the Problem and Alternative Solutions

In recent years, noninnocent pyridine diimine (PDI) complexes featuring first-row transition metals have emerged as prominent catalysts, demonstrating efficacy in a diverse range of vital organometallic transformations. However, the inherent complexity of the fundamental reactivity paradigm in these systems arises from the presence of a noninnocent ligand and the multispin feasibility of 3d metals. While density functional theory (DFT) has been widely used to unravel mechanistic insights, its limitations as a single-reference method can potentially misrepresent spin-state energetics, compromising our understanding of these intricate systems. In this study, we employ extensive high-level ab initio state averaged-complete active space self-consistent field/N-electron valence state perturbation theory (SA-CASSCF/NEVPT2) calculations in combination with DFT to investigate an iron-PDI-catalyzed [2 + 2] cycloaddition reaction of alkenes. The transformation proceeds through two major steps: oxidative cyclization and reductive elimination. Contrary to the predictions of DFT calculations, which suggest two-state reactivity in the reaction and identify reductive elimination as the turnover-limiting step, SA-CASSCF/NEVPT2-corrected results unequivocally establish a single-state reactivity scenario with oxidative cyclization as the turnover-limiting step. SA-CASSCF/NEVPT2-based insights into electronic ground states and electron distribution elucidate the intriguing interactions between the PDI ligand and the iron center, revealing the highly multiconfigurational nature of these species and providing a precise depiction of metal-ligand cooperativity throughout the transformation. A comparative assessment of several widely recognized DFT functionals against SA-CASSCF/NEVPT2-corrected data indicates that single-point energy calculations using the modern density functional MN15 on TPSSh geometries offer the most reliable density functional methodology, in scenarios where SA-CASSCF/NEVPT2 computational cost is a consideration.

Approaching the Complete Basis Set Limit for Spin-State Energetics of Mononuclear First-Row Transition Metal Complexes

Convergence to the complete basis set (CBS) limit is analyzed for the problem of spin-state energetics in mononuclear first-row transition metal (TM) complexes by taking under scrutiny a benchmark set of 18 energy differences between spin states for 13 chemically diverse TM complexes. The performance of conventional CCSD(T) and explicitly correlated CCSD(T)-F12a/b calculations in approaching the CCSD(T)/CBS limits is systematically studied. An economic computational protocol is developed based on the CCSD-F12a approximation and (here proposed) modified scaling of the perturbative triples term (T#). This computational protocol recovers the relative spin-state energetics of the benchmark set in excellent agreement with the reference CCSD(T)/CBS limits (mean absolute deviation of 0.4, mean signed deviation of 0.2, and maximum deviation of 0.8 kcal/mol) and enables performing canonical CCSD(T) calculations for mononuclear TM complexes sized up to ca. 50 atoms, which is illustrated by application to heme-related metalloporphyrins. Furthermore, a good transferability of the basis set incompleteness error (BSIE) is demonstrated for spin-state energetics computed using CCSD(T) and other wave function methods (MP2, CASPT2, CASPT2/CC, NEVPT2, and MRCI + Q), which justifies efficient focal-point approximations and simplifies the construction of multimethod benchmark studies.

Mechanisms of arsenic oxidation in the presence of pyrite: An experimental and theoretical study

The mobility and toxicity of arsenic are significantly influenced by the natural minerals. A comprehensive understanding of the interaction between arsenic and minerals is crucial for elucidating the natural behavior of arsenic and advancing arsenic remediation strategies. In this study, the mechanism of As (III) oxidation in the presence of pyrite without light irritation was investigated by experimental and theoretical approaches. Quenching experiment and electron paramagnetic resonance analysis confirm •OH and •O2H is the predominant oxidant of As (III) under acidic and alkaline condition, respectively. Density Functional Theory (DFT) calculations indicate on the pyrite surface, the surface oxygen species is insignificant in As(III) oxidation but crucial for the generation of reactive oxygen species (ROS). In the solution, •OH, •O2H, Fe(IV), and 1O2 are the favored oxidants for As(III), while ROS, 3O2, and Fe(III) possess the capability to convert As(IV) to As(V). The major mechanism of As(III) oxidation in the presence of pyrite without light irritation primarily involves three elementary reactions: (1) •OH facilitating As(III) conversion to As(IV), (2) 3O2 oxidizing As(IV) to As(V) and •O2H, and (3) As(V) and •OH generating in •O2H reacting with As(III). As(IV) emerges as a critical intermediate capable of initiating chain reactions in arsenic oxidation. This study provides atomic-scale insight into the As(III) oxidation in pyrite suspension, which is important for understanding arsenic behavior in analogous oxidation systems.

Modeling Fe(II) Complexes Using Neural Networks

We report a Fe(II) data set of more than 23000 conformers in both low-spin (LS) and high-spin (HS) states. This data set was generated to develop a neural network model that is capable of predicting the energy and the energy splitting as a function of the conformation of a Fe(II) organometallic complex. In order to achieve this, we propose a type of scaled electronic embedding to cover the long-range interactions implicitly in our neural network describing the Fe(II) organometallic complexes. For the total energy prediction, the lowest MAE is 0.037 eV, while the lowest MAE of the splitting energy is 0.030 eV. Compared to baseline models, which only incorporate short-range interactions, our scaled electronic embeddings improve the accuracy by over 70% for the prediction of the total energy and the splitting energy. With regard to semiempirical methods, our proposed models reduce the MAE, with respect to these methods, by 2 orders of magnitude.

Iron Heme Enzyme-Catalyzed Cyclopropanations with Diazirines as Carbene Precursors: Computational Explorations of Diazirine Activation and Cyclopropanation Mechanism

The mechanism of cyclopropanations with diazirines as air-stable and user-friendly alternatives to commonly employed diazo compounds within iron heme enzyme-catalyzed carbene transfer reactions has been studied by means of density functional theory (DFT) calculations of model systems, quantum mechanics/molecular mechanics (QM/MM) calculations, and molecular dynamics (MD) simulations of the iron carbene and the cyclopropanation transition state in the enzyme active site. The reaction is initiated by a direct diazirine-diazo isomerization occurring in the active site of the enzyme. In contrast, an isomerization mechanism proceeding via the formation of a free carbene intermediate in lieu of a direct, one-step isomerization process was observed for model systems. Subsequent reaction with benzyl acrylate takes place through stepwise C-C bond formation via a diradical intermediate, delivering the cyclopropane product. The origin of the observed diastereo- and enantioselectivity in the enzyme was investigated through MD simulations, which indicate a preferred formation of the cis-cyclopropane by steric control.

Rebound or Cage Escape? The Role of the Rebound Barrier for the Reactivity of Non-Heme High-Valent FeIV =O Species

Owing to their high reactivity and selectivity, variations in the spin ground state and a range of possible pathways, high-valent FeIV =O species are popular models with potential bioinspired applications. An interesting example of a structure-reactivity pattern is the detailed study with five nonheme amine-pyridine pentadentate ligand FeIV =O species, including N4py: [(L1 )FeIV =O]2+ (1), bntpen: [(L2 )FeIV =O]2+ (2), py2 tacn: [(L3 )FeIV =O]2+ (3), and two isomeric bispidine derivatives: [(L4 )FeIV =O]2+ (4) and [(L5 )FeIV =O]2+ (5). In this set, the order of increasing reactivity in the hydroxylation of cyclohexane differs from that with cyclohexadiene as substrate. A comprehensive DFT, ab initio CASSCF/NEVPT2 and DLPNO-CCSD(T) study is presented to untangle the observed patterns. These are well reproduced when both activation barriers for the C-H abstraction and the OH rebound are taken into account. An MO, NBO and deformation energy analysis reveals the importance of π(pyr) → π*xz (FeIII -OH) electron donation for weakening the FeIII -OH bond and thus reducing the rebound barrier. This requires that pyridine rings are oriented perpendicularly to the FeIII -OH bond and this is a subtle but crucial point in ligand design for non-heme iron alkane hydroxylation.

Benchmarks for transition metal spin-state energetics: why and how to employ experimental reference data?

Accurate prediction of energy differences between alternative spin states of transition metal complexes is essential in computational (bio)inorganic chemistry-for example, in characterization of spin crossover materials and in the theoretical modeling of open-shell reaction mechanisms-but it remains one of the most compelling problems for quantum chemistry methods. A part of this challenge is to obtain reliable reference data for benchmark studies, as even the highest-level applicable methods are known to give divergent results. This Perspective discusses two possible approaches to method benchmarking for spin-state energetics: using either theoretically computed or experiment-derived reference data. With the focus on the latter approach, an extensive general review is provided for the available experimental data of spin-state energetics and their interpretations in the context of benchmark studies, targeting the possibility of back-correcting the vibrational effects and the influence of solvents or crystalline environments. With a growing amount of experience, these effects can be now not only qualitatively understood, but also quantitatively modeled, providing the way to derive nearly chemically accurate estimates of the electronic spin-state gaps to be used as benchmarks and advancing our understanding of the phenomena related to spin states in condensed phases.

Natural Abiotic Iron-Oxido-Mediated Formation of C1 and C2 Compounds from Environmentally Important Methyl-Substituted Substrates

Organic and inorganic volatile compounds containing one carbon atom (C1), such as carbon dioxide, methane, methanol, formaldehyde, carbon monoxide, and chloromethane, are ubiquitous in the environment, are key components in global carbon cycling, play an important role in atmospheric physics and chemistry, e.g., as greenhouse gases, destroy stratospheric and tropospheric ozone, and control the atmospheric oxidation capacity. Up to now, most C1 compounds in the environment were associated with complex metabolic and enzymatic pathways in organisms or to combustion processes of organic matter. We now present compelling evidence that many C1 and C2 compounds have a common origin in methyl groups of methyl-substituted substrates that are cleaved by the iron oxide-mediated formation of methyl radicals. This scenario is derived from experiments with a mechanistically well-studied bispidine-iron-oxido complex as oxidant and dimethyl sulfoxide as the environmentally relevant model substrate and is supported by computational modeling based on density functional theory and ab initio quantum-chemical studies. The exhaustive experimental model studies, also involving extensive isotope labeling, are complemented with the substitution of the bispidine model system by environmentally relevant iron oxides and, finally, a collection of soils with varying iron and organic matter contents. The combination of all data suggests that the iron oxide-mediated formation of methyl radicals from methyl-substituted substrates is a common abiotic source for widespread C1 and C2 compounds in the environment.

Spin state and magnetic coupling in polynuclear Ni(II) complexes from density functional theory: is there an optimal amount of Fock exchange?

Reliable prediction of the ground-state spin and magnetic coupling constants in transition-metal complexes is a well-known challenge for density functional theory (DFT). One popular strategy for addressing this long-standing issue involves the modification of the fraction of Fock exchange in a hybrid functional. Here we explore the viability of this approach using three polynuclear metal-organic complexes based on a Ni4O4 cubane motif, having different ground state spin values (S = 0, 2, 4) owing to the use of different ligands. We systematically search for an optimum fraction of Fock exchange, across various global, range-separated, and double hybrid functionals. We find that for all functionals tested, at best there only exists a very narrow range of Fock exchange fractions which results in a correct prediction of the ground-state spin for all three complexes. The useful range is functional dependent, but general trends can be identified. Typically, at least two similar systems must be used in order to determine both an upper and lower limit of the optimal range. This is likely owing to conflicting demands of minimizing delocalization errors, which typically requires a higher percentage of Fock exchange, and addressing static correlation, which typically requires a lower one. Furthermore, we find that within the optimal range of Fock exchange, the sign and relative magnitude of Ni-Ni magnetic coupling constants are reasonably well reproduced, but there is still room for quantitative improvement in the prediction. Thus, the prediction of spin state and magnetic coupling in polynuclear complexes remains an ongoing challenge for DFT.

Density Functional Theory-Based Protocol to Calculate the Redox Potentials of First-row Transition Metal Complexes for Aqueous Redox Targeting Flow Batteries

Transition metal complexes are a promising class of redox mediators for targeting redox flow batteries due to the tunability of their electrochemical potentials. However, reliable time-efficient tools for the prediction of their reduction potentials are needed. In this work, we establish a suitable density functional theory protocol for their prediction using an initial experimental data set of aqueous iron complexes with bidentate ligands. The approach is then cross-validated using different complexes found in the redox-flow literature. We find that the solvation model affects the prediction accuracy more than the functional or basis set. The smallest errors are obtained using the COSMO-RS solvation model (mean average error (MAE)=0.24 V). With implicit solvation models, a general deviation from experimental results is observed. For a set of similar ligands, they can be corrected using simple linear regression (MAE=0.051 V for the initial set of iron complexes).

The role of agostic interaction in the mechanism of ethylene polymerisation using Cr(III) half-sandwich complexes: What dictates the reactivity?

Chromium-based catalysts play a significant role in the production of ultra-high molecular weight polyethylene, and half-sandwich functionalised-metallocene complexes were proven to be one of the most suitable candidates as catalysts for generating such large polymeric-length olefins. Earlier experimental studies on olefin polymerisation using a series of catalysts such as [L1-2CrCl2] (where L1 = 1-((pyridin-2-yl)methyl)indenyl (1) and L2 = 2-methyl-1-{[4-(yridinene-1-yl)yridine-2-yl]methyl}-1H-indenyl (2)) reveal significant variation where peripheral substitution on the ligand was found to influence the reactivity significantly. However, the specific ligand position that affects the reactivity has not been established. As these reactions are fast and robust, it is challenging to establish reactive intermediates via experiments, and therefore, mechanistic clues for such reactions are elusive. Here we have undertaken a detailed computational study by employing an array of DFT (uB3LYP-D3/def2-TZVP, CASSCF/NEVPT2, and DLPNO-CCSD(T) methods to explore the substituted and non-substituted pyridine-cyclo-pentadienyl chromium complexes and their influence on the catalytic activity in ethylene polymerisation. Our study not only unravels the catalytic pathway for olefin polymerisation for such Cr(III)-half-sandwich complexes but also reveals that the energetics of the formation of pseudo-three-coordinate alkyl intermediates is key to the variation in the reactivity observed. A detailed examination using MO and NBO analysis unveils the presence of a C-H⋯Cr agostic interaction that is found to significantly stabilise this intermediate when the pyridine ligand has strong electron-donating groups at its para position. The other substitutions, such as on the cyclopentadienyl ligand, neither yield the desired stability nor the desired interaction. Further studies on models support this proposal. In order to improve the efficiency and selectivity of catalytic systems in olefin polymerisation, we strongly advocate for the integration of agostic interactions as a crucial criterion in the design of future catalysts. Considering the prevalence of electron-deficient metal centres in successful olefin polymerisation catalysts, this research prompts a broader mechanistic inquiry to propose a unified approach for this industrially crucial reaction.

Coordinatively Unsaturated Metallates of Cobalt(II), Nickel(II), and Zinc(II) Guarded by a Rigid and Narrow Void

Both natural enzymatic systems and synthetic porous material catalysts utilize well-defined and uniform channels to dictate reaction selectivities on the basis of size or shape. Mimicry of this design element in homogeneous systems is generally difficult owing to the flexibility inherent in most small molecular species. Herein, we report the synthesis of a tripodal ligand scaffold that orients a narrow and rigid cavity atop accessible metal coordination space. The permanent void is formed through a macrocyclization reaction whereby the 3,5-dihydroxyphenyl arms are covalently linked through methylene bridges. Deprotonative metallation leads to anionic and coordinatively unsaturated complexes of divalent cobalt, nickel, and zinc. An analogous series of trigonal monopyramidal complexes bearing a nonmacrocyclized variant of the tripodal ligand are also reported. Physical characterization of the coordination complexes has been carried out using multiple spectroscopic techniques (NMR, EPR, and UV-vis), cyclic voltammetry, and X-ray diffraction. Complexes of the macrocyclized [L^OCH2O]^3- ligand retain a rigid cavity upon metallation, with this cavity guarding the entrance to the open axial coordination site. Through a combination of spectroscopic and computational studies, it is shown that acetonitrile entry into the void is sterically precluded, disrupting anticipated coordination at the intracavity site.

Comparison of the Performance of Density Functional Methods for the Description of Spin States and Binding Energies of Porphyrins

This work analyzes the performance of 250 electronic structure theory methods (including 240 density functional approximations) for the description of spin states and the binding properties of iron, manganese, and cobalt porphyrins. The assessment employs the Por21 database of high-level computational data (CASPT2 reference energies taken from the literature). Results show that current approximations fail to achieve the "chemical accuracy" target of 1.0 kcal/mol by a long margin. The best-performing methods achieve a mean unsigned error (MUE) <15.0 kcal/mol, but the errors are at least twice as large for most methods. Semilocal functionals and global hybrid functionals with a low percentage of exact exchange are found to be the least problematic for spin states and binding energies, in agreement with the general knowledge in transition metal computational chemistry. Approximations with high percentages of exact exchange (including range-separated and double-hybrid functionals) can lead to catastrophic failures. More modern approximations usually perform better than older functionals. An accurate statistical analysis of the results also casts doubts on some of the reference energies calculated using multireference methods. Suggestions and general guidelines for users are provided in the conclusions. These results hopefully stimulate advances for both the wave function and the density functional side of electronic structure calculations.

Mechanism of Hydroboration of CO2 Using an Fe Catalyst: What Controls the Reactivity and Product Selectivity?

Using a combination of density functional theory (DFT) and ab initio complete active space self-consistent field (CASSCF) calculations, various elementary steps in the mechanism of the reductive hydroboration of CO₂ to two-electron-reduced boryl formate, four-electron-reduced bis(boryl)acetal, and six-electron-reduced methoxy borane by the [Fe(H)₂(dmpe)₂] catalyst were established. The replacement of hydride by oxygen ligation after the boryl formate insertion step is the rate-determining step. Our work unveils, for the first time, (i) how a substrate steers product selectivity in this reaction and (ii) the importance of configurational mixing in contracting the kinetic barrier heights. Based on the reaction mechanism established, we have further focused on the effect of other metals, such as Mn and Co, on rate-determining steps and on catalyst regeneration.

Photodissociation Spectroscopy and Photofragment Imaging of the Fe+(Acetylene) Complex

Tunable laser photodissociation spectroscopy in the 700-400 nm region and photofragment imaging experiments are employed to investigate the Fe⁺(acetylene) ion-molecule complex. At energies above a threshold at 679 nm, continuous dissociation is detected throughout the visible wavelength region, with regions of broad structure. Comparison to the spectrum predicted by time-dependent density functional theory (TD-DFT) indicates that the complex has a quartet ground state. The dissociation threshold for Fe⁺(acetylene) at 679 nm provides the dissociation energy on the quartet potential energy surface. Correction for the atomic quartet-sextet spin state energy difference provides an adiabatic dissociation energy of 36.8 ± 0.2 kcal/mol. Photofragment imaging of the Fe⁺ photoproduct produced at 603.5 nm produces significant kinetic energy release (KER). The photon energy and the maximum value of the KER provide an upper limit on the dissociation energy of D₀ ≤ 34.6 ± 3.2 kcal/mol. The dissociation energies determined from the spectroscopy and photofragment imaging experiments agree nicely with the value determined previously by collision-induced dissociation (38.0 ± 2.6 kcal/mol). However, both values are significantly lower than those produced by computational chemistry at the DFT level using different functionals recommended for transition-metal chemistry.

Spin-state gaps and self-interaction-corrected density functional approximations: Octahedral Fe(II) complexes as case study

Accurate prediction of a spin-state energy difference is crucial for understanding the spin crossover phenomena and is very challenging for density functional approximations, especially for local and semi-local approximations due to delocalization errors. Here, we investigate the effect of the self-interaction error removal from the local spin density approximation (LSDA) and Perdew-Burke-Ernzerhof generalized gradient approximation on the spin-state gaps of Fe(II) complexes with various ligands using recently developed locally scaled self-interaction correction (LSIC) by Zope et al. [J. Chem. Phys. 151, 214108 (2019)]. The LSIC method is exact for one-electron density, recovers the uniform electron gas limit of the underlying functional, and approaches the well-known Perdew-Zunger self-interaction correction (PZSIC) as a particular case when the scaling factor is set to unity. Our results, when compared with reference diffusion Monte Carlo results, show that the PZSIC method significantly overestimates spin-state gaps favoring low spin states for all ligands and does not improve upon density functional approximations. The perturbative LSIC-LSDA using PZSIC densities significantly improves the gaps with a mean absolute error of 0.51 eV but slightly overcorrects for the stronger CO ligands. The quasi-self-consistent LSIC-LSDA, such as coupled-cluster single double and perturbative triple [CCSD(T)], gives a correct sign of spin-state gaps for all ligands with a mean absolute error of 0.56 eV, comparable to that of CCSD(T) (0.49 eV).

Does the Spin State and Oriented External Electric Field Boost the Efficiency of Fe(II) Pincer Catalyst toward CO2 Hydrogenation Reaction?

In this study, we have explored the catalytic reactivities of four PNP-pincer supported Fe(II) complexes, namely, [(^iPrPN^MeP)FeH₂(CO)] (1), [(^iPrPN^MeP)FeH(CO)(BH₄)] (2), [(^iPrPN^HP)FeH₂(CO)] (3), and [(^iPrPN^MeP)FeH(BH₄)] (4) (^iPrPN^MeP = MeN{CH₂CH₂(PⁱPr₂)}₂ and ^iPrPN^HP = HN{CH₂CH₂(PⁱPr₂)}₂) toward reductive CO₂ hydrogenation for formate production. Our density functional theory and ab initio complete active space self-consistent field study have identified three fundamental steps in this catalytic transformation: (i) anchoring of the CO₂ molecule in the vicinity of the metal using noncovalent interactions, (ii) catalyst regeneration via H₂ cleavage, and (iii) formate rebound step leading to catalytic poisoning. The variations in the catalytic efficiency observed among these catalysts were attributed to either easing of steps (i) and (ii) or the hampering step (iii). This can be achieved in various chemical/non-chemical ways, for instance, (a) incorporation of strong-field ligands such as CO facilitating single-state reactivity and eliminating two-state reactivity that generally enhances the rate and (b) inclusion of Lewis acids such as LiOTf and strong bases found to either avoid catalytic poisoning or ease the H-H cleavages, to enhance the rate of reaction (c) evading mixing of excited open-shell singlet states to the ground closed-shell singlet state that hampers the catalytic regeneration. We have probed the role of oriented external electric fields (OEEFs) in the entire mechanistic profile for the best and worst catalyst, and our study suggests that imposing OEEFs opposite to the reaction axis (z-axis) fastens the catalytic regeneration step and, at the same time, hampers catalytic poisoning. The application of OEEFs is found to regulate the energetics of various spin states and can hamper two-state reactivity, therefore increasing the efficiency. Thus, this study provides insights into the CO₂ hydrogenation mechanism where the role of bases/Lewis acid, ligand design, spin states, and electric field in a particular direction has been established and is, therefore, likely to pave the way forward for a new generation of catalysts.

Rational design of iron catalysts for C-X bond activation

We have quantum chemically studied the iron-mediated CX bond activation (X = H, Cl, CH₃ ) by d⁸ -FeL₄ complexes using relativistic density functional theory at ZORA-OPBE/TZ2P. We find that by either modulating the electronic effects of a generic iron-catalyst by a set of ligands, that is, CO, BF, PH₃ , BN(CH₃ )₂ , or by manipulating structural effects through the introduction of bidentate ligands, that is, PH₂ (CH₂ )_n PH₂ with n = 6-1, one can significantly decrease the reaction barrier for the CX bond activation. The combination of both tuning handles causes a decrease of the CH activation barrier from 10.4 to 4.6 kcal mol^-1 . Our activation strain and Kohn-Sham molecular orbital analyses reveal that the electronic tuning works via optimizing the catalyst-substrate interaction by introducing a strong second backdonation interaction (i.e., "ligand-assisted" interaction), while the mechanism for structural tuning is mainly caused by the reduction of the required activation strain because of the pre-distortion of the catalyst. In all, we present design principles for iron-based catalysts that mimic the favorable behavior of their well-known palladium analogs in the bond-activation step of cross-coupling reactions.

Spin-State Splittings in 3d Transition-Metal Complexes Revisited: Toward a Reliable Theory Benchmark

A new composite method for the calculation of spin-crossover energies in 3d transition-metal complexes based on multireference methods is presented. The method reduces to MRCISD+Q at the complete-basis-set (CBS) level for atomic ions, for which it gives excitation energies with a mean absolute error of only ca. 0.01 eV. For molecular complexes, the CASPT2+δMRCI composite approach corresponds to a CASPT2/CBS calculation augmented by a high-level MRCISD+Q-CASPT2 correction with a smaller ligand basis set. For a set of [Fe(He)6]n+ test complexes, the approach reproduces full MRCISD+Q/CBS results to within better than 0.04 eV, without depending on any arbitrary IPEA shifts. The high-quality CASPT2+δMRCI method has then been applied to a series of 3d transition-metal hexaqua complexes in aqueous solution, augmented by an elaborate 3D-RISM-SCF solvent treatment of the underlying structures. It provides unprecedented agreement with experiment for the lowest-lying vertical spin-flip excitation energies, except for the Fe³⁺ system. Closer examination of the latter case provides strong evidence that the observed lowest-energy excitation at 1.56 eV, which has been used frequently for evaluating quantum-chemical methods, does not arise from the iron(III) hexaqua complex in solution, but from its singly deprotonated counterpart, [Fe(H2O)5OH]2+.

Coordination and Spin States in Fe+(C2H2)n Complexes Studied with Selected-Ion Infrared Spectroscopy

Fe⁺(acetylene)_n ion-molecule complexes are produced in a supersonic molecular beam with pulsed laser vaporization. These ions are mass selected and studied with infrared photodissociation spectroscopy in the C-H stretching region, complemented by computational chemistry calculations. All C-H stretch vibrations are shifted to frequencies lower than the vibrations of isolated acetylene because of the charge transfer that occurs between the metal ion and the molecules. Complexes in the size range of n = 1-4 are found to have structures with individual acetylene molecules bound to the core metal ion via cation-π interactions. The coordination is completed with four ligands in a structure close to a distorted tetrahedron. Larger complexes in the range of n = 5-8 have external acetylene molecules solvating this n = 4 core ion via CH-π bonding to inner-shell ligands. DFT computations predict that quartet spin states are more stable for all complex sizes, but infrared spectra for quartet and doublet spin states are quite similar, precluding definitive determination of the spin states. There is no evidence for any of these complexes having acetylenes coupled into reacted structures. This is consistent with computed thermochemistry, which finds significant activation barriers to such reactions.

Spin-State Splittings in 3d Transition-Metal Complexes Revisited: Benchmarking Approximate Methods for Adiabatic Spin-State Energy Differences in Fe(II) Complexes

The CASPT2+δMRCI composite approach reported in a companion paper has been extended and used to provide high-quality reference data for a series of adiabatic spin gaps (defined as ΔE = E_quintet - E_singlet) of [Fe^IIL₆]²⁺ complexes (L = CNH, CO, NCH, NH₃, H₂O), either at nonrelativistic level or including scalar relativistic effects. These highly accurate data have been used to evaluate the performance of various more approximate methods. Coupled-cluster theory with singles, doubles, and perturbative triples, CCSD(T), is found to agree well with the new reference data for Werner-type complexes but exhibits larger underestimates by up to 70 kJ/mol for the π-acceptor ligands, due to appreciable static correlation in the low-spin states of these systems. Widely used domain-based local CCSD(T) calculations, DLPNO-CCSD(T), are shown to depend very sensitively on the cutoff values used to construct the localized domains, and standard values are not sufficient. A large number of density functional approximations have been evaluated against the new reference data. The B2PLYP double hybrid gives the smallest deviations, but several functionals from different rungs of the usual ladder hierarchy give mean absolute deviations below 20 kJ/mol. This includes the B97-D semilocal functional, the PBE0* global hybrid with 15% exact-exchange admixture, as well as the local hybrids LH07s-SVWN and LH07t-SVWN. Several further functionals achieve mean absolute errors below 30 kJ/mol (M06L-D4, SSB-D, B97-1-D4, LC-ωPBE-D4, LH12ct-SsirPW92-D4, LH12ct-SsifPW92-D4, LH14t-calPBE-D4, LHJ-HFcal-D4, and several further double hybrids) and thereby also still overall outperform CCSD(T) or uncorrected CASPT2. While exact-exchange admixture is a crucial factor in favoring high-spin states, the present evaluations confirm that other aspects can be important as well. A number of the better-performing functionals underestimate the spin gaps for the π-acceptor ligands but overestimate them for L = NH₃, H₂O. In contrast to a previous suggestion, non-self-consistent density functional theory (DFT) computations on top of Hartree-Fock orbitals are not a promising path to produce accurate spin gaps in such complexes.

Structural and electronic properties of the active site of [ZnFe] SulE

The function of the recently isolated sulerythrin (SulE) has been investigated using a combination of structural and electronic analyses based on quantum mechanical calculations. In the SulE structure of Fushinobu et al. (2003), isolated from a strictly aerobic archaeon, Sulfolobus tokadaii, a dioxygen-containing species was tentatively included at the active site during crystallographic refinement although the substrate specificity of SulE remains unclear. Studies have suggested that a structurally related enzyme, rubrerythrin, functions as a hydrogen peroxide reductase. Since SulE is a truncated version of rubrerythrin, the enzymes are hypothesized to function similarly. Hence, using available X-ray crystallography data (1.7 Å), we constructed various models of SulE containing a ZnII–Fe active site, differing in the nature of the substrate specificity (O2, H2O2), the oxidation level and the spin state of the iron ion, and the protonation states of the coordinating glutamate residues. Also, the substrate H2O2 is modeled in two possible configurations, differing in the orientation of the hydrogen atoms. Overall, the optimized geometries with an O2 substrate do not show good agreement with the experimentally resolved geometry. In contrast, excellent agreement between crystal structure arrangement and optimized geometries is achieved considering a H2O2 substrate and FeII in both spin states, when Glu92 is protonated. These results suggest that the dioxo species detected at the [ZnFe] active site of sulerythrin is H2O2, rather than an O2 molecule in agreement with experimental data indicating that only the diferrous oxidation state of the dimetal site in rubrerythrin reacts rapidly with H2O2. Based on our computations, we proposed a possible reaction pathway for substrate binding at the ZnFeII site of SulE with a H2O2 substrate. In this reaction pathway, Fe or another electron donor, such as NAD(P)H, catalyzes the reduction of H2O2 to water at the zinc–iron site.

Dimerization of [FeIII(bpy)3]3+ in Aqueous Solutions: Elucidating a Mechanism Based on Historical Proposals, Electrochemical Data, and Computational Free Energy Analysis

Iron(II) tris-bipyridine, [Fe^II(bpy)₃]²⁺, is a historically significant organometallic coordination complex with attractive redox and photophysical properties. With respect to energy storage, it is a low-cost, high-redox potential complex and thus attractive for use as a catholyte in aqueous redox flow batteries. Despite these favorable characteristics, its oxidized Fe(III) form undergoes dimerization to form μ-O-[Fe^III(bpy)₂(H₂O)]₂⁴⁺, leading to a dramatic ∼0.7 V decrease during battery discharge. To date, the energetics and complete mechanism of this slow, sequential electrochemical-chemical (EC) process, which includes electron transfer, nucleophilic attack, ligand cleavage, μ-oxo bond formation, and spin state transition, have not been elucidated. Using cyclic voltammetry, redox flow battery data, and density functional theory calculations guided by previously proposed mechanisms, we modeled more than 100 complexes and performed more than 50 geometry scans to resolve the key steps dictating these complex chemical processes. Quantitative free energy surfaces are developed to model the mechanism of dimerization accounting for the spins and identities of any possible Fe(II), Fe(III), or Fe(IV) intermediates. Electrochemical reduction of the dimer regenerates [Fe^II(bpy)₃]²⁺ in an overall reversible process. Computational electrochemistry interrogates the influence of spin state, coordination environment, and molecular conformation at the electrode-electrolyte interface through a proposed stepwise dimer reduction process. Experimentally, we show that the considerable overpotential associated with this event can be catalytically mitigated with disparate materials, including platinum, copper hexacyanoferrate, and activated carbon. The findings are of fundamental and applied significance and could elevate [Fe^II(bpy)₃]²⁺ and its derivatives to play a vital role in the burgeoning renewable energy economy.

Reconciling Local Coupled Cluster with Multireference Approaches for Transition Metal Spin-State Energetics

Spin-state energetics of transition metal complexes remain one of the most challenging targets for electronic structure methods. Among single-reference wave function approaches, local correlation approximations to coupled cluster theory, most notably the domain-based local pair natural orbital (DLPNO) approach, hold the promise of bringing the accuracy of coupled cluster theory with single, double, and perturbative triple excitations, CCSD(T), to molecular systems of realistic size with acceptable computational cost. However, recent studies on spin-state energetics of iron-containing systems raised doubts about the ability of the DLPNO approach to adequately and systematically approximate energetics obtained by the reference-quality complete active space second-order perturbation theory with coupled-cluster semicore correlation, CASPT2/CC. Here, we revisit this problem using a diverse set of iron complexes and examine several aspects of the application of the DLPNO approach. We show that DLPNO-CCSD(T) can accurately reproduce both CASPT2/CC and canonical CCSD(T) results if two basic principles are followed. These include the consistent use of the improved iterative (T₁) versus the semicanonical perturbative triple corrections and, most importantly, a simple two-point extrapolation to the PNO space limit. The latter practically eliminates errors arising from the default truncation of electron-pair correlation spaces and should be viewed as standard practice in applications of the method to transition metal spin-state energetics. Our results show that reference-quality results can be readily achieved with DLPNO-CCSD(T) if these principles are followed. This is important also in view of the applicability of the method to larger single-reference systems and multinuclear clusters, whose treatment of dynamic correlation would be challenging for multireference-based approaches.

Ionization Energies and Redox Potentials of Hydrated Transition Metal Ions: Evaluation of Domain-Based Local Pair Natural Orbital Coupled Cluster Approaches

Hydrated transition metal ions are prototypical systems that can be used to model properties of transition metals in complex chemical environments. These seemingly simple systems present challenges for computational chemistry and are thus crucial in evaluations of quantum chemical methods for spin-state and redox energetics. In this work, we explore the applicability of the domain-based pair natural orbital implementation of coupled cluster (DLPNO-CC) theory to the calculation of ionization energies and redox potentials for hydrated ions of all first transition row (3d) metals in the 2+/3+ oxidation states, in connection with various solvation approaches. In terms of model definition, we investigate the construction of a minimally explicitly hydrated quantum cluster with a first and second hydration layer. We report on the convergence with respect to the coupled cluster expansion and the PNO space, as well as on the role of perturbative triple excitations. A recent implementation of the conductor-like polarizable continuum model (CPCM) for the DLPNO-CC approach is employed to determine self-consistent redox potentials at the coupled cluster level. Our results establish conditions for the convergence of DLPNO-CCSD(T) energetics and stress the absolute necessity to explicitly consider the second solvation sphere even when CPCM is used. The achievable accuracy for redox potentials of a practical DLPNO-based approach is, on average, 0.13 V. Furthermore, multilayer approaches that combine a higher-level DLPNO-CCSD(T) description of the first solvation sphere with a lower-level description of the second solvation layer are investigated. The present work establishes optimal and transferable methodological choices for employing DLPNO-based coupled cluster theory, the associated CPCM implementation, and cost-efficient multilayer derivatives of the approach for open-shell transition metal systems in complex environments.

Catalytic properties of the ferryl ion in the solid state: a computational review

This review summarises the last findings in the emerging field of heterogeneous catalytic oxidation of light alkanes by ferryl species supported on solid-state systems such as the conversion of methane into methanol by FeO-MOF74.

Concentration effects on optical properties, DFT, crystal characterization and α-glucosidase activity studies: Novel Zn(II) complex

A novel Zn(II) complex of 6-ClpicH and picH was synthesized and its structure was determined by XRD technique. The detailed experimental optical susceptibility and band gap, refractive index, linear polarizability, optical and electrical conductivity parameters in various concentrations were investigated by means of the UV-Vis spectroscopic data. The optical band gap, refractive index (n), linear optical susceptibility (χ⁽¹⁾), third-order nonlinear optical susceptibility (χ⁽³⁾), second- and third-order nonlinear optical (β and γ) parameters were examined by using DFT/M06-L and ωB97XD/6-311++G(d,p) levels. The IC₅₀ value of Zn(II) complex against α-glucosidase was also obtained at 0.44 mM. The experimental band gap of the Zn(II) complex at 13, 33, 44 and 94 µM concentrations in ethanol were found to be 4.38, 4.37, 4.35 and 4.28 eV, respectively. The third-order NLO susceptibility χ⁽³⁾ parameter at 94 µM concentration corresponding to the photon energies of 4.6 and 5.7 eV in the UV-Vis region were observed at 206.6 × 10^-13 and 294.3 × 10^-13 esu, respectively. Besides, the theoretical χ⁽³⁾ values were obtained at 50.58 × 10^-13 and 20.37 × 10^-13 esu by using M06-L level. These results indicate that Zn(II) complex could be an effective third-order NLO candidate material. In brief, the detailed theoretical and experimental structural, spectral and optical properties of the Zn(II) complex were presented comparatively.

Non-Heme-Iron-Mediated Selective Halogenation of Unactivated Carbon-Hydrogen Bonds

Oxidation of the iron(II) precursor [(L¹)Fe^IICl₂], where L¹ is a tetradentate bispidine, with soluble iodosylbenzene (^sPhIO) leads to the extremely reactive ferryl oxidant [(L¹)(Cl)Fe^IV=O]⁺ with a cis disposition of the chlorido and oxido coligands, as observed in non‐heme halogenase enzymes. Experimental data indicate that, with cyclohexane as substrate, there is selective formation of chlorocyclohexane, the halogenation being initiated by C−H abstraction and the result of a rebound of the ensuing radical to an iron‐bound Cl⁻. The time‐resolved formation of the halogenation product indicates that this primarily results from ^sPhIO oxidation of an initially formed oxido‐bridged diiron(III) resting state. The high yield of up to >70 % (stoichiometric reaction) as well as the differing reactivities of free Fe²⁺ and Fe³⁺ in comparison with [(L¹)Fe^IICl₂] indicate a high complex stability of the bispidine‐iron complexes. DFT analysis shows that, due to a large driving force and small triplet‐quintet gap, [(L¹)(Cl)Fe^IV=O]⁺ is the most reactive small‐molecule halogenase model, that the Fe^III/radical rebound intermediate has a relatively long lifetime (as supported by experimentally observed cage escape), and that this intermediate has, as observed experimentally, a lower energy barrier to the halogenation than the hydroxylation product; this is shown to primarily be due to steric effects.

DFT Functionals for Modeling of Polyethylene Chains Cross-Linked by Metal Atoms. DLPNO-CCSD(T) Benchmark Calculations

Density functional theory (DFT) functionals for calculations of binding energies (BEs) of the polyethylene (PE) chains cross-linked by selected metal atoms (M) are benchmarked against DLPNO-CCSD(T) and DLPNO-CCSD(T1) data. PEX-M-PEX complexes as compared with plain parallel PEX···PEX chains with X = 3-9 carbon atoms are model species characterized by a cooperative effect of covalent C-M-C bonds and interchain dispersion interactions. The accuracy of DLPNO-CC methods was assessed by a comparison of BEs with the canonical CCSD(T) results for small PE3-M-PE3 complexes. Functionals for PEX···PEX and closed-shell PEX-M-PEX complexes (M = Be, Mg, Zn) were benchmarked against DLPNO-CCSD(T) BEs; open-shell complexes (M = Li, Ag, Au) were benchmarked against the DLPNO-CCSD(T1) method with iterative triples. Three dispersion corrections were combined with 25 DFT functionals for calculations of BEs with respect to PEX-M and PEX fragments employing def2-TZVPP and def2-QZVPP basis sets. Accuracy to within 5% for the closed-shell PEX-M-PEX complexes was achieved with five functionals. Less accurate are functionals for the open-shell PEX-M-PEX complexes; only two functionals deviate by less than 15% from DLPNO-CCSD(T1). Particularly problematic were PEX-Li-PEX complexes. A reasonable overall performance across all complexes in terms of the mean absolute percentage error is found for the range-separated hybrid functionals ωB97X-D3 and CAM-B3LYP/D3(BJ)-ABC.

Mechanistic Insights into the Oxygen Atom Transfer Reactions by Nonheme Manganese Complex: A Computational Case Study on the Comparative Oxidative Ability of Manganese-Hydroperoxo vs High-Valent MnIV═O and MnIV-OH Intermediates

Understanding the comparative oxidative abilities of high-valent metal-oxo/hydroxo/hydroperoxo species holds the key to robust biomimic catalysts that perform desired organic transformations with very high selectivity and efficiency. The comparative oxidative abilities of popular high-valent iron-oxo and manganese-oxo species are often counterintuitive, for example, oxygen atom transfer (OAT) reaction by [(Me₂EBC)Mn^IV-OOH]³⁺, [(Me₂EBC)Mn^IV-OH]³⁺, and [(Me₂EBC)Mn^IV═O]²⁺ (Me₂EBC = 4,11-dimethyl-1,4,8,11-tetraazabicyclo[6.6.2]hexadecane) shows extremely high reactivity for Mn^IV-OOH species and no reactivity for Mn^IV-OH and Mn^IV═O species toward alkyl/aromatic sulfides. Using a combination of density functional theory (DFT) and ab initio domain-based local pair natural orbital coupled-cluster with single, double, and perturbative triples excitation (DLPNO-CCSD(T)) and complete-active space self-consistent field/N-electron valence perturbation theory second order (CASSCF/NEVPT2) calculations, here, we have explored the electronic structures and sulfoxidation mechanism of these species. Our calculations unveil that Mn^IV-OOH reacts through distal oxygen atom with the substrate via electron transfer (ET) mechanism with a very small kinetic barrier (16.5 kJ/mol), placing this species at the top among the best-known catalysts for such transformations. The Mn^IV-OH and Mn^IV═O species have a much larger barrier. The mechanism has also been found to switch from ET in the former to concerted in the latter, rendering both unreactive under the tested experimental conditions. Intrinsic differences in the electronic structures, such as the presence and absence of the multiconfigurational character coupled with the steric effects, are responsible for such variations observed. This comparative oxidative ability that runs contrary to the popular iron-oxo/hydroperoxo reactivity will have larger mechanistic implications in understanding the reactivity of biomimic catalysts and the underlying mechanisms in PSII.

Pathways of the Extremely Reactive Iron(IV)-oxido complexes with Tetradentate Bispidine Ligands

The nonheme iron(IV)-oxido complex trans-N3-[(L1 )FeIV =O(Cl)]+ , where L1 is a derivative of the tetradentate bispidine 2,4-di(pyridine-2-yl)-3,7-diazabicyclo[3.3.1]nonane-1-one, is known to have an S=1 electronic ground state and to be an extremely reactive oxidant for oxygen atom transfer (OAT) and hydrogen atom abstraction (HAA) processes. Here we show that, in spite of this ferryl oxidant having the "wrong" spin ground state, it is the most reactive nonheme iron model system known so far and of a similar order of reactivity as nonheme iron enzymes (C-H abstraction of cyclohexane, -90 °C (propionitrile), t1/2 =3.5 sec). Discussed are spectroscopic and kinetic data, supported by a DFT-based theoretical analysis, which indicate that substrate oxidation is significantly faster than self-decay processes due to an intramolecular demethylation pathway and formation of an oxido-bridged diiron(III) intermediate. It is also shown that the iron(III)-chlorido-hydroxido/cyclohexyl radical intermediate, resulting from C-H abstraction, selectively produces chlorocyclohexane in a rebound process. However, the life-time of the intermediate is so long that other reaction channels (known as cage escape) become important, and much of the C-H abstraction therefore is unproductive. In bulk reactions at ambient temperature and at longer time scales, there is formation of significant amounts of oxidation product - selectively of chlorocyclohexane - and it is shown that this originates from oxidation of the oxido-bridged diiron(III) resting state.

DFT mechanistic study on the formation of 8-oxoguanine and spiroiminodihydantoin mediated by iron Fenton reactions

Fenton reactions unavoidably take place in the human body and have been demonstrated to cause oxidative DNA damage. However, the molecular-level understanding of DNA damage mediated by Fenton reactions is limited. Herein, density functional theory (DFT) calculations were made to investigate the counterion effects on aqueous Fenton reactions and the detailed mechanisms of chemical modifications to guanine induced by Fenton reactions. Our calculations show that the activation energy of the Fenton reaction catalyzed by a pure aquo complex [FeII(H2O)6]2+ is too high to agree with experiments, whereas complexation with counteranions reduces the activation energy to a reasonable range. This result suggests that FeII-counteranion complexes are the real catalyst for fast aqueous Fenton reactions. In addition, we found that the Fenton oxidation mediated by FeII bonded to the N7 atom of guanine can result in the formation of 8-oxoguanine and spiroiminodihydantoin through multiple reaction pathways, including the electrophilic addition of ˙OH, H-abstraction by ˙OH, and oxygen atom transfer of oxoiron(iv) species. The activation of hydrogen peroxide by ferrous iron is the rate-determining step. The guanine N7-bound iron ion and the coordinated counteranion were found to play an important role in the Fenton oxidation of guanine.

Direct Deoxydehydration of Cyclic trans-Diol Substrates: An Experimental and Computational Study of the Reaction Mechanism of Vanadium(V)-based Catalysis*

The deoxydehydration of carbohydrates represents a key target to leverage renewable biomass resources chemically. Using a vanadium(V)-based catalyst, it was possible to directly deoxydehydrate cyclic trans-diol substrates. Accompanying mechanistic characterisation of this process by density functional calculations pointed to an energetically tractable route for deoxydehydration of cyclic trans-diol substrates involving stepwise cleavage of the diol C-O bonds via the triplet state; experimentally, this was supported by light dependence of the reaction. Calculations also indicated that cyclic cis-diols and a linear diol substrate could additionally proceed by a concerted singlet DODH mechanism. This work potentially opens a new and cost-effective way to efficiently convert carbohydrates of trans-diol stereochemistry into alkenes.

Structures and relative stability of hydrated ferrous ion clusters and temperature effects

Structures of solvated ferrous ion clusters have been investigated in the singlet and quintet spin states of the ferrous ion. Relative stabilities of isomers are also discussed at different temperatures.

Spin Splitting Energy of Transition Metals: A New, More Affordable Wave Function Benchmark Method and Its Use to Test Density Functional Theory

Accurately predicting the spin splitting energy of chemical species is important for understanding their reactivity and magnetic properties, but it is very challenging, especially for molecules containing transition metals. One impediment to progress is the scarcity of accurate benchmark data. Here we report a set of calculations designed to yield reliable benchmarks for simple transition-metal complexes that can be used to test density functional methods that are affordable for large systems of more practical interest. Various wave function methods are tested against experiment for Fe²⁺, Fe³⁺, and Co³⁺, including CASSCF, CASPT2, CASPT3, MRCISD, MRCISD+Q, ACPF, AQCC, CCSD(T), and CASPT2/CCSD(T) and also a new method called CASPT2.5, which is performed by taking the average of the CASPT2 and CASPT3 energies. We find that MRCISD+Q, ACPF, and AQCC require smaller active spaces for good accuracy than are required by CASPT2 and CASPT3, and this aspect may be important for calculations on larger molecules; here we find that CASPT2.5 extrapolated to a complete basis set is the most suitable method-in terms of computational cost and in terms of accuracy on monatomic systems-and therefore we chose this method for molecular benchmarks. Then Kohn-Sham density functional calculations with 60 exchange-correlation functionals are tested for FeF₂, FeCl₂, and CoF₂. We find that MN15-L, M06-SX, and revM06 have very good agreement with CASPT2.5 benchmarks in terms of both the spin splitting energy and the optimized geometry for each spin state. In addition, we recommend def2-TZVP as the most suitable basis set to perform density functional calculations for molecular spin splitting energies; extra polarization functions in the basis set do not help to increase the accuracy of the spin splitting energy in KS calculations.

Seeing Is Believing: Experimental Spin States from Machine Learning Model Structure Predictions

Determination of ground-state spins of open-shell transition-metal complexes is critical to understanding catalytic and materials properties but also challenging with approximate electronic structure methods. As an alternative approach, we demonstrate how structure alone can be used to guide assignment of ground-state spin from experimentally determined crystal structures of transition-metal complexes. We first identify the limits of distance-based heuristics from distributions of metal–ligand bond lengths of over 2000 unique mononuclear Fe(II)/Fe(III) transition-metal complexes. To overcome these limits, we employ artificial neural networks (ANNs) to predict spin-state-dependent metal–ligand bond lengths and classify experimental ground-state spins based on agreement of experimental structures with the ANN predictions. Although the ANN is trained on hybrid density functional theory data, we exploit the method-insensitivity of geometric properties to enable assignment of ground states for the majority (ca. 80–90%) of structures. We demonstrate the utility of the ANN by data-mining the literature for spin-crossover (SCO) complexes, which have experimentally observed temperature-dependent geometric structure changes, by correctly assigning almost all (>95%) spin states in the 46 Fe(II) SCO complex set. This approach represents a promising complement to more conventional energy-based spin-state assignment from electronic structure theory at the low cost of a machine learning model.

Revealing the Iron-Catalyzed β-Methyl Scission of tert-Butoxyl Radicals via the Mechanistic Studies of Carboazidation of Alkenes

We describe here a mechanistic study of the iron-catalyzed carboazidation of alkenes involving an intriguing metal-assisted β-methyl scission process. Although t-BuO radical has frequently been observed in experiments, the β-methyl scission from a t-BuO radical into a methyl radical and acetone is still broadly believed to be thermodynamically spontaneous and difficult to control. An iron-catalyzed β-methyl scission of t-BuO is investigated in this work. Compared to a free t-BuO radical, the coordination at the iron atom reduces the activation energy for the scission from 9.3 to 3.9 ~ 5.2 kcal/mol. The low activation energy makes the iron-catalyzed β-methyl scission of t-BuO radicals almost an incomparably facile process and explains the selective formation of methyl radicals at low temperature in the presence of some iron catalysts. In addition, a radical relay process and an outer-sphere radical azidation process in the iron-catalyzed carboazidation of alkenes are suggested by density functional theory (DFT) calculations.

Transition Metal Spin-State Energetics by MC-PDFT with High Local Exchange

The energetics of the spin states of transition metal complexes have been explored with a variety of electronic structure methods, but the calculations require a compromise between accuracy and affordability. In this work, the spin splittings of several iron complexes are studied with multiconfiguration pair-density functional theory (MC-PDFT). The results are compared to previously published results obtained by complete active space second-order perturbation theory (CASPT2) and CASPT2 with coupled-cluster semicore correlation (CASPT2/CC). In contrast to CASPT2's systematic overstabilization of high-spin states with respect to the CASPT2/CC reference, MC-PDFT with the tPBE on-top functional understabilizes high-spin states. This systematic understabilization is largely corrected by revising the exchange and correlation contributions to the on-top functional using the high local-exchange approximation (tPBE-HLE). Moreover, tPBE-HLE correctly predicts the spin of the ground state in most cases, while CASPT2 incorrectly predicts high-spin ground states in all cases. This is encouraging for practical work because tPBE and tPBE-HLE are faster than CASPT2 by a factor of 50 even in a moderately sized example.

Large-scale comparison of 3d and 4d transition metal complexes illuminates the reduced effect of exchange on second-row spin-state energetics

The origin of distinct 3d vs. 4d transition metal complex sensitivity to exchange is explored over a large data set.

Appraising spin-state energetics in transition metal complexes using double-hybrid models: accountability of SOS0-PBESCAN0-2(a) as a promising paradigm

Through a comprehensive survey, reliable double-hybrid models have been validated and proposed for spin-state energetics in transition metal complexes.