Assessment of the applicability of DFT methods to [Cp*Rh]-catalyzed hydrogen evolution processes

The present computational study provides a benchmark of density functional theory (DFT) methods in describing hydrogen evolution processes catalyzed by [Cp*Rh]-containing organometallic complexes. A test set was composed of 26 elementary reactions featuring chemical transformations and bonding situations essential for the field, including the emerging concept of non-innocent Cp* behavior. Reference values were obtained from a highly accurate 3/4 complete basis set and 6/7 complete PNO space extrapolated DLPNO-CCSD(T) energies. The performance of lower-level extrapolation procedures was also assessed. We considered 84 density functionals (DF) (including 13 generalized gradient approximations (GGA), nine meta-GGAs, 33 hybrids, and 29 double-hybrids) and three composite methods (HF-3c, PBEh-3c, and r2SCAN-3c), combined with different types of dispersion corrections (D3(0), D3BJ, D4, and VV10). The most accurate approach is the PBE0-DH-D3BJ (MAD of 1.36 kcal mol-1) followed by TPSS0-D3BJ (MAD of 1.60 kcal mol-1). Low-cost r2SCAN-3c composite provides a less accurate but much faster alternative (MAD of 2.39 kcal mol-1). The widely used Minnesota-family M06-L, M06, and M06-2X DFs should be avoided (MADs of 3.70, 3.94, and 4.01 kcal mol-1, respectively).

Synthesis, Characterization, and Reactivity of Bispidine-Iron(IV)-Tosylimido Species

Reported are the synthesis and detailed studies of the iron(IV)-tosylimido complexes of two isomeric pentadentate bispidine ligands (bispidines are 3,7-diazabicyclo[3.3.1]nonane derivatives). This completes a series of five tosylimido complexes with comparable pentadentate amine/pyridine ligands, where the corresponding [(L)FeIV═O]2+ oxidants have been studied in detail. The characterization of the two new complexes in solution (UV-vis-NIR, Mössbauer, HR-ESI-MS) shows that these oxidants have an intermediate spin (S = 1) electronic ground state. The reactivities have been studied as oxidants in C-H activation at 1,3-cyclohexadiene and nitrogen atom transfer to thioanisole. For the latter substrate, the entire set of data for the five ligands and for both nitrogen and oxygen atom transfer is now available and the interesting observation is that oxygen atom transfer is, as expected, generally faster than nitrogen atom transfer, with the exception of the two ligands that have four and three pyridine groups oriented parallel to the Fe-O and Fe-N axes. A thorough DFT analysis indicates that this is due to steric effects in the case of the [(L)FeIV═O]2+ species, which are less important in the [(L)FeIV═NTs]2+ compounds due to partial electron transfer from the thioanisole substrate to the iron(IV)-tosylimido oxidant.

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.

C-H bond activation by high-valent iron/cobalt-oxo complexes: a quantum chemical modeling approach

High-valent metal-oxo species serve as key intermediates in the activation of inert C-H bonds. Here, we present a comprehensive DFT analysis of the parameters that have been proposed as influencing factors in modeled high-valent metal-oxo mediated C-H activation reactions. Our approach involves utilizing DFT calculations to explore the electronic structures of modeled FeIVO (species 1) and CoIVO ↔ CoIII-O˙ (species 2), scrutinizing their capacity to predict improved catalytic activity. DFT and DLPNO-CCSD(T) calculations predict that the iron-oxo species possesses a triplet as the ground state, while the cobalt-oxo has a doublet as the ground state. Furthermore, we have investigated the mechanistic pathways for the first C-H bond activation, as well as the desaturation of the alkanes. The mechanism was determined to be a two-step process, wherein the first hydrogen atom abstraction (HAA) represents the rate-limiting step, involving the proton-coupled electron transfer (PCET) process. However, we found that the second HAA step is highly exothermic for both species. Our calculations suggest that the iron-oxo species (Fe-O = 1.672 Å) exhibit relatively sluggish behavior compared to the cobalt-oxo species (Co-O = 1.854 Å) in C-H bond activation, attributed to a weak metal-oxygen bond. MO, NBO, and deformation energy analysis reveal the importance of weakening the M-O bond in the cobalt species, thereby reducing the overall barrier to the reaction. This catalyst was found to have a C-H activation barrier relatively smaller than that previously reported in the literature.

Benchmarking Density Functional Theory Methods for Metalloenzyme Reactions: The Introduction of the MME55 Set

We present a new benchmark set of metalloenzyme model reaction energies and barrier heights that we call MME55. The set contains 10 different enzymes, representing eight transition metals, both open and closed shell systems, and system sizes of up to 116 atoms. We use four DLPNO-CCSD(T)-based approaches to calculate reference values against which we then benchmark the performance of a range of density functional approximations with and without dispersion corrections. Dispersion corrections improve the results across the board, and triple-ζ basis sets provide the best balance of efficiency and accuracy. Jacob's ladder is reproduced for the whole set based on averaged mean absolute (percent) deviations, with the double hybrids SOS0-PBE0-2-D3(BJ) and revDOD-PBEP86-D4 standing out as the most accurate methods for the MME55 set. The range-separated hybrids ωB97M-V and ωB97X-V also perform well here and can be recommended as a reliable compromise between accuracy and efficiency; they have already been shown to be robust across many other types of chemical problems, as well. Despite the popularity of B3LYP in computational enzymology, it is not a strong performer on our benchmark set, and we discourage its use for enzyme energetics.

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

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

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.

Sterically attenuated electronic communication in cobalt complexes of meridional isoquinoline-derived ligands for applications in electrocatalysis

The ability to synthetically tune the ligand frameworks of redox-active molecules is of critical importance to the economy of solar fuels because manipulating their redox properties can afford control over the operating potentials of sustained electrocatalytic or photoelectrocatalytic processes. The electronic and steric properties of 2,2':6',2″-terpyridine (Terpy) ligand frameworks can be tuned by functional group substitution on ligand backbones, and these correlate strongly to their Hammett parameters. The synthesis of a new series of tridentate meridional ligands of 2,4,6-trisubstituted pyridines that engineers the ability to finely tune the redox potentials of cobalt complexes to more positive potentials than that of their Terpy analogs is achieved by aryl-functionalizing at the four-position and by including isoquinoline at the two- and six-positions of pyridine (Aryl-DiQ). Their cobalt complex syntheses, their electronic properties, and their catalytic activity for carbon dioxide (CO2) reduction are reported and compared to their Terpy analogs. The cobalt derivatives generally experience a positive shift in their redox features relative to the Terpy-based analogs, covering a complementary potential range. Although those evaluated fail to produce any quantifiable products for the reduction of CO2 and suffer from long-term instability, these results suggest possible alternate strategies for stabilizing these compounds during catalysis. We speculate that lower equilibrium association constants to the cobalt center are intrinsic to these ligands, which originate from a steric interaction between protons on the pyridine and isoquinoline moieties. Nevertheless, the new Aryl-DiQ ligand framework has been engineered to selectively tune homoleptic cobalt complexes' redox potentials.

High-throughput screening of spin states for transition metal complexes with spin-polarized extended tight-binding methods

The semiempirical GFNn-xTB ( n = 1 , 2 ) tight-binding methods are extended with a spin-dependent energy term (spin-polarization), enabling the fast and efficient screening of different spin states for transition metal complexes. While GFNn-xTB methods inherently can not differentiate properly between high-spin (HS) and low-spin (LS) states, this shortcoming is corrected with the presented methods termed spGFNn-xTB. The performance of spGFNn-xTB methods for spin state energy splittings is evaluated on a newly compiled benchmark set of 90 complexes (27 HS and 63 LS complexes) containing 3d, 4d, and 5d transition metals (termed TM90S) employing DFT references at the TPSSh-D4/def2-QZVPP level of theory. The challenging TM90S set contains complexes with charges between - 4 and +3, spin multiplicities between 1 and 6, and spin-splitting energies that range from - 47.8 to 146.6 kcal/mol with a mean average of 32.2 kcal/mol. On this set the (sp)GFNn-xTB methods, the PM6-D3H4 method, and the PM7 method are evaluated with spGFN1-xTB yielding the lowest MAD of 19.6 kcal/mol followed by spGFN2-xTB with 24.8 kcal/mol. While for the 4d and 5d subsets small or no improvements are observed with spin-polarization, large improvements are obtained for the 3d subset with spGFN1-xTB yielding the smallest MAD of 14.2 kcal/mol followed by spGFN2-xTB with 17.9 kcal/mol and PM6-D3H4 with 28.4 kcal/mol. The correct sign of the spin state splittings is obtained with spGFN2-xTB in 89% of all cases closely followed by spGFN1-xTB with 88%. On the full set, a pure semiempirical vertical spGFN2-xTB//GFN2-xTB-based workflow for screening purposes yields a slightly better MAD of 22.2 kcal/mol due to error compensation, while being qualitative correct for one additional case. In combination with their low computational cost (scanning spin states in seconds), the spGFNn-xTB methods represent robust tools for pre-screening steps of spin state calculations and high-throughput workflows.

Mechanism and origins of cobalt-catalyzed ligand-controlled regiodivergent C-H functionalization of aldehydes with enynes

The influence of the P-M-P bite angle in diphosphine ligands on selectivity has been observed in various catalytic reactions. A better understanding of the ligand bite angle concept is important for the rational design of efficient catalytic systems. In the present work, the mechanism of cobalt-catalyzed C-H functionalization of aldehydes with enynes and how the diphosphine ligands alter regioselectivity were investigated by density functional theory (DFT) calculations. The catalytic cycle is initiated by the oxidative cyclization of enynes rather than the oxidative addition of aldehydes. Regioselectivity arises from competing σ-bond metathesis and migratory insertion steps, in which the steric effects of diphosphine ligands are the dominant factors influencing the activation barriers. The calculations indicate that σ-bond metathesis is more challenging and its feasibility is highly dependent on the ligand bite angle. The improved mechanistic understanding will enable further design of transition-metal-catalyzed selective cyclization reactions.

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.

Cobalt-catalysed nucleophilic fluorination in organic carbonates

The novel P-N ligand 1-((diphenylphosphaneyl)methyl)-1H-benzo-1,2,3-triazole (1), based on a benzotriazole scaffold, has been prepared. The reaction of 1 with [CoCp*(CH₃CN)₃][BF₄]₂ and [CoCp*(I)₂]₂ (Cp* = pentamethylcyclopentadienyl) affords the chelate complexes [CoCp*(CH₃CN)(P-N)][BF₄]₂ (2) and [CoCp*(I)(P-N)]I (3), respectively. Complexes 2 and 3 were studied as catalysts in the fluorination of aromatic and aliphatic acyl chlorides in CH₂Cl₂, with 3 showing notably higher activities than 2. Subsequently, organic carbonates (dimethyl carbonate and propylene carbonate) were also employed as solvents, which led to shorter reaction times and to the broadening of the substrate scope to a variety of aliphatic halides. Comparative studies between 3 and the analogous complex [CoCp*(I)₂(PMePh₂)], which features a monodentate phosphane ligand, showed that higher yields were obtained in the case of the former. DFT calculations and experimental studies were performed in order to shed light on the reaction mechanism, which entails the formation of a cobalt fluoride species that reacts via nucleophilic attack with the substrate to afford the corresponding fluorinated compounds.

Ionization energies of metallocenes: a coupled cluster study of cobaltocene

Open-shell transition metal chemistry presents challenges to contemporary electronic structure methods, based on either density functional or wavefunction theory. While CCSD(T) is the well-trusted gold standard for maingroup thermochemistry, the accuracy and robustness of the method is less clear for open-shell transition metal chemistry, requiring benchmarking of CCSD(T)-based protocols against either higher-level theory or experiment. Ionization energies (IEs) of metallocenes provide an interesting test case with metallocenes being common redox reagents as well as playing roles as redox mediators and cocatalysts in redox catalysis. Using highly accurate ZEKE-MATI experimental measurements of gas phase adiabatic (5.3275 ± 0.0006 eV) and vertical (5.4424 ± 0.0006 eV) ionization energies of cobaltocene, we systematically assessed the accuracy of the local coupled-cluster method DLPNO-CCSD(T) with respect to geometry, reference determinant, basis set size and extrapolation schemes, PNO cut-off and extrapolation, local triples approximation, relativistic effects and core-valence correlation. We show that PNO errors are controllable via the recently introduced PNO extrapolation schemes and that the expensive iterative triples (T₁) contribution can be made more manageable by calculating it as a smaller-basis/smaller PNO-cutoff correction. The reference determinant turns out to be a critical aspect in these calculations with the HF determinant resulting in large DLPNO-CCSD(T) errors, likely due to the qualitatively flawed molecular orbital spectrum. The BP86 functional on the other hand was found to provide reference orbitals giving small DLPNO-CCSD(T) errors, likely due to more realistic orbitals as suggested by the more consistent MO spectrum compared to HF. A protocol including complete basis set extrapolations with correlation-consistent basis sets, complete PNO space extrapolations, iterative triples- and core-valence correlation corrections was found to give errors of -0.07 eV and -0.03 eV for adiabatic- and vertical-IE of cobaltocene, respectively, giving close to chemical accuracy for both properties. A computationally efficient DLPNO-CCSD(T) protocol was devised and tested against adiabatic ionization energies of 6 different metallocenes (V, Cr, Mn, Fe, Co, Ni). For the other metallocenes, the iterative triples (T₁) and PNO extrapolation contributions turn out to be even more important. The results give errors close to the experimental uncertainty, similar to recent auxiliary-field quantum Monte Carlo results. The quality of the reference determinant orbitals is identified as the main source of uncertainty in CCSD(T) calculations of metallocenes.

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.

Comparative oxidative ability of mononuclear and dinuclear high-valent iron-oxo species towards the activation of methane: does the axial/bridge atom modulate the reactivity?

Over the years, mononuclear Fe^IVO species have been extensively studied, but the presence of dinuclear Fe^IVO species in soluble methane monooxygenase (sMMO) has inspired the development of biomimic models that could activate inert substrates such as methane. There are some successful attempts; particularly the [(Por)(m-CBA) Fe^IV(μ-N)Fe^IV(O)(Por˙⁺)]^- species has been reported to activate methane and yield decent catalytic turnover numbers and therefore regarded as the closest to the sMMO enzyme functional model, as no mononuclear Fe^IVO analogues could achieve this feat. In this work, we have studied a series of mono and dinuclear models using DFT and ab initio DLPNO-CCSD(T) calculations to probe the importance of nuclearity in enhancing the reactivity. We have probed the catalytic activities of four complexes: [(HO)Fe^IV(O)(Por)]^- (1), [(HO)Fe^IV(O)(Por˙⁺)] (2), μ-oxo dinuclear iron species [(Por)(m-CBA)Fe^IV(μ-O)Fe^IV(O) (Por˙⁺)]^- (3) and N-bridged dinuclear iron species [(Por)(m-CBA)Fe^IV(μ-N)Fe^IV(O)(Por˙⁺)]^- (4) towards the activation of methane. Additionally, calculations were performed on the mononuclear models [(X)Fe^IV(O)(Por˙⁺)]ⁿ {X = N 4a (n = -2), NH 4b (n = -1) and NH₂4c (n = 0)} to understand the role of nuclearity in the reactivity. DFT calculations performed on species 1-4 suggest an interesting variation among them, with species 1-3 possessing an intermediate spin (S = 1) as a ground state and species 4 possessing a high-spin (S = 2) as a ground state. Furthermore, the two Fe^IV centres in species 3 and 4 are antiferromagnetically coupled, yielding a singlet state with a distinct difference in their electronic structure. On the other hand, species 2 exhibits a ferromagnetic coupling between the Fe^IV and the Por˙⁺ moiety. Our calculations suggest that the higher barriers for the C-H bond activation of methane and the rebound step for species 1 and 3 are very high in energy, rendering them unreactive towards methane, while species 2 and 4 have lower barriers, suggesting their reactivity towards methane. Studies on the system reveal that model 4a has multiple FeN bonds facilitating greater reactivity, whereas the other two models have longer Fe-N bonds and less radical character with steeper barriers. Strong electronic cooperativity is found to be facilitated by the bridging nitride atom, and this cooperativity is suppressed by substituents such as oxygen, rendering them inactive. Thus, our study unravels that apart from enhancing the nuclearity, bridging atoms that facilitate strong cooperation between the metals are required to activate very inert substrates such as methane, and our results are broadly in agreement with earlier experimental findings.

Homogeneous Electrocatalytic Reduction of CO2 by a CrN3O Complex: Electronic Coupling with a Redox-Active Terpyridine Fragment Favors Selectivity for CO

Electrocatalyst design and optimization strategies continue to be an active area of research interest for the applied use of renewable energy resources. The electrocatalytic conversion of carbon dioxide (CO₂) is an attractive approach in this context because of the added potential benefit of addressing its rising atmospheric concentrations. In previous experimental and computational studies, we have described the mechanism of the first molecular Cr complex capable of electrocatalytically reducing CO₂ to carbon monoxide (CO) in the presence of an added proton donor, which contained a redox-active 2,2'-bipyridine (bpy) fragment, CrN₂O₂. The high selectivity for CO in the bpy-based system was dependent on a delocalized Cr^II(bpy^•-) active state. Subsequently, we became interested in exploring how expanding the polypyridyl ligand core would impact the selectivity and activity during electrocatalytic CO₂ reduction. Here, we report a new CrN₃O catalyst, Cr(tpy^tbupho)Cl₂ (1), where 2-(2,2':6',2″-terpyridin-6-yl)-4,6-di-tert-butylphenolate = [tpy^tbupho]^-, which reduces CO₂ to CO with almost quantitative selectivity via a different mechanism than our previously reported Cr(^tbudhbpy)Cl(H₂O) catalyst. Computational analyses indicate that, although the stoichiometry of both reactions is identical, changes in the observed rate law are the combined result of a decrease in the intrinsic ligand charge (L₃X vs L₂X₂) and an increase in the ligand redox activity, which result in increased electronic coupling between the doubly reduced tpy fragment of the ligand and the Cr^II center. The strong electronic coupling enhances the rate of protonation and subsequent C-OH bond cleavage, resulting in CO₂ binding becoming the rate-determining step, which is an uncommon mechanism during protic CO₂ reduction.

Accurate computed singlet-triplet energy differences for cobalt systems: implication for two-state reactivity

Accurate singlet-triplet energy differences for cobalt and rhodium complexes were calculated by using several wave function methods, such as MRCISD, CASPT2, CCSD(T) and BCCD(T). Relaxed energy differences were obtained by considering the singlet and triplet complexes, each at the minimum of their potential energy surfaces. Active spaces for multireference calculations were carefully checked to provide accurate results. The considered systems are built by increasing progressively the first coordination sphere around the metal. We included in our set two CpCoX complexes (Cp = cyclopentadienyl, X = alkenyl ligand), which have been suggested as intermediates in cycloaddition reactions. Indeed, cobalt systems have been used for more than a decade as active species in this kind of transformations, for which a two-state reactivity has been proposed. Most of the considered systems display a triplet ground state. However, in the case of a reaction intermediate, while a triplet ground state was predicted on the basis of Density Functional Theory results, our calculations suggest a singlet ground state. This stems from the competition between the exchange term (stabilising the triplet) and the accessibility of an intramolecular coordination (stabilising the singlet). This finding has an impact on the general mechanism of the cycloaddition reaction. Analogous rhodium systems were also studied and, as expected, they have a larger tendency to electron pairing than cobalt species.

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.

[Ni(NHC)2 ] as a Scaffold for Structurally Characterized trans [H-Ni-PR2 ] and trans [R2 P-Ni-PR2 ] Complexes

The addition of PPh2 H, PPhMeH, PPhH2 , P(para-Tol)H2 , PMesH2 and PH3 to the two-coordinate Ni0 N-heterocyclic carbene species [Ni(NHC)2 ] (NHC=IiPr2 , IMe4 , IEt2 Me2 ) affords a series of mononuclear, terminal phosphido nickel complexes. Structural characterisation of nine of these compounds shows that they have unusual trans [H-Ni-PR2 ] or novel trans [R2 P-Ni-PR2 ] geometries. The bis-phosphido complexes are more accessible when smaller NHCs (IMe4 >IEt2 Me2 >IiPr2 ) and phosphines are employed. P-P activation of the diphosphines R2 P-PR2 (R2 =Ph2 , PhMe) provides an alternative route to some of the [Ni(NHC)2 (PR2 )2 ] complexes. DFT calculations capture these trends with P-H bond activation proceeding from unconventional phosphine adducts in which the H substituent bridges the Ni-P bond. P-P bond activation from [Ni(NHC)2 (Ph2 P-PPh2 )] adducts proceeds with computed barriers below 10 kcal mol-1 . The ability of the [Ni(NHC)2 ] moiety to afford isolable terminal phosphido products reflects the stability of the Ni-NHC bond that prevents ligand dissociation and onward reaction.

Redox Isomerism in the S3 State of the Oxygen-Evolving Complex Resolved by Coupled Cluster Theory

The electronic and geometric structures of the water-oxidizing complex of photosystem II in the steps of the catalytic cycle that precede dioxygen evolution remain hotly debated. Recent structural and spectroscopic investigations support contradictory redox formulations for the active-site Mn4 CaOx cofactor in the final metastable S3 state. These range from the widely accepted MnIV 4 oxo-hydroxo model, which presumes that O-O bond formation occurs in the ultimate transient intermediate (S4 ) of the catalytic cycle, to a MnIII 2 MnIV 2 peroxo model representative of the contrasting "early-onset" O-O bond formation hypothesis. Density functional theory energetics of suggested S3 redox isomers are inconclusive because of extreme functional dependence. Here, we use the power of the domain-based local pair natural orbital approach to coupled cluster theory, DLPNO-CCSD(T), to present the first correlated wave function theory calculations of relative stabilities for distinct redox-isomeric forms of the S3 state. Our results enabled us to evaluate conflicting models for the S3 state of the oxygen-evolving complex (OEC) and to quantify the accuracy of lower-level theoretical approaches. Our assessment of the relevance of distinct redox-isomeric forms for the mechanism of biological water oxidation strongly disfavors the scenario of early-onset O-O formation advanced by literal interpretations of certain crystallographic models. This work serves as a case study in the application of modern coupled cluster implementations to redox isomerism problems in oligonuclear transition metal systems.

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.

Successes, challenges, and opportunities for quantum chemistry in understanding metalloenzymes for solar fuels research

Overview of the rich and diverse contributions of quantum chemistry to understanding the structure and function of the biological archetypes for solar fuel research, photosystem II and hydrogenases.

Spin-state energetics of metallocenes: How do best wave function and density functional theory results compare with the experimental data?

We benchmark the accuracy of quantum-chemical methods, including wave function theory methods [coupled cluster theory at the CCSD(T) level, multiconfigurational perturbation-theory (CASPT2, NEVPT2) and internally contracted multireference configuration interaction (MRCI)] and 30 density functional theory (DFT) approximations, in reproducing the spin-state splittings of metallocenes. The reference values of the electronic energy differences are derived from the experimental spin-crossover enthalpy for manganocene and the spectral data of singlet-triplet transitions for ruthenocene, ferrocene, and cobaltocenium. For ferrocene and cobaltocenium we revise the previous experimental interpretations regarding the lowest triplet energy; our argument is based on the comparison with the lowest singlet excitation energy and herein reported, carefully determined absorption spectrum of ferrocene. When deriving vertical energies from the experimental band maxima, we go beyond the routine vertical energy approximation by introducing vibronic corrections based on simulated vibrational envelopes. The benchmarking result confirms the high accuracy of the CCSD(T) method (in particular, for UCCSD(T) based on Hartree-Fock orbitals we find for our dataset: maximum error 0.12 eV, weighted mean absolute error 0.07 eV, weighted mean signed error 0.01 eV). The high accuracy of the single-reference method is corroborated by the analysis of a multiconfigurational character of the complete active space wave function for the triplet state of ferrocene. On the DFT side, our results confirm the non-universality problem with approximate functionals. The present study is an important step toward establishing an extensive and representative benchmark set of experiment-derived spin-state energetics for transition metal complexes.