Theoretical Characterization of End-On and Side-On Peroxide Coordination in Ligated Cu2O2 Models

Towards reliable and efficient modeling of [Cu2O2]2+-based compound electronic structures with the partially fixed reference space protocols

This work reports a computationally efficient approach for reliable modeling of complex electronic structures based on [Cu2O2]2+ moieties. Specifically, we explore the recently developed partially fixed reference space (PFRS) protocol to minimize the active space size, taking into account the double d-shell effects. We show that the ground-state electronic structure of the core [Cu2O2]2+ model system is dominated by the d9/d10 occupations. The PFRS-crafted active spaces are further used to generate the reference wave functions for the multi-reference coupled cluster, configuration interaction, and multi-reference perturbation theory calculations. Specifically, we demonstrate that the bare [Cu2O2]2+ core can be modeled qualitatively using active spaces as small as CAS(2,2)PFRS. To obtain quantitative agreement with the reference DMRG(32,62)CI calculations, the CAS(4,4) has to be used in conjunction with the MRCCSD correction on top of it. This reliable and computationally efficient protocol is further used to model the electronic structure and properties of ammonia coordinated [Cu2O2]2+ complexes. Finally, based on the large amount of available experimental data regarding the oxo-peroxo equilibrium of [Cu2O2]2+-based systems, it is possible to formulate educated guesses regarding the effect of each experimental variable over each d-occupancy-specific state. With a large sample size of d-occupancy-specific state dependence with ligands and solvents, it should be possible to propose new ligands with specific d-occupancy and, therefore, oxidative properties based on the d-occupancy energy gaps of relatively low-cost calculations.

Spectroscopy of End-On Copper(II) Superoxido Complexes: A Wave Function-Based Analysis

Wave function methods are employed to analyze the ground and low-lying excited states of bipyramid trigonal copper(II) superoxido complexes, up to their characteristic ligand to metal charge transfer band. Several multireference methods have been combined to provide new insights into the interpretation of their experimental absorption spectra. We show that the intraligand transition on the dioxygen leads to a dark state. Among the results, we shall highlight the finding of doubly excited states in the region of the d-d transitions and the subtle interplay between Cu(I) and Cu(II) in the ground and excited states. Some of these findings could be obtained only with multireference methods.

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.

A framework for constructing linear free energy relationships to design molecular transition metal catalysts

A computational framework for ligand-driven design of transition metal complexes is presented in this work. We propose a general procedure for the construction of active site-specific linear free energy relationships (LFERs), which are inspired from Hammett and Taft correlations in organic chemistry and grounded in the activation strain model (ASM). Ligand effects are isolated and quantified in terms of their contribution to interaction and strain energy components of ASM. Scalar descriptors that are easily obtainable are then employed to construct the complete LFER. We successfully demonstrate proof-of-concept by constructing and applying an LFER to CH activation with enzyme-inspired [Cu2O2]2+ complexes. The key benefit of using ASM is a built-in compensation or error cancellation between LFER prediction of interaction and strain terms, resulting in accurate barrier predictions for 37 of the 47 catalysts examined in this study. The LFER is also transferable with respect to level of theory and flexible towards the choice of reference system. The absence of interaction-strain compensation or poor model performance for the remaining systems is a consequence of the approximate nature of the chosen interaction energy descriptor and LFER construction of the strain term, which focuses largely on trends in substrate and not catalyst strain.

Mechanistic Insights into the ortho-Defluorination-Hydroxylation of 2-Halophenolates Promoted by a Bis(μ-oxo)dicopper(III) Complex

C-F bonds are one of the most inert functionalities. Nevertheless, some [Cu₂O₂]²⁺ species are able to defluorinate-hydroxylate ortho-fluorophenolates in a chemoselective manner over other ortho-halophenolates. Albeit it is known that such reactivity is promoted by an electrophilic attack of a [Cu₂O₂]²⁺ core over the arene ring, the crucial details of the mechanism that explain the chemo- and regioselectivity of the reaction remain unknown, and it has not being determined either if Cu^II₂(η²:η²-O₂) or Cu^III₂(μ-O)₂ species are responsible for the initial attack on the arene. Herein, we present a combined theoretical and experimental mechanistic study to unravel the origin of the chemoselectivity of the ortho-defluorination-hydroxylation of 2-halophenolates by the [Cu₂(O)₂(DBED)₂]²⁺ complex (DBED = N,N'-di-tert-butylethylenediamine). Our results show that the equilibria between (side-on)peroxo (P) and bis(μ-oxo) (O) isomers plays a key role in the mechanism, with the latter being the reactive species. Furthermore, on the basis of quantum-mechanical calculations, we were able to rationalize the chemoselective preference of the [Cu₂(O)₂(DBED)₂]²⁺ catalyst for the C-F activation over C-Cl and C-H activations.

Structure and Reactivity of Oxygen-Bridged Diamino Dicopper(II) Complexes in Cu-Ion-Exchanged Chabazite Catalyst for NH3-Mediated Selective Catalytic Reduction

The NH3-mediated selective catalytic reduction (NH3-SCR) of NOx over Cu-ion-exchanged chabazite (Cu-CHA) catalysts is the basis of the technology for abatement of NOx from diesel vehicles. A crucial step in this reaction is the activation of oxygen. Under conditions for low-temperature NH3-SCR, oxygen only reacts with CuI ions, which are present as mobile CuI diamine complexes [CuI(NH3)2]+. To determine the structure and reactivity of the species formed by oxidation of these CuI diamine complexes with oxygen at 200 °C, we have followed this reaction, using a Cu-CHA catalyst with a Si/Al ratio of 15 and 2.6 wt% Cu, by X-ray absorption spectroscopies (XANES and EXAFS) and diffuse reflectance UV-Vis spectroscopy, with the support of DFT calculations and advanced EXAFS wavelet transform analysis. The results provide unprecedented direct evidence for the formation of a [Cu2(NH3)4O2]2+ mobile complex with a side-on μ-η2,η2-peroxo diamino dicopper(II) structure, accounting for 80-90% of the total Cu content. These [Cu2(NH3)4O2]2+ are completely reduced to [CuI(NH3)2]+ at 200 °C in a mixture of NO and NH3. Some N2 is formed as well, which suggests the role of the dimeric complexes in the low-temperature NH3-SCR reaction. The reaction of [Cu2(NH3)4O2]2+ complexes with NH3 leads to a partial reduction of the Cu without any formation of N2. The reaction with NO results in an almost complete reduction to CuI, under the formation of N2. This indicates that the low-temperature NH3-SCR reaction proceeds via a reaction of these complexes with NO.

Theoretical rationalization for the equilibrium between (μ-η2:η2-peroxido)CuIICuII and bis(μ-oxido)CuIIICuIII complexes: perturbational effects from ligand frameworks

DFT calculations are carried out to investigate the geometric effects of the supporting ligands in the relative energies of the (μ-η2:η2-peroxido)CuIICuII complex 1 and the bis(μ-oxido)CuIIICuIII complex 2. The N3-tridentate ligand bearing acyclic propane diamine framework La preferentially provided 1, whereas the N3-tridentate ligand with cyclic diamine framework such as 1,4-diazacycloheptane Lb gave 2 after the oxygenation of the corresponding CuI complexes as reported previously [S. Itoh, et al., Inorg. Chem., 2014, 53, 8786-8794]. Calculations at the B3LYP*-D3 level of theory can reasonably explain the experimental results in relative energies, structures and harmonic frequencies of 1 and 2. Perturbational effects of the diamine chelates of La and Lb especially on the equilibrium of 1 and 2 are investigated in detail. In the range from 2.30 Å to 3.40 Å of the N-N distance in the diamine moiety, 1 is more stable than 2 by 8.4 kcal mol-1 at the distance of 3.40 Å. Calculated potential energies indicate that the decrease in the N-N distance is associated with a decrease in energy of 2, leading that 2 can be most stabilized at the N-N distance of 2.60 Å. Furthermore, molecular orbitals analyses are performed to explain that the energy gaps between the σ* orbital of the O-O bond and the dx2-y2 orbitals of the CuII ions of 1 get small as the diamine moiety is shrunk, leading to facilitate the O-O bond cleavage from 1 to 2.

A comparative test of different density functionals for calculations of NH3-SCR over Cu-Chabazite

A general challenge in density functional theory calculations is to simultaneously account for different types of bonds. One such example is reactions in zeolites where both van der Waals and chemical bonds should be described accurately. Here, we use different exchange-correlation functionals to explore O₂ dissociation over pairs of Cu(NH₃)₂⁺ complexes in Cu-Chabazite. This is an important part of selective catalytic reduction of NO_x using NH₃ as a reducing agent. The investigated functionals are PBE, PBE+U, PBE+D, PBE+U+D, PBE-cx, BEEF and HSE06+D. We find that the potential energy landscape for O₂ activation and dissociation depends critically on the choice of functional. However, the van der Waals contributions are similarly described by the functionals accounting for this interaction. The discrepancies in the potential energy surface are instead related to different descriptions of the Cu-O chemical bond. By investigating the electronic, structural and energetic properties of reference systems including bulk copper oxides and (Cu₂O₂)²⁺ enzymatic crystals, we find that the PBE+U approach together with van der Waals corrections provides a reasonable simultaneous accuracy of the different bonds in the systems.

Extending spin-symmetry projected coupled-cluster to large model spaces using an iterative null-space projection technique

Recently, we introduced an orbital-invariant approximate coupled-cluster (CC) method in the spin-projection manifold. The multi-determinantal property of spin-projection means that the parametrization in the spin-extended CC (ECC) ansatz is nonorthogonal and overcomplete. Therefore, the linear dependencies must be removed by an orthogonalization procedure to obtain meaningful solutions. Multi-reference methods often achieve this by diagonalizing a metric of the equation system, but this is not feasible with ECC because of the enormous size of the metric, a consequence of the incomplete active space of the spin-projected Hartree-Fock reference. As a result, the applicability of ECC has been limited to small benchmark systems, for which the ansatz was shown to be superior to the configuration interaction and linearized approximations. In this article, we provide a solution to this problem that completely avoids the metric diagonalization by iteratively projecting out its null-space from the working equations. As the additional computational cost required for this iterative projection is only marginal, it greatly expands the application range of ECC. We demonstrate the potential of approximate ECC by studying the complete basis set limit of F₂ and transition metal complexes such as NiO, Mn₂ , and [Cu₂ O₂ ]²⁺ , which have all been hindered by the prohibitively large metric size. We also identify the potential inadequacy of the molecular orbitals given by spin-projected Hartree-Fock in some cases, and propose possible solutions. © 2018 Wiley Periodicals, Inc.

Computational strategies to probe CH activation in dioxo-dicopper complexes

We employ density functional theory and energy decomposition analysis to probe the mechanism of CH activation in dioxo-dicopper complexes. The electrophilicity of monodentate N-donor ligands coordinated to Cu is systematically varied to examine the response of barriers to the two proposed pathways - one-step oxo-insertion and two-step radical recombination. Electron-withdrawing ligand stabilize the oxo-insertion transition state via charge transfer interactions, and therefore lead to lower barriers. On the other hand, barriers to the CH activation step in the radical recombination mechanism exhibit almost no dependence on N-donor electrophilicity. Based on the similarities between calculated and experimental Hammett relationships, the oxo-insertion pathway appears to be the preferred mechanism of CH activation in dioxo-dicopper catalysts.

Relativistic effects at the Cu2O2 core - a density functional theory study

This work presents for the first time the impact of relativistic effects on the Cu₂O₂ peroxide dicopper(ii)-bis(μ-oxo) dicopper (iii) equilibrium bonding motif in existing tyrosinase model complexes [Cu₂(btmgp)₂(μ-O)₂]²⁺ and [Cu₂{HC(tBuPz)₂Py}₂(O₂)]²⁺ [S. Herres et al., Inorg. Chim. Acta, 2005, 358, 1089; S. Herres-Pawlis et al., Eur. J. Inorg. Chem., 2005, 3815; A. Hoffmann et al., Angew. Chem., Int. Ed., 2013, 52, 5398]. We use density functional theory (TPSSh/cc-pVTZ+D3BJ) with various relativistic approaches (ECPs, DKH, ZORA) to tackle the question of impact and find, as already known for small model complexes in the literature, that the O core is more stabilized with respect to the P core by the relativistic influence [D. G. Liakos and F. Neese, J. Chem. Theory Comput., 2011, 7, 1511]. Whereas DKH and ZORA yield similar results, ECPs underestimate the predicted effect. By calculating the functional of the relativistic overlap change, we can exactly identify the relativistic changes at the molecular orbital level and narrow down the affected MOs. Thus, by performing a detailed bond analysis utilizing the overlap population, we are able to rationalize the effects at the chemical level by finding relativistic bond stabilization in both isomers, which is more dominating in the O core. In conclusion, relativistic effects already play an important role in dicopper cores and should be considered.

A radical rebound mechanism for the methane oxidation reaction promoted by the dicopper center of a pMMO enzyme: a computational perspective

Hydrogen Atom Transfer (HAT) promoted by a triplet state of the bis-oxoCu₂(iii) core generates a new radical rebound mechanism for the hydroxylation of methane catalyzed by the binuclear copper site of a pMMO enzyme.

Donor-driven conformational flexibility in a real-life catalytic dicopper(ii) peroxo complex

The conformers of the real-life tyrosinase model [Cu₂O₂{HC(3-tBuPz)₂(Py)}₂]²⁺which displays catalytic hydroxylation reactivity were investigated by density functional theory (DFT) studies including second-order perturbation theory and charge decomposition analysis (CDA).

Adaptive multiconfigurational wave functions

A method is suggested to build simple multiconfigurational wave functions specified uniquely by an energy cutoff Λ. These are constructed from a model space containing determinants with energy relative to that of the most stable determinant no greater than Λ. The resulting Λ-CI wave function is adaptive, being able to represent both single-reference and multireference electronic states. We also consider a more compact wave function parameterization (Λ+SD-CI), which is based on a small Λ-CI reference and adds a selection of all the singly and doubly excited determinants generated from it. We report two heuristic algorithms to build Λ-CI wave functions. The first is based on an approximate prescreening of the full configuration interaction space, while the second performs a breadth-first search coupled with pruning. The Λ-CI and Λ+SD-CI approaches are used to compute the dissociation curve of N2 and the potential energy curves for the first three singlet states of C2. Special attention is paid to the issue of energy discontinuities caused by changes in the size of the Λ-CI wave function along the potential energy curve. This problem is shown to be solvable by smoothing the matrix elements of the Hamiltonian. Our last example, involving the Cu2O2(2+) core, illustrates an alternative use of the Λ-CI method: as a tool to both estimate the multireference character of a wave function and to create a compact model space to be used in subsequent high-level multireference coupled cluster computations.

Quantum mechanics/molecular mechanics study of oxygen binding in hemocyanin

We report a combined quantum mechanics/molecular mechanics (QM/MM) study on the mechanism of reversible dioxygen binding in the active site of hemocyanin (Hc). The QM region is treated by broken-symmetry density functional theory (DFT) with spin projection corrections. The X-ray structures of deoxygenated (deoxyHc) and oxygenated (oxyHc) hemocyanin are well reproduced by QM/MM geometry optimizations. The computed relative energies strongly depend on the chosen density functional. They are consistent with the available thermodynamic data for oxygen binding in hemocyanin and in synthetic model complexes when the BH&HLYP hybrid functional with 50% Hartree-Fock exchange is used. According to the QM(BH&HLYP)/MM results, the reaction proceeds stepwise with two sequential electron transfer (ET) processes in the triplet state followed by an intersystem crossing to the singlet product. The first ET step leads to a nonbridged superoxo CuB(II)-O2(•-) intermediate via a low-barrier transition state. The second ET step is even more facile and yields a side-on oxyHc complex with the characteristic Cu2O2 butterfly core, accompanied by triplet-singlet intersystem crossing. The computed barriers are very small so that the two ET processes are expected to very rapid and nearly simultaneous.

Toward a mechanistic understanding of oxidative homocoupling: the Glaser–Hay reaction

The full reaction mechanism for the copper catalyzed oxidative coupling of two terminal alkynes is computationally characterized with DFT methods

Complete σ* intramolecular aromatic hydroxylation mechanism through O2 activation by a Schiff base macrocyclic dicopper(I) complex

In this work we analyze the whole molecular mechanism for intramolecular aromatic hydroxylation through O2 activation by a Schiff hexaazamacrocyclic dicopper(I) complex, [Cu(I) 2(bsH2m)](2+). Assisted by DFT calculations, we unravel the reaction pathway for the overall intramolecular aromatic hydroxylation, i.e., from the initial O2 reaction with the dicopper(I) species to first form a Cu(I)Cu(II)-superoxo species, the subsequent reaction with the second Cu(I) center to form a μ-η(2):η(2)-peroxo-Cu(II) 2 intermediate, the concerted peroxide O-O bond cleavage and C-O bond formation, followed finally by a proton transfer to an alpha aromatic carbon that immediately yields the product [Cu(II) 2(bsH2m-O)(μ-OH)](2+).

Correlated wavefunction methods in bioinorganic chemistry

In this commentary the challenges faced in the application of wavefunction-based ab initio methods to (open-shell) transition metal complexes of (bio)inorganic interest are briefly touched on. Both single-reference and multireference methods are covered. It is stressed that the generation and nature of the reference wavefunction is a subject of major importance. How erroneous results can be easily obtained even with coupled-cluster theory is illustrated through the example of the septet-quintet separation in iron(IV)-oxo complexes. Second, the interplay between relativistic and correlation effects is important. This is demonstrated with coupled-cluster calculations on models for dinuclear copper active sites, where relativity has a major influence on the relative stabilities of the bis(μ-oxo) and side-on peroxo species.

Extensive regularization of the coupled cluster methods based on the generating functional formalism: application to gas-phase benchmarks and to the SN2 reaction of CHCl3 and OH- in water

The recently introduced energy expansion based on the use of generating functional (GF) [K. Kowalski and P. D. Fan, J. Chem. Phys. 130, 084112 (2009)] provides a way of constructing size-consistent noniterative coupled cluster (CC) corrections in terms of moments of the CC equations. To take advantage of this expansion in a strongly interacting regime, the regularization of the cluster amplitudes is required in order to counteract the effect of excessive growth of the norm of the CC wave function. Although proven to be efficient, the previously discussed form of the regularization does not lead to rigorously size-consistent corrections. In this paper we address the issue of size-consistent regularization of the GF expansion by redefining the equations for the cluster amplitudes. The performance and basic features of proposed methodology are illustrated on several gas-phase benchmark systems. Moreover, the regularized GF approaches are combined with quantum mechanical molecular mechanics module and applied to describe the S(N)2 reaction of CHCl(3) and OH(-) in aqueous solution.

Density functional theory for transition metals and transition metal chemistry

We introduce density functional theory and review recent progress in its application to transition metal chemistry. Topics covered include local, meta, hybrid, hybrid meta, and range-separated functionals, band theory, software, validation tests, and applications to spin states, magnetic exchange coupling, spectra, structure, reactivity, and catalysis, including molecules, clusters, nanoparticles, surfaces, and solids.

Theoretical study of the hydroxylation of phenolates by the Cu(2)O (2)(N,N'-dimethylethylenediamine) (2) (2+) complex

Tyrosinase catalyzes the ortho hydroxylation of monophenols and the subsequent oxidation of the diphenolic products to the resulting quinones. In efforts to create biomimetic copper complexes that can oxidize C-H bonds, Stack and coworkers recently reported a synthetic mu-eta(2):eta(2)-peroxodicopper(II)(DBED)(2) complex (DBED is N,N'-di-tert-butylethylenediamine), which rapidly hydroxylates phenolates. A reactive intermediate consistent with a bis-mu-oxo-dicopper(III)-phenolate complex, with the O-O bond fully cleaved, is observed experimentally. Overall, the evidence for sequential O-O bond cleavage and C-O bond formation in this synthetic complex suggests an alternative mechanism to the concerted or late-stage O-O bond scission generally accepted for the phenol hydroxylation reaction performed by tyrosinase. In this work, the reaction mechanism of this peroxodicopper(II) complex was studied with hybrid density functional methods by replacing DBED in the mu-eta(2):eta(2)-peroxodicopper(II)(DBED)(2) complex by N,N'-dimethylethylenediamine ligands to reduce the computational costs. The reaction mechanism obtained is compared with the existing proposals for the catalytic ortho hydroxylation of monophenol and the subsequent oxidation of the diphenolic product to the resulting quinone with the aim of gaining some understanding about the copper-promoted oxidation processes mediated by 2:1 Cu(I)O(2)-derived species.

The restricted active space followed by second-order perturbation theory method: theory and application to the study of CuO2 and Cu2O2 systems

A multireference second-order perturbation theory using a restricted active space self-consistent field wave function as reference (RASPT2/RASSCF) is described. This model is particularly effective for cases where a chemical system requires a balanced orbital active space that is too large to be addressed by the complete active space self-consistent field model with or without second-order perturbation theory (CASPT2 or CASSCF, respectively). Rather than permitting all possible electronic configurations of the electrons in the active space to appear in the reference wave function, certain orbitals are sequestered into two subspaces that permit a maximum number of occupations or holes, respectively, in any given configuration, thereby reducing the total number of possible configurations. Subsequent second-order perturbation theory captures additional dynamical correlation effects. Applications of the theory to the electronic structure of complexes involved in the activation of molecular oxygen by mono- and binuclear copper complexes are presented. In the mononuclear case, RASPT2 and CASPT2 provide very similar results. In the binuclear cases, however, only RASPT2 proves quantitatively useful, owing to the very large size of the necessary active space.