Electronic Structures of Nickel(II)-Bis(indanyloxazoline)-dihalide Catalysts: Understanding Ligand Field Contributions That Promote C(sp2)-C(sp3) Cross-Coupling.

NiII(IB) dihalide [IB = (3aR,3a'R,8aS,8a'S)-2,2'-(cyclopropane-1,1-diyl)bis(3a,8a-dihydro-8H-indeno[1,2-d]-oxazole)] complexes are representative of a growing class of first-row transition-metal catalysts for the enantioselective reductive cross-coupling of C(sp2) and C(sp3) electrophiles. Recent mechanistic studies highlight the complexity of these ground-state cross-couplings but also illuminate new reactivity pathways stemming from one-electron redox and their significant sensitivities to reaction conditions. For the first time, a diverse array of spectroscopic methods coupled to electrochemistry have been applied to NiII-based precatalysts to evaluate specific ligand field effects governing key Ni-based redox potentials. We also experimentally demonstrate DMA solvent coordination to catalytically relevant Ni complexes. Coordination is shown to favorably influence key redox-based reaction steps and prevent other deleterious Ni-based equilibria. Combined with electronic structure calculations, we further provide a direct correlation between reaction intermediate frontier molecular orbital energies and cross-coupling yields. Considerations developed herein demonstrate the use of synergic spectroscopic and electrochemical methods to provide concepts for catalyst ligand design and rationalization of reaction condition optimization.

Reactivity Factors in Catalytic Methanogenesis and Their Tuning upon Coenzyme F430 Biosynthesis.

Methyl-coenzyme M reductase, responsible for the biological production of methane by catalyzing the reaction between coenzymes B (CoBS-H) and M (H3C-SCoM), hosts in its core an F430 cofactor with the low-valent NiI ion. The critical methanogenic step involves F430-assisted reductive cleavage of the H3C-S bond in coenzyme M, yielding the transient CH3 radical capable of hydrogen atom abstraction from the S-H bond in coenzyme B. Here, we computationally explored whether and why F430 is unique for methanogenesis in comparison to four identified precursors formed consecutively during its biosynthesis. Indeed, all precursors are less proficient than the native F430, and catalytic competence improves at each biosynthetic step toward F430. Against the expectation that F430 is tuned to be the strongest possible reductant to expedite the rate-determining reductive cleavage of H3C-S by NiI, we discovered the opposite. The unfavorable increase in reduction potential along the F430 biosynthetic pathway is outweighed by strengthening of the Ni-S bond formed upon reductive cleavage of the H3C-S bond. We found that F430 is the weakest electron donor, compared to its precursors, giving rise to the most covalent Ni-S bond, which stabilizes the transition state and hence reduces the rate-determining barrier. In addition, the transition state displays high pro-reactive motion of the transient CH3 fragment toward the H-S bond, superior to its biosynthetic ancestors and likely preventing the formation of a deleterious radical intermediate. Thus, we show a plausible view of how the evolutionary driving force shaped the biocatalytic proficiency of F430 toward CH4 formation.

Comprehensive Theoretical View of the [Cu2 O2 ] Side-on-Peroxo-/Bis-µ-Oxo Equilibria.

Coupled binuclear copper (CBC) sites are employed by many metalloenzymes to catalyze a broad set of biochemical transformations. Typically, the CBC catalytic sites are activated by the O2 molecule to form various [Cu2 O2 ] reactive species. This has also inspired synthesis and development of various biomimetic inorganic complexes featuring the CBC core. From theoretical perspective, the [Cu2 O2 ] reactivity often hinges on the side-on-peroxo-dicopper(II) (P) vs. bis-µ-oxo-dicopper(III) (O) isomerism - an equilibrium that has become almost iconic in theoretical bioinorganic chemistry. Herein, we present a comprehensive calibration and evaluation of the performance of various composite computational protocols available in contemporary computational chemistry, involving coupled-cluster and multireference (relativistic) wave function methods, popular density functionals and solvation models. Starting with the well-studied reference [Cu2 O2 (NH3 )6 ]2+ system, we compared the performance of electronic structure methods and discussed the relativistic effects. This allowed us to select several 'calibrated' DFT functionals that can be conveniently employed to study ten experimentally well-characterized [Cu2 O2 ] inorganic systems. We mostly predicted the lowest-energy structures (P vs. O) of the studied systems correctly. In addition, we present calibration of the used electronic structure methods for prediction of the spectroscopic features of the [Cu2 O2 ] core, mostly provided by the resonance Raman (rR) spectroscopy.

Beyond the Classical Contributions to Exchange Coupling in Binuclear Transition Metal Complexes.

Complexes with two or more magnetically coupled metal ions have attracted considerable attention as catalysts of many vital processes, single-molecule magnets, or spin-crossover compounds. Elucidation of their electronic structures is essential for understanding their catalytic and magnetic properties. Here, we provide an unprecedented insight into exchange-coupling mechanisms between the magnetic centers in six prototypical bis-µ-oxo bimetallic M2O2 complexes, including two biologically relevant models of non-heme iron enzymes. Employing multiconfigurational/multireference methods and related orbital entanglement analysis, we revealed the essential and counterintuitive role of predominantly unoccupied valence metal d orbitals in their strong antiferromagnetic coupling. We found that the participation of these orbitals is twofold. First, they enhance the superexchange between the singly occupied d orbitals. Second, they become substantially occupied and thus directly magnetically active, which we perceive as a new mechanism of the exchange interaction between the magnetic transition metal centers.

Interpretation of Exchange Interaction through Orbital Entanglement.

Recently, the analysis of single-orbital entropy and mutual information has been introduced as a tool for the investigation of contributions to the exchange (J) coupling between open-shell metal ions [Stein et al. J. Phys. Chem. Lett. 2019, 10, 6762-6770]. Here, we show that this analysis may lead to an incorrect interpretation of the J-coupling mechanism. Instead, we propose an orbital-entanglement analysis that is based on the two-electron density and that provides a coherent picture of the contributing exchange pathways, which seems fully consistent with the available J values. For this purpose, we used a prototypical bis-µ-oxo binuclear manganese complex ([Mn2O2(NH3)8]4+) and demonstrated that its antiferromagnetism (J < 0), calculated by using the active space composed of all valence pO and dMn orbitals, correlates well with the largest elements in the differential low-spin vs high-spin entanglement map. These elements correspond to interactions between the pairs of dMn orbitals mediated by the oxo-bridging out-of-plane p orbitals, representing the π superexchange pathway. We also show that the reduction of active space to manifold of the singly occupied magnetic orbitals does not lead to discrepancy between the calculated J values and entanglement maps. This contrasts to analysis of mutual information, which suggests the "direct" dMn-dMn interactions to play a dominant role for the J coupling, irrespective of the size of active space as well as of the antiferromagnetism expected. The failure is attributed to the large contribution of spin entanglement contained in the mutual information of the low-spin state, which may be regarded as the origin of the different complexity of its wave function and electron density.

Proton-Electron Transfer to the Active Site Is Essential for the Reaction Mechanism of Soluble Δ9-Desaturase.

A full understanding of the catalytic action of non-heme iron (NHFe) and non-heme diiron (NHFe2) enzymes is still beyond the grasp of contemporary computational and experimental techniques. Many of these enzymes exhibit fascinating chemo-, regio-, and stereoselectivity, in spite of employing highly reactive intermediates which are necessary for activations of most stable chemical bonds. Herein, we study in detail one intriguing representative of the NHFe2 family of enzymes: soluble Δ9 desaturase (Δ9D), which desaturates rather than performing the thermodynamically favorable hydroxylation of substrate. Its catalytic mechanism has been explored in great detail by using QM(DFT)/MM and multireference wave function methods. Starting from the spectroscopically observed 1,2-µ-peroxo diferric P intermediate, the proton-electron uptake by P is the favored mechanism for catalytic activation, since it allows a significant reduction of the barrier of the initial (and rate-determining) H-atom abstraction from the stearoyl substrate as compared to the "proton-only activated" pathway. Also, we ruled out that a Q-like intermediate (high-valent diamond-core bis-µ-oxo-[FeIV]2 unit) is involved in the reaction mechanism. Our mechanistic picture is consistent with the experimental data available for Δ9D and satisfies fairly stringent conditions required by Nature: the chemo-, stereo-, and regioselectivity of the desaturation of stearic acid. Finally, the mechanisms evaluated are placed into a broader context of NHFe2 chemistry, provided by an amino acid sequence analysis through the families of the NHFe2 enzymes. Our study thus represents an important contribution toward understanding the catalytic action of the NHFe2 enzymes and may inspire further work in NHFe(2) biomimetic chemistry.

Vibrational Structure in Magnetic Circular Dichroism Spectra of Polycyclic Aromatic Hydrocarbons.

Absorption and magnetic circular dichroism (MCD) spectroscopies are powerful and simple methods to discriminate among various compounds. Polycyclic aromatic hydrocarbons provide particularly strong signal, which, for example, facilitates their detection in the environment. However, interpretation of the spectra is often based on quantum-chemical simulations, providing a limited precision only. In the present work, we use time-dependent density functional theory and complete active space second-order perturbation theories to understand spectral features observed in a series of naphthalene, anthracene, phenanthrene, and three larger compounds. The electronic computations provided reasonable agreement with the experiment for the smaller molecules, while a large error persisted for the bigger ones. However, many discrepancies could be explained by vibrational splitting of the electronic transitions across the entire spectral range. Compared to plain absorption, MCD spectral bands and their vibrational splitting were more specific for each aromatic molecule. The computational tools allowing simulations of detailed vibrational features in the electronic spectra thus promise to open a qualitatively new chapter in the spectroscopy of aromatic compounds.

Multistate Complete-Active-Space Second-Order Perturbation Theory Based on Density Matrix Renormalization Group Reference States.

We present the development of the multistate multireference second-order perturbation theory (CASPT2) with multiroot references, which are described using the density matrix renormalization group (DMRG) method to handle a large active space. The multistate first-order wave functions are expanded into the internally contracted (IC) basis of the single-state single-reference (SS-SR) scheme, which is shown to be the most feasible variant to use DMRG references. The feasibility of the SS-SR scheme comes from two factors: first, it formally does not require the fourth-order transition reduced density matrix (TRDM) and second, the computational complexity scales linearly with the number of the reference states. The extended multistate (XMS) treatment is further incorporated, giving suited treatment of the zeroth-order Hamiltonian despite the fact that the SS-SR based IC basis is not invariant with respect to the XMS rotation. In addition, the state-specific fourth-order reduced density matrix (RDM) is eliminated in an approximate fashion using the cumulant reconstruction formula, as also done in the previous state-specific DMRG-cu(4)-CASPT2 approach. The resultant method, referred to as DMRG-cu(4)-XMS-CASPT2, uses the RDMs and TRDMs of up to third-order provided by the DMRG calculation. The multistate potential energy curves of the photoisomerization of diarylethene derivatives with CAS(26e,24o) are presented to illustrate the applicability of our theoretical approach.

Mono- and binuclear non-heme iron chemistry from a theoretical perspective.

In this minireview, we provide an account of the current state-of-the-art developments in the area of mono- and binuclear non-heme enzymes (NHFe and NHFe2) and the smaller NHFe(2) synthetic models, mostly from a theoretical and computational perspective. The sheer complexity, and at the same time the beauty, of the NHFe(2) world represents a challenge for experimental as well as theoretical methods. We emphasize that the concerted progress on both theoretical and experimental side is a conditio sine qua non for future understanding, exploration and utilization of the NHFe(2) systems. After briefly discussing the current challenges and advances in the computational methodology, we review the recent spectroscopic and computational studies of NHFe(2) enzymatic and inorganic systems and highlight the correlations between various experimental data (spectroscopic, kinetic, thermodynamic, electrochemical) and computations. Throughout, we attempt to keep in mind the most fascinating and attractive phenomenon in the NHFe(2) chemistry, which is the fact that despite the strong oxidative power of many reactive intermediates, the NHFe(2) enzymes perform catalysis with high selectivity. We conclude with our personal viewpoint and hope that further developments in quantum chemistry and especially in the field of multireference wave function methods are needed to have a solid theoretical basis for the NHFe(2) studies, mostly by providing benchmarking and calibration of the computationally efficient and easy-to-use DFT methods.

Complete active space second-order perturbation theory with cumulant approximation for extended active-space wavefunction from density matrix renormalization group.

We report an extension of our previous development that incorporated quantum-chemical density matrix renormalization group (DMRG) into the complete active space second-order perturbation theory (CASPT2) [Y. Kurashige and T. Yanai, J. Chem. Phys. 135, 094104 (2011)]. In the previous study, the combined theory, referred to as DMRG-CASPT2, was built upon the use of pseudo-canonical molecular orbitals (PCMOs) for one-electron basis. Within the PCMO basis, the construction of the four-particle reduced density matrix (4-RDM) using DMRG can be greatly facilitated because of simplicity in the multiplication of 4-RDM and diagonal Fock matrix in the CASPT2 equation. In this work, we develop an approach to use more suited orbital basis in DMRG-CASPT2 calculations, e.g., localized molecular orbitals, in order to extend the domain of applicability. Because the multiplication of 4-RDM and generalized Fock matrix is no longer simple in general orbitals, an approximation is made to it using the cumulant reconstruction neglecting higher-particle cumulants. Also, we present the details of the algorithm to compute 3-RDM of the DMRG wavefunction as an extension of the 2-RDM algorithm of Zgid et al. [J. Chem. Phys. 128, 144115 (2008)] and Chan et al. [J. Chem. Phys. 128, 144117 (2008)]. The performance of the extended DMRG-CASPT2 approach was examined for large-scale multireference systems, such as low-lying excited states of long-chain polyenes and isomerization potential of {[Cu(NH3)3]2O2}(2+).

Reactivity of the binuclear non-heme iron active site of Δ9 desaturase studied by large-scale multireference ab initio calculations.

The results of density matrix renormalization group complete active space self-consistent field (DMRG-CASSCF) and second-order perturbation theory (DMRG-CASPT2) calculations are presented on various structural alternatives for the O-O and first C-H activating step of the catalytic cycle of the binuclear nonheme iron enzyme Δ(9) desaturase. This enzyme is capable of inserting a double bond into an alkyl chain by double hydrogen (H) atom abstraction using molecular O2. The reaction step studied here is presumably associated with the highest activation barrier along the full pathway; therefore, its quantitative assessment is of key importance to the understanding of the catalysis. The DMRG approach allows unprecedentedly large active spaces for the explicit correlation of electrons in the large part of the chemically important valence space, which is apparently conditio sine qua non for obtaining well-converged reaction energetics. The derived reaction mechanism involves protonation of the previously characterized 1,2-µ peroxy Fe(III)Fe(III) (P) intermediate to a 1,1-µ hydroperoxy species, which abstracts an H atom from the C10 site of the substrate. An Fe(IV)-oxo unit is generated concomitantly, supposedly capable of the second H atom abstraction from C9. In addition, several popular DFT functionals were compared to the computed DMRG-CASPT2 data. Notably, many of these show a preference for heterolytic C-H cleavage, erroneously predicting substrate hydroxylation. This study shows that, despite its limitations, DMRG-CASPT2 is a significant methodological advancement toward the accurate computational treatment of complex bioinorganic systems, such as those with the highly open-shell diiron active sites.

Radical O-O coupling reaction in diferrate-mediated water oxidation studied using multireference wave function theory.

The O-O (oxygen-oxygen) bond formation is widely recognized as a key step of the catalytic reaction of dioxygen evolution from water. Recently, the water oxidation catalyzed by potassium ferrate (K2FeO4) was investigated on the basis of experimental kinetic isotope effect analysis assisted by density functional calculations, revealing the intramolecular oxo-coupling mechanism within a di-iron(vi) intermediate, or diferrate [Sarma et al., J. Am. Chem. Soc., 2012, 134, 15371]. Here, we report a detailed examination of this diferrate-mediated O-O bond formation using scalable multireference electronic structure theory. High-dimensional correlated many-electron wave functions beyond the one-electron picture were computed using the ab initio density matrix renormalization group (DMRG) method along the O-O bond formation pathway. The necessity of using large active space arises from the description of complex electronic interactions and varying redox states both associated with two-center antiferromagnetic multivalent iron-oxo coupling. Dynamic correlation effects on top of the active space DMRG wave functions were additively accounted for by complete active space second-order perturbation (CASPT2) and multireference configuration interaction (MRCI) based methods, which were recently introduced by our group. These multireference methods were capable of handling the double shell effects in the extended active space treatment. The calculations with an active space of 36 electrons in 32 orbitals, which is far over conventional limitation, provide a quantitatively reliable prediction of potential energy profiles and confirmed the viability of the direct oxo coupling. The bonding nature of Fe-O and dual bonding character of O-O are discussed using natural orbitals.

Flexible nuclear screening approximation to the two-electron spin-orbit coupling based on ab initio parameterization.

The derivation, implementation, and validation of a new approximation to the two-electron spin-orbit coupling (SOC) terms is reported. The approximation, referred to as flexible nuclear screening spin-orbit, is based on the effective one-electron spin-orbit operator and accounts for two-electron SOC effects by screening nuclear charges. A highly flexible scheme for the nuclear screening is developed, mainly using parameterization based on ab initio atomic SOC calculations. Tabulated screening parameters are provided for contracted and primitive Gaussian-type basis functions of the ANO-RCC basis set for elements from H to Cm. The strategy for their adaptation to any other Gaussian basis set is presented and validated. A model to correct for the effect of splitting of transition metal d orbitals on their SOC matrix elements is introduced. The method is applied to a representative set of molecules, and compared to exact treatment and other approximative approaches at the same level of relativistic theory. The calculated SOC matrix elements are in very good agreement with their "exact" values; deviation below 1% is observed on average. The presented approximation is considered to be generally applicable, simple to implement, highly efficient, and accurate.

Multireference ab initio calculations of g tensors for trinuclear copper clusters in multicopper oxidases.

EPR spectroscopy has proven to be an indispensable tool in elucidating the structure of metal sites in proteins. In recent years, experimental EPR data have been complemented by theoretical calculations, which have become a standard tool of many quantum chemical packages. However, there have only been a few attempts to calculate EPR g tensors for exchange-coupled systems with more than two spins. In this work, we present a quantum chemical study of structural, electronic, and magnetic properties of intermediates in the reaction cycle of multicopper oxidases and of their inorganic models. All these systems contain three copper(II) ions bridged by hydroxide or O(2-) anions and their ground states are antiferromagnetically coupled doublets. We demonstrate that only multireference methods, such as CASSCF/CASPT2 or MRCI can yield qualitatively correct results (compared to the experimental values) and consider the accuracy of the calculated EPR g tensors as the current benchmark of quantum chemical methods. By decomposing the calculated g tensors into terms arising from interactions of the ground state with the various excited states, the origin of the zero-field splitting is explained. The results of the study demonstrate that a truly quantitative prediction of the g tensors of exchange-coupled systems is a great challenge to contemporary theory. The predictions strongly depend on small energy differences that are difficult to predict with sufficient accuracy by any quantum chemical method that is applicable to systems of the size of our target systems.

Effect of spin-orbit coupling on reduction potentials of octahedral ruthenium(II/III) and osmium(II/III) complexes.

Reduction potentials of several M(2+/3+) (M = Ru, Os) octahedral complexes, namely, [M(H2O)6](2+/3+), [MCl6](4-/3-), [M(NH3)6](2+/3+), [M(en)3](2+/3+) [M(bipy)3](2+/3+), and [M(CN)6](4-/3-), were calculated using the CASSCF/CASPT2/CASSI and MRCI methods including spin-orbit coupling (SOC) by means of first-order quasi-degenerate perturbation theory. It was shown that the effect of SOC accounts for a systematic shift of approximately -70 mV in the reduction potentials of the studied ruthenium (II/III) complexes and an approximately -300 mV shift for the osmium(II/III) complexes. SOC splits the sixfold-degenerate (2)T(2g) ground electronic state (in ideal octahedral symmetry) of the M(3+) ions into the E((5/2)g) Kramers doublet and G((3/2)g) quartet, which were calculated to split by 1354-1573 cm(-1) in the Ru(3+) complexes and 4155-5061 cm(-1) in the Os(3+) complexes. It was demonstrated that this splitting represents the main contribution to the stabilization of the M(3+) ground state with respect to the closed-shell (1)A(1g) ground state in M(2+) systems. Moreover, it was shown that the accuracy of the calculated reduction potentials depends on the calculated solvation energies of both the oxidized and reduced forms. For smaller ligands, it involves explicit inclusion of the second solvation sphere into the calculations, whereas implicit solvation models yield results of sufficient accuracy for complexes with larger ligands. In such cases (e.g., [M(bipy)3](2+/3+) and its derivatives), very good agreement between the calculated (SOC-corrected) values of the reduction potentials and the available experimental values was obtained. These results led us to the conclusion that especially for Os(2+/3+) complexes, inclusion of SOC is necessary to avoid systematic errors of approximately 300 mV in the calculated reduction potentials.

Quasiplanarity of the peptide bond.

The vibrational motions of the model peptide unit represented by the main-chain carbonyl carbon, oxygen, nitrogen, and amide hydrogen are analyzed quantum-mechanically using formamide, cis-N-methylformamide, trans-N-methylformamide, N,N-dimethylformamide, l-alanyl-l-alanine, and N-benzoylphenylalanine as dynamical models. To make this analysis computationally feasible, the peptide unit vibrational motions were first separated from the remaining molecular vibrational motions by means of the crude adiabatic (Born-Oppenheimer) approximation, and then, using the same approximate separation, the peptide unit dynamical problem was separated into sets of high- and low-frequency subproblems. Importantly, the simplest dynamical (one-dimensional) problem based on the separation of the amide out-of-plane motion from the rest of the peptide unit motions allows for a physically correct description of the effective "ground state" molecular geometry of all studied systems. The separation is thus believed to be also suitable for reliable estimation of the dynamical effects on the geometry of the peptide unit in other molecular systems.

Multireference ab initio calculations on reaction intermediates of the multicopper oxidases.

The multicopper oxidases (MCOs) couple the four-electron reduction of dioxygen to water with four one-electron oxidations of various substrates. Extensive spectroscopic studies have identified several intermediates in the MCO catalytic cycle, but they have not been able to settle the structures of three of the intermediates, viz. the native intermediate (NI), the peroxy intermediate (PI), and the peroxy adduct (PA). The suggested structures have been further refined and characterized by quantum mechanical/molecular mechanical (QM/MM) calculations. In this paper, we try to establish a direct link between theory and experiment, by calculating spectroscopic parameters for these intermediates using multireference wave functions from the multistate CASPT2 and MRDDCI2 methods. Thereby, we have been able to reproduce low-spin ground states (S = 0 or S = 1/2) for all the MCO intermediates, as well as a low-lying (approximately 150 cm-1) doublet state and a doublet-quartet energy gap of approximately 780 cm-1 for the NI. Moreover, we reproduce the zero-field splitting (approximately 70 cm-1) of the ground 2E state in a D3 symmetric hydroxy-bridged trinuclear Cu(II) model of the NI and obtain a quantitatively correct quartet-doublet splitting (164 cm-1) for a mu3-oxo-bridged trinuclear Cu(II) cluster. All results support the suggestion that the NI has an O2- atom in the center of the trinuclear cluster, whereas both the PI and PA have an O22- ion in the center of the cluster, in agreement with the QM/MM results and spectroscopic measurements.