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

Understanding the Exchange Interaction between Paramagnetic Metal Ions and Radical Ligands: DFT and Ab Initio Study on Semiquinonato Cu(II) Complexes

The exchange coupling, represented by the J parameter, is of tremendous importance in understanding the reactivity and magnetic behavior of open-shell molecular systems. In the past, it was the subject of theoretical investigations, but these studies are mostly limited to the interaction between metallic centers. The exchange coupling between paramagnetic metal ions and radical ligands has hitherto received scant attention in theoretical studies, and thus the understanding of the factors governing this interaction is lacking. In this paper, we use DFT, CASSCF, CASSCF/NEVPT2, and DDCI3 methods to provide insight into exchange interaction in semiquinonato copper(II) complexes. Our primary objective is to identify structural features that affect this magnetic interaction. We demonstrate that the magnetic character of Cu(II)-semiquinone complexes are mainly determined by the relative position of the semiquinone ligand to the Cu(II) ion. The results can support the experimental interpretation of magnetic data for similar systems and can be used for the in-silico design of magnetic complexes with radical ligands.

From Gas Phase Observations to Solid State Reality: The Identification and Isolation of Trinuclear Salicylaldoximato Copper Complexes

Conditions have been identified in which phenolic aldoximes and ketoximes of the types used in commercial solvent extraction processes can be doubly deprotonated and generate polynuclear Cu complexes with lower extractant:Cu molar ratios than those found in commercial operations. Electrospray mass spectrometry has provided an insight into the solution speciation in extraction experiments and has identified conditions to allow isolation and characterization of polynuclear Cu-complexes. Elevation of pH is effective in enhancing the formation of trinuclear complexes containing planar {Cu₃-μ₃-O}⁴⁺ or {Cu₃-μ₃-OH}⁵⁺ units. DFT calculations suggest that such trinuclear complexes are more stable than other polynuclear species. Solid structures of complexes formed by a salicylaldoxime with a piperidino substituent ortho to the phenolic OH group (L⁹H₂) contain two trinuclear units in a supramolecular assembly, {[Cu₃OH(L⁹H)₃(ClO₄)](ClO₄)} ₂, formed by H-bonding between the central {Cu₃-μ₃-OH}⁵⁺ units and oxygen atoms in the ligands of an adjacent complex. Whilst the lower ligand:Cu molar ratios provide more efficient Cu-loading in solvent extraction processes, the requirement to raise the pH of the aqueous phase to achieve this will make it impractical in most commercial operations because extraction will be accompanied by the precipitation (as oxyhydroxides) of Fe(III) which is present in significant quantities in feed solutions generated by acid leaching of most Cu ores.

X-ray Structure and Magnetic Properties of Heterobimetallic Chains Based on the Use of an Octacyanidodicobalt(III) Complex as Metalloligand

The assembly of [Co2III(μ-2,5-dpp)(CN)8]2− anions and [MII(CH3OH)2(DMSO)2]2+ cations resulted into the formation of two heterobimetallic 1D coordination polymers of formula [MII(CH3OH)2(DMSO)2(μ-NC)2Co2III(μ-2,5-dpp)(CN)6]n·4nCH3OH [M = CoII (1)/FeII (2) and 2,5-dpp = 2,5-bis(2-pyridyl)pyrazine. The [Co2III(μ-2,5-dpp)(CN)8]2− metalloligand coordinates the paramagnetic [MII(CH3OH)2(DMSO)2]2+ complex cations, in a bis-monodentate fashion, to give rise to neutral heterobimetallic chains. Cryomagnetic dc (1.9–300 K) and ac (2.0–13 K) magnetic measurements for 1 and 2 show the presence of Co(II)HS (1) and Fe(II)HS (2) ions (HS – high-spin), respectively, with D values of +53.7(5) (1) and −5.1(3) cm−1 (2) and slow magnetic relaxation for 1, this compound being a new example of SIM with transversal magnetic anisotropy. Low-temperature Q-band EPR study of 1 confirms that D value is positive, which reveals the occurrence of a strong asymmetry in the g-tensors and allows a rough estimation of the E/D ratio, whereas 2 is EPR silent. Theoretical calculations by CASSCF/NEVPT2 on 1 and 2 support the results from magnetometry and EPR. The analysis of the ac magnetic measurements of 1 shows that the relaxation of M takes place in the ground state under external magnetic dc fields through dominant Raman and direct spin-phonon processes.

Slow magnetic relaxation and water oxidation activity of dinuclear CoIICoIII and unique triangular CoIICoIICoIII mixed-valence complexes

Construction of efficient multifunctional materials is one of the greatest challenges of our time. We herein report the magnetic and catalytic characterization of dinuclear [CoIIICoII(HL1)2(EtOH)(H2O)]Cl·2H2O (1) and trinuclear [CoIIICoII2(HL2)2(L2)Cl2]·3H2O (2) mixed valence complexes. Relevant structural features of the complexes have been mentioned to correlate with their magnetic and catalytic properties. Unique structural features, especially in terms of significant distortions around the CoII centre(s), prompted us to test both spin-orbit coupling (SOC) and zero field splitting (ZFS) methodologies for the systems. The positive sign of D values has been established from X-band EPR spectra recorded in the 5-40 K temperature range and reaffirmed by CAS/NEVPT2 calculations. ZFS tensors are also extracted for the compounds along with CoIIGaIII and CoIIZnIICoIII model species. Interestingly, 1 shows slow relaxation of magnetization below 6.5 K in the presence of a 1000 Oe external dc field with two relaxation processes (Ueff = 37.0 K with τ0 = 1.57 × 10-8 s for the SR process and Ueff = 7 K with τ0 = 1.66 × 10-6 s for the FR process). As mixed valence cobalt complexes with various nuclearities are central to the quest for water oxidation catalysts, we were prompted to explore their features and to our surprise, water oxidation ability has been realized for both 1 and 2 with significant nuclearity control.

Magneto-structural diversity of Co(ii) compounds with 1-benzylimidazole induced by linear pseudohalide coligands

The magneto-structural diversity of 1-benzylimidazole-containing cobalt(ii) compounds with linear pseudohalide ions (NCS⁻, NCO⁻, and N₃⁻) is explored.

Coligand Effects on the Field-Induced Double Slow Magnetic Relaxation in Six-Coordinate Cobalt(II) Single-Ion Magnets (SIMs) with Positive Magnetic Anisotropy

Two mononuclear cobalt(II) compounds of formula [Co(dmphen)₂(OOCPh)]ClO₄·1/2H₂O·1/2CH₃OH (1) and [Co(dmbipy)₂(OOCPh)]ClO₄ (2) (dmphen = 2,9-dimethyl-1,10-phenanthroline, dmbipy = 6,6'-dimethyl-2,2'-bipyridine and HOOCPh = benzoic acid) are prepared and magnetostructurally investigated. Each cobalt(II) ion is six-coordinate with a distorted octahedral CoN₄O₂ environment. The complex cations are interlinked leading to supramolecular chains (1) and pairs (2) that grow along the crystallographic c-axis with racemic mixtures of (Δ,Λ)-Co units. FIRMS allowed us to directly measure the zero-field splitting between the two lowest Kramers doublets, which led to axial anisotropy values of 58.3 cm^-1 ≤ D < 60.7 cm^-1 (1) and 63.8 cm^-1 ≤ D < 64.1 cm^-1 (2). HFEPR spectra of polycrystalline samples of 1 and 2 at low temperatures confirm the positive sign of D and provide an estimate of the E/D quotient [0.147/0.187 (1) and 0.052 (2)]. Detailed ac and dc magnetic studies reveal that 1 and 2 are new examples of field-induced single-ion magnets (SIMs) with small transversal anisotropy. CASSCF/NEVPT2 calculations support these results. Two Orbach processes or one Orbach plus a direct relaxation mechanism provide similar agreements with the nonlinear experimental Arrhenius plots at H_dc = 500 and 2500 G for 1. Two independent relaxation processes occur in 2, but in contrast to 1, an observed linear dependence of ln(τ) vs 1/T substantiates Orbach processes against the most widely proposed Raman and direct mechanisms. The analysis of each relaxation process in 2 provided values for E_a and τ₀ that are very close to those found for 1, validating the predominant role of the Orbach relaxations in both compounds and, probably, also in other cobalt(II) SIMs. A mechanism based on a spin-phonon coupling is proposed to account for the SIM behavior in 1 and 2 with any Raman or direct processes being discarded.

Influence of the pyrazine substituent on the structure and magnetic properties of dicyanamide-bridged cobalt(ii) complexes

Substituted pyrazines were successfully used to prepare two new coordination polymers of formulas {[Co(dca)2(NH2pyz)2]·H2O}n (1) and [Co3(dca)6(HOpyz)5(H2O)2]n (2) [dca = dicyanamide, NH2pyz = 2-aminopyrazine and HOpyz = 2-hydroxypyrazine] whose structures were determined by single-crystal X-ray crystallography. The structure of 1 consists of a two-dimensional rhombus grid of cobalt(ii) ions where the dca ligand adopts the μ1,5 bridging mode with trans-positioned monodentate NH2pyz molecules completing the six-coordination around each metal ion. Compound 2 exhibits a stair-like two-dimensional structure where the intralayer connections are performed by the dca and HOpyz groups exhibiting μ1,5 and bis-monodentate coordination modes, respectively. The values of the cobalt-cobalt separation through the dca bridges are 8.2107(3) (1) and 8.4746(4) and 8.5249(4) Å (2) whereas the value through the hydroxypyrazine is 7.2052(6) Å (2). Solid-state direct-current magnetic susceptibility analyses in the temperature range of 1.9-300 K for 1 and 2 reveal the occurrence of magnetically isolated high-spin cobalt(ii) ions with a significant contribution to the magnetic moment (1 and 2), D = +95.4 (1) and +76.5 cm-1 (2) and the antiferromagnetically coupled pairs of cobalt(ii) centres through the bis-monodentate 2-hydroxypyrazine, J = -0.3 cm-1 (2). Both compounds exhibit frequency dependence of the out-of-phase alternating current (ac) magnetic susceptibility (χ''M) under non-zero applied dc fields, a feature which is characteristic of single-ion magnet behaviour (SIM). Q-band EPR studies on the polycrystalline samples of 1 and 2 at low temperatures confirm the positive sign of D and reveal the occurrence of a strong asymmetry in the g-tensors. Theoretical calculations by CASSCF/NEVPT2 support these results. An analysis of the dynamic behaviour of 1 and 2 suggests that the relaxation of the magnetization occurs in the ground state under applied fields through two Orbach processes possibly bound to low-lying vibrational modes in the high temperature range, and to the slowing down of the fast interconversion between the two contributions of the ground Kramers doublet at lower temperatures induced by the applied dc field.

Field-induced slow magnetic relaxation in pseudooctahedral cobalt(ii) complexes with positive axial and large rhombic anisotropy

The preparation, X-ray crystal structure, spectroscopic and variable-temperature dc and ac magnetic properties of two six-coordinate cobalt(ii) complexes of formula [Co(bim)₄(tcm)₂] (1) and [Co(bmim)₄(tcm)₂] (2) are reported.

Highly efficient perturbative + variational strategy based on orthogonal valence bond theory for the evaluation of magnetic coupling constants. Application to the trinuclear Cu(ii) site of multicopper oxidases

A new perturbative + variational strategy: a low-cost, quantitative and rational evaluation of the magnetic coupling constant in complex systems.

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.

Can anisotropic exchange be reliably calculated using density functional methods? A case study on trinuclear Mn(III)-M(III)-Mn(III) (M=Fe, Ru, and Os) cyanometalate single-molecule magnets

Density functional studies have been performed on a set of trinuclear single-molecule magnets (SMMs) of general formula [{Mn2(5-Br salen)2(MeOH)2}M(CN)6](NEt4) (M=Fe(III) (1), Ru(III) (2) and Os(III) (3); 5-Brsalen=N,N'-ethylenebis(5-bromosalicylidene)iminato anion). We have computed the orbital-dependent exchange interaction for all three complexes for the first time using DFT and complete active space self-consistent field (CASSCF) methods. DFT calculations yield the anisotropic exchange as J(ξξ)=3.5 cm(-1) for 1; J(ξξ)=12.1 cm(-1), J(ζζ)=-6.9 cm(-1) and J(ηη)=-14 cm(-1) for 2; and J(ξξ)=23.7 cm(-1) and J(ζζ) =-11.1 cm(-1) for 3. The computed values are in agreement with the experimental report, and this suggests that the established methodology can be used to compute the anisotropic exchange in larger clusters. Our calculations reiterate the fact that the exchange is described by a three-axis anisotropic exchange for complexes 2 and 3 as evidenced by the experiments. A stronger exchange coupling as we move down the periodic table from 3d to 5d is reproduced by our calculations, and the origin of this enhancement in the exchange interaction has been probed by using molecular orbital analysis. The electronic origin of different types of exchange observed in this series is found to be related to the energy difference between possible degenerate pairs and the nature of orbital interactions. By computing the exchange interaction, the single-ion anisotropy of Mn(III) and zero-field splitting of the S=9/2 ground state of complexes 1-3 using CASSCF and/or DFT methods, we have attempted to shed light on the issue of anisotropic exchange and the barrier height for the magnetisation reversal in SMMs. Comprehensive magneto-structural correlations have been developed to offer clues on how to further enhance the barrier height in this class of SMMs.

Reorganization energy for internal electron transfer in multicopper oxidases

We have calculated the reorganization energy for the intramolecular electron transfer between the reduced type 1 copper site and the peroxy intermediate of the trinuclear cluster in the multicopper oxidase CueO. The calculations are performed at the combined quantum mechanics and molecular mechanics (QM/MM) level, based on molecular dynamics simulations with tailored potentials for the two copper sites. We obtain a reorganization energy of 91-133 kJ/mol, depending on the theoretical treatment. The two Cu sites contribute by 12 and 22 kJ/mol to this energy, whereas the solvent contribution is 34 kJ/mol. The rest comes from the protein, involving small contributions from many residues. We have also estimated the energy difference between the two electron-transfer states and show that the reduction of the peroxy intermediate is exergonic by 43-87 kJ/mol, depending on the theoretical method. Both the solvent and the protein contribute to this energy difference, especially charged residues close to the two Cu sites. We compare these estimates with energies obtained from QM/MM optimizations and QM calculations in a vacuum and discuss differences between the results obtained at various levels of theory.

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.

Systematic theoretical study of the zero-field splitting in coordination complexes of Mn(III). Density functional theory versus multireference wave function approaches

This paper presents a detailed evaluation of the performance of density functional theory (DFT) as well as complete active space self-consistent field (CASSCF)-based methods (CASSCF and second-order N-electron valence state perturbation theory, NEVPT2) to predict the zero-field splitting (zfs) parameters for a series of coordination complexes containing the Mn(III) ion. The physical origin of the experimentally determined zfs's was investigated by studying the different contributions to these parameters. To this end, a series of mononuclear Mn(III) complexes was chosen for which the structures have been resolved by X-ray diffraction and the zfs parameters have been accurately determined by high-field EPR spectroscopy. In a second step, small models have been constructed to allow for a systematic assessment of the factors that dominate the variations in the observed zfs parameters and to establish magnetostructural correlations. Among the tested functionals, the best predictions have been obtained with B3LYP, followed by the nonhybrid BP86 functional, which in turn is more successful than the meta-hybrid GGA functional TPSSh. For the estimation of the spin-orbit coupling (SOC) part of the zfs, it was found that the coupled perturbed SOC approach CP is more successful than the Pederson-Khanna method. Concerning the spin-spin interaction (SS), the restricted open-shell Kohn-Sham (ROKS) approach led to a slightly better agreement with the experiment than the unrestricted KS (UKS) approach. The ab initio state-averaged CASSCF (SA-CASSCF) method with a minimal active space and the most recent implementation that treats the SOC and SS contributions on an equal footing provides the best predictions for the zfs. The analysis demonstrates that the major contribution to the axial zfs parameter (D) originates from the SOC interaction but that the SS part is far from being negligible (between 10 and 20% of D). Importantly, the various excited triplet ligand field states account for roughly half of the value of D, contrary to popular ligand field models. Despite covering dynamic correlation contributions to the transition energies, NEVPT2 does not lead to large improvements in the results as the excitation energies of the Mn(III) d-d transitions are already fairly accurate at the SA-CASSCF level. For a given type of coordination sphere (e.g., elongated or compressed octahedron), the magnetic anisotropy of the Mn(III) ion, D, does not appear to be highly sensitive to the nature of the ligands, while the E/D ratio is notably affected by all octahedral distortions. Furthermore, the introduction of different halides into the coordination sphere of Mn(III) only leads to small effects on D. Nevertheless, it appears that oxygen-based ligands afford larger D values than nitrogen-based ligands.

Multiconfigurational Second-Order Perturbation Theory Restricted Active Space (RASPT2) Method for Electronic Excited States: A Benchmark Study

The recently developed second-order perturbation theory restricted active space (RASPT2) method has been benchmarked versus the well-established complete active space (CASPT2) approach. Vertical excitation energies for valence and Rydberg excited states of different groups of organic (polyenes, acenes, heterocycles, azabenzenes, nucleobases, and free base porphin) and inorganic (nickel atom and copper tetrachloride dianion) molecules have been computed at the RASPT2 and multistate (MS) RASPT2 levels using different reference spaces and compared with CASPT2, CCSD, and experimental data in order to set the accuracy of the approach, which extends the applicability of multiconfigurational perturbation theory to much larger and complex systems than previously. Relevant aspects in multiconfigurational excited state quantum chemistry such as the valence-Rydberg mixing problem in organic molecules or the double d-shell effect for first-row transition metals have also been addressed.