A first-principles approach to the calculation of the on-site zero-field splitting in polynuclear transition metal complexes

Probing the dynamic behaviour and magnetic identification of seven coordinated Mn(II) complexes: a combined AIMD and multi-reference approach

We present an in-depth solution phase dynamics of rare seven coordinated pentagonal bipyramidal Mn(II) complexes, together with their binding affinity anticipated using ab initio molecular dynamics (AIMD) simulations and density functional theory (DFT). Moreover, the simulations at different temperatures (25 °C and 90 °C) interpret the rigidity and stability of the ligands with Mn(II) ions. An intuitive approach for modulating the easy plane magnetic anisotropy of the mononuclear Mn(II) complex has been revealed by this work. In this regard, we have performed an extensive theoretical study based on the ab initio CASSCF/NEVPT2 method, exhibiting the presence of an easy plane magnetic anisotropy with a positive value of axial zero-field splitting (ZFS) parameter D. The complex's magnetic properties and electronic relaxation reveal that the rhombic ZFS term (E) can be modulated as the symmetry around the Mn(II) ion varies. The magnitude of the D-value increased with a more symmetrical equatorial ligand as found in the order of [Mn(pydpa)(H2O)] > [Mn(cbda)(H2O)]- > [Mn(dpaaa)(H2O)]- > [Mn(dpasam)(H2O)]-. Furthermore, we found that substituting the equatorial oxygen atom with heavier S and Se-donor atoms switches the sign of magnetic anisotropy for the Mn(II) complexes. The magnitude of the D-value increased when the energy levels of the ground state (GS) and the first excited state (ES) decreased. The observed magneto-structural correlation reveals that shortening the distance of the axial water molecule (Mn-O(w)) increases the D-value by an order of magnitude for the symmetrical [Mn(pydpa)(H2O)] complex. Overall, the combined analysis of solution phase dynamics of Mn(II) complexes and their magnetic characterization opens up new avenues in coordination chemistry, molecular magnetism, spin-crossover materials, and catalysis.

Binuclear cobalt(II) and two-dimensional manganese(II) coordination compounds self-assembled by mixed bipyridine-tetracarboxylic ligands with single-ion magnet properties

A cobalt(II) complex and manganese(II) coordination polymer, formulated as [Co2(H2btca)(mbpy)4][H2btca]·4H2O (1) and {Mn2(btca)(mbpy)2(H2O)2}n (2) (H4btca = 1,2,4,5-benzenetetracarboxylic acid; mbpy = 4,4'-dimethyl-2,2'-bipyridyl), constructed by mixed bipyridine-tetracarboxylic ligands were synthesized and characterized. Single-crystal structural analyses reveal that compound 1 is a discrete neutral binuclear molecule, while compound 2 is a two-dimensional (2D) coordination polymer. The metal ions in these compounds are well isolated, with an intramolecular Co2+⋯Co2+ distance of 9.170 Å for 1 and Mn2+⋯Mn2+ separation of 10.984 and 11.164 Å for 2 due to the bulk tetracarboxylic linker. This isolation gives rise to a single-ion magnetism origin of the compounds. Magnetic studies reveal a large zero-field splitting parameter D of 82.6 cm-1 for 1, while a very small D of 0.42 cm-1 was observed for 2. Interestingly, dynamic ac magnetic measurements exhibited slow magnetic relaxation under the external dc field of the two compounds, revealing the field-supported single-ion magnet (SIM) of 1 and 2. The detailed theoretical calculations were further applied to understand the electronic structures, magnetic anisotropy, and relaxation dynamics in 1 and 2. Combined with our recently reported compound (Eur. J. Inorg. Chem., 2022, e202200354), the foregoing results provide not only a rare binuclear cobalt(II) SIM and the first 2D manganese(II) SIM coordination polymer but also a bipyridine-tetracarboxylic ligand approach toward novel SIMs.

Simulating Spin-Orbit Coupling with Quasidegenerate N-Electron Valence Perturbation Theory

We present the first implementation of spin-orbit coupling effects in fully internally contracted second-order quasidegenerate N-electron valence perturbation theory (SO-QDNEVPT2). The SO-QDNEVPT2 approach enables the computations of ground- and excited-state energies and oscillator strengths combining the description of static electron correlation with an efficient treatment of dynamic correlation and spin-orbit coupling. In addition to SO-QDNEVPT2 with the full description of one- and two-body spin-orbit interactions at the level of two-component Breit-Pauli Hamiltonian, our implementation also features a simplified approach that takes advantage of spin-orbit mean-field approximation (SOMF-QDNEVPT2). The accuracy of these methods is tested for the group 14 and 16 hydrides, 3d and 4d transition metal ions, and two actinide dioxides (neptunyl and plutonyl dications). The zero-field splittings of group 14 and 16 molecules computed using SO-QDNEVPT2 and SOMF-QDNEVPT2 are in good agreement with the available experimental data. For the 3d transition metal ions, the SO-QDNEVPT2 method is significantly more accurate than SOMF-QDNEVPT2, while no substantial difference in the performance of two methods is observed for the 4d ions. Finally, we demonstrate that for the actinide dioxides the results of SO-QDNEVPT2 and SOMF-QDNEVPT2 are in good agreement with the data from previous theoretical studies of these systems. Overall, our results demonstrate that SO-QDNEVPT2 and SOMF-QDNEVPT2 are promising multireference methods for treating spin-orbit coupling with a relatively low computational cost.

Water oxidation in oxygenic photosynthesis studied by magnetic resonance techniques

The understanding of light-induced biological water oxidation in oxygenic photosynthesis is of great importance both for biology and (bio)technological applications. The chemically difficult multistep reaction takes place at a unique protein-bound tetra-manganese/calcium cluster in photosystem II whose structure has been elucidated by X-ray crystallography (Umena et al. Nature 2011, 473, 55). The cluster moves through several intermediate states in the catalytic cycle. A detailed understanding of these intermediates requires information about the spatial and electronic structure of the Mn₄ Ca complex; the latter is only available from spectroscopic techniques. Here, the important role of Electron Paramagnetic Resonance (EPR) and related double resonance techniques (ENDOR, EDNMR), complemented by quantum chemical calculations, is described. This has led to the elucidation of the cluster's redox and protonation states, the valence and spin states of the manganese ions and the interactions between them, and contributed substantially to the understanding of the role of the protein surrounding, as well as the binding and processing of the substrate water molecules, the O-O bond formation and dioxygen release. Based on these data, models for the water oxidation cycle are developed.

Impact of the electric field on isotropic and anisotropic spin Hamiltonian parameters

One may obviously think that the best way to control magnetic properties relies on using a magnetic field. However, it is not convenient to focus a magnetic field on a small object, whereas it is much easier to do so with an electric field. Magnetoelectric coupling allows one to control the magnetization with the electric field and the polarization with the magnetic field and could therefore provide a solution to this problem. This paper aims at quantifying the impact of the electric field on both the isotropic magnetic exchange and the Dzyaloshinskii–Moriya interaction in the case of a binuclear system of S = 1/2 spins. This study follows previous studies that showed that very high Dzyaloshinskii–Moriya interaction, i.e., the antisymmetric exchange, can be generated when close to first order spin orbit coupling. We will, therefore, explore this regime in a model Cu(II) complex that exhibits a quasi-degeneracy of the [Formula: see text] and d xy orbitals. This situation is indeed the one that allows us to obtain the largest spin orbit couplings in transition metal complexes. We will show that both the magnetic exchange and the Dzyaloshinskii–Moriya interaction are very sensitive to the electric field and that it would therefore be possible to modulate and control magnetic properties by the electric field. Finally, rationalizations of the obtained results will be proposed.

Orientational Jahn-Teller Isomerism in the Dark-Stable State of Nature's Water Oxidase

The tetramanganese–calcium cluster of the oxygen‐evolving complex of photosystem II adopts electronically and magnetically distinct but interconvertible valence isomeric forms in its first light‐driven oxidized catalytic state, S₂. This bistability is implicated in gating the final catalytic states preceding O−O bond formation, but it is unknown how the biological system enables its emergence and controls its effect. Here we show that the Mn₄CaO₅ cluster in the resting (dark‐stable) S₁ state adopts orientational Jahn–Teller isomeric forms arising from a directional change in electronic configuration of the “dangler” Mn^III ion. The isomers are consistent with available structural data and explain previously unresolved electron paramagnetic resonance spectroscopic observations on the S₁ state. This unique isomerism in the resting state is shown to be the electronic origin of valence isomerism in the S₂ state, establishing a functional role of orientational Jahn–Teller isomerism unprecedented in biological or artificial catalysis.

Magnetic Anisotropy in a Cubane-like Ni4 Complex: An Ab Initio Perspective

Magnetic anisotropy, in the absence of an external magnetic field, relates to the degeneracy lift of energy levels. In the standard case of transition metal complexes, this property is usually modeled by an anisotropic spin Hamiltonian and one speaks of "zero-field splitting" (ZFS) of spin states. While the case of mononuclear complexes has been extensively described by means of ab initio quantum mechanical calculations, the literature on polynuclear complexes studied with these methodologies is rather scarce. In this work, advanced multiconfigurational wave function theory methods are applied to compute the ZFS of the ground S = 4 state of an actual tetranickel(II) complex, displaying a magnet behavior below 0.5 K. First, the isotropic couplings are computed in the absence of the spin-orbit coupling operator, in the full complex and also in clusters with only two active nickel(II) centers, confirming the occurrence of weak ferromagnetic couplings in this system. Second, the single-site magnetic anisotropies are computed on a cluster bearing only one active nickel(II) site, showing that the single-site anisotropy axes are not oriented in an optimal fashion for generating a large uniaxial molecular anisotropy. Furthermore, the possibility for involving only a few local orbital excited states in the calculation is assessed, actually opening the way for a consistent and manageable treatment of the ZFS of the ground S = 4 state. Third, multiconfigurational calculations are performed on the full complex, confirming the weak uniaxial anisotropy occurring for this state and also, interestingly, revealing a significant contribution of the lowest-lying orbitally excited S = 3 states. Overall, by comparison with the experiment, the reported results question the common habit of using only one structure, in particular derived from a crystallography experiment, to compute magnetic anisotropy parameters.

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.

Magnetic Properties and Electronic Structure of the S = 2 Complex [MnIII{(OPPh2)2N}3] Showing Field-Induced Slow Magnetization Relaxation

The high-spin S = 2 Mn(III) complex [Mn{(OPPh₂)₂N}₃] (1_Mn) exhibits field-induced slow relaxation of magnetization (Inorg. Chem. 2013, 52, 12869). Magnetic susceptibility and dual-mode X-band electron paramagnetic resonance (EPR) studies revealed a negative value of the zero-field-splitting (zfs) parameter D. In order to explore the magnetic and electronic properties of 1_Mn in detail, a combination of experimental and computational studies is presented herein. Alternating-current magnetometry on magnetically diluted samples (1_Mn/1_Ga) of 1_Mn in the diamagnetic gallium analogue, [Ga{(OPPh₂)₂N}₃], indicates that the slow relaxation behavior of 1_Mn is due to the intrinsic properties of the individual molecules of 1_Mn. Investigation of the single-crystal magnetization of both 1_Mn and 1_Mn/1_Ga by a micro-SQUID device reveals hysteresis loops below 1 K. Closed hysteresis loops at a zero direct-current magnetic field are observed and attributed to fast quantum tunneling of magnetization. High-frequency and -field EPR (HFEPR) spectroscopic studies reveal that, apart from the second-order zfs terms (D and E), fourth-order terms (B₄^m) are required in order to appropriately describe the magnetic properties of 1_Mn. These studies provide accurate spin-Hamiltonian (sH) parameters of 1_Mn, i.e., zfs parameters |D| = 3.917(5) cm^-1, |E| = 0.018(4) cm^-1, B⁰₄ = B₄² = 0, and B₄⁴ = (3.6 ± 1.7) × 10^-3 cm^-1 and g = [1.994(5), 1.996(4), 1.985(4)], and confirm the negative sign of D. Parallel-mode X-band EPR studies on 1_Mn/1_Ga and CH₂Cl₂ solutions of 1_Mn probe the electronic-nuclear hyperfine interactions in the solid state and solution. The electronic structure of 1_Mn is investigated by quantum-chemical calculations by employing recently developed computational protocols that are grounded on ab initio wave function theory. From computational analysis, the contributions of spin-spin and spin-orbit coupling to the magnitude of D are obtained. The calculations provide also computed values of the fourth-order zfs terms B₄^m, as well as those of the g and hyperfine interaction tensor components. In all cases, a very good agreement between the computed and experimentally determined sH parameters is observed. The magnetization relaxation properties of 1_Mn are rationalized on the basis of the composition of the ground-state wave functions in the absence or presence of an external magnetic field.

Model Dimeric Manganese(IV) Complexes Featuring Terminal Tris-hydroxotetraazaadamantane and Various Bridging Ligands

A series of model dinuclear manganese(IV) complexes of the general formula [(H₃COH)(L')Mn^IV(μ-L)₂Mn^IV(L')(HOCH₃)] is presented. These compounds feature capping 4,6,10-trihydroxo-3,5,7-trimethyl-1,4,6,10-tetraazaadamantane ligands derived from a polydentate oxime compound (L'). The bridging ligands L include azide (1), methoxide (2), and oxalate (3) anions. The magnetic properties and high-field (HF) EPR spectra of 1-3 were studied in detail and revealed varying weak antiferromagnetic coupling and modest zero-field splitting (ZFS) of the local quartet spin sites. Our HF EPR studies provide insight into the dimer ZFS, including determination of the corresponding parameters by giant spin approach for methoxido-bridged complex 2. Furthermore, the physicochemical properties of 1-3 were studied using IR, UV-vis, and electrochemical (cyclic voltammetry) methods. Theoretical exchange coupling constants were obtained using broken-symmetry (BS) density functional theory (DFT). Computational estimates of the local quartet ground spins state ZFSs of 1-3 were obtained using coupled-perturbed (CP) DFT and complete active space self-consistent field (CASSCF) calculations with n-electron valence state perturbation theory (NEVPT2) corrections. We found that the CP DFT calculations which used the B3LYP functional and models derived experimental structures performed best in reproducing both the magnitude and the sign of the experimental D values. Moreover, our computational investigation of 1-3 suggests that we observe metals sites which have an increased +3 character and are supported by redox noninnocent 4,6,10-trihydroxo-3,5,7-trimethyl-1,4,6,10-tetraazaadamantane ligands. The latter conclusion is further corroborated by the observation that the free ligand can be readily oxidized to yield a NO-based radical.

Dinuclear manganese(iii) complexes with bioinspired coordination and variable linkers showing weak exchange effects: a synthetic, structural, spectroscopic and computation study

High-resolution HFEPR indicates weak exchange interactions between Mn^III ions in agreement with DFT calculations.

Hyperfine tensors for a model system for the oxygen evolving complex of photosystem II: calculation of the anisotropy shift that occurs beyond the strong exchange limit

Broken-symmetry density functional calculations have been used to calculate effective ⁵⁵Mn hyperfine (A) tensors for a mixed-valence tetranuclear manganese complex, a model system for the S₂ state of the oxygen-evolving complex of photosystem II.

Noncollinear Two-Component Quasirelativistic Description of Spin Interactions in Exchange-Coupled Systems. Mapping Generalized Broken-Symmetry States to Effective Spin Hamiltonians

We provide a consistent mapping of noncollinear two-component quasirelativistic DFT energies with appropriate orientations of localized spinor quantization axes for multinuclear exchange-coupled transition-metal complexes onto an uncoupled anisotropic effective spin Hamiltonian. This provides access to the full exchange interaction tensor between the centers of spin-coupled systems in a consistent way. The proposed methodology may be best viewed as a generalized broken-symmetry density functional theory approach (gBS-DFT). While the calculations provided are limited to trinuclear systems ([M₃O(OOCH)₆(H₂O)₃]⁺, where M = Cr(III), Mn(III), Fe(III)) with C₃ symmetry, the method provides a general framework that is extendable to arbitrary systems. It offers an alternative to previous approaches to single-ion zero-field splittings, and it provides access to the less often examined antisymmetric Dzyaloshinskii-Moriya exchange interaction. Spin-orbit coupling is included self-consistently. This will be of particular importance for complexes involving 4d or 5d transition metal centers or possibly also for f-block elements, where a perturbational treatment of spin-orbit coupling may not be valid anymore. While a comparison with experimental data was indirect due to simplifications in the chosen model structures, the agreement obtained indicates the essential soundness of the presented approach.

Transient versus Static Electron Spin Relaxation in Mn(2+) Complexes Relevant as MRI Contrast Agents

The zero-field splitting (ZFS) parameters of the [Mn(EDTA)(H2O)](2-)·2H2O and [Mn(MeNO2A)(H2O)]·2H2O systems were estimated by using DFT and ab initio CASSCF/NEVPT2 calculations (EDTA = 2,2',2″,2‴-(ethane-1,2-diylbis(azanetriyl))tetraacetate; MeNO2A = 2,2'-(7-methyl-1,4,7-triazonane-1,4-diyl)diacetate). Subsequent molecular dynamics calculations performed within the atom-centered density matrix propagation (ADMP) approach provided access to the transient and static ZFS parameters, as well as to the correlation time of the transient ZFS. The calculated ZFS parameters present a reasonable agreement with the experimental values obtained from the analysis of (1)H relaxation data. The correlation times calculated for the two systems investigated turned out to be very short (τc ∼ 0.02-0.05 ps), which shows that the transient ZFS is modulated by molecular vibrations. On the contrary, the static ZFS is modulated by the rotation of the complexes in solution, which for the small complexes investigated here is characterized by rotational correlation times of τR ∼ 35-60 ps. As a result, electron spin relaxation in small Mn(2+) complexes is dominated by the static ZFS.

A five-coordinate Mn(iv) intermediate in biological water oxidation: spectroscopic signature and a pivot mechanism for water binding

Among the four photo-driven transitions of the water-oxidizing tetramanganese-calcium cofactor of biological photosynthesis, the second-last step of the catalytic cycle, that is the S₂ to S₃ state transition, is the crucial step that poises the catalyst for the final O-O bond formation. This transition, whose intermediates are not yet fully understood, is a multi-step process that involves the redox-active tyrosine residue and includes oxidation and deprotonation of the catalytic cluster, as well as the binding of a water molecule. Spectroscopic data has the potential to shed light on the sequence of events that comprise this catalytic step, which still lacks a structural interpretation. In this work the S₂-S₃ state transition is studied and a key intermediate species is characterized: it contains a Mn₃O₄Ca cubane subunit linked to a five-coordinate Mn(iv) ion that adopts an approximately trigonal bipyramidal ligand field. It is shown using high-level density functional and multireference wave function calculations that this species accounts for the near-infrared absorption and electron paramagnetic resonance observations on metastable S₂-S₃ intermediates. The results confirm that deprotonation and Mn oxidation of the cofactor must precede the coordination of a water molecule, and lead to identification of a novel low-energy water binding mode that has important implications for the identity of the substrates in the mechanism of biological water oxidation.