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

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.

Computational Insights into Electronic Excitations, Spin-Orbit Coupling Effects, and Spin Decoherence in Cr(IV)-Based Molecular Qubits

The great success of point defects and dopants in semiconductors for quantum information processing has invigorated a search for molecules with analogous properties. Flexibility and tunability of desired properties in a large chemical space have great advantages over solid-state systems. The properties analogous to point defects were demonstrated in the Cr(IV)-based molecular family, Cr(IV)(aryl)₄, where the electronic spin states were optically initialized, read out, and controlled. Despite this kick-start, there is still a large room for enhancing properties crucial for molecular qubits. Here, we provide computational insights into key properties of the Cr(IV)-based molecules aimed at assisting the chemical design of efficient molecular qubits. Using the multireference ab initio methods, we investigate the electronic states of Cr(IV)(aryl)₄ molecules with slightly different ligands, showing that the zero-phonon line energies agree with the experiment and that the excited spin-triplet and spin-singlet states are highly sensitive to small chemical perturbations. By adding spin-orbit interaction, we find that the sign of the uniaxial zero-field splitting (ZFS) parameter is negative for all considered molecules and discuss optically induced spin initialization via non-radiative intersystem crossing. We quantify (super)hyperfine coupling to the ⁵³Cr nuclear spin and to the ¹³C and ¹H nuclear spins, and we discuss electron spin decoherence. We show that the splitting or broadening of the electronic spin sub-levels due to superhyperfine interaction with ¹H nuclear spins decreases by an order of magnitude when the molecules have a substantial transverse ZFS parameter.

Computational design of magnetic molecules and their environment using quantum chemistry, machine learning and multiscale simulations

Having served as a playground for fundamental studies on the physics of d and f electrons for almost a century, magnetic molecules are now becoming increasingly important for technological applications, such as magnetic resonance, data storage, spintronics and quantum information. All of these applications require the preservation and control of spins in time, an ability hampered by the interaction with the environment, namely with other spins, conduction electrons, molecular vibrations and electromagnetic fields. Thus, the design of a novel magnetic molecule with tailored properties is a formidable task, which does not only concern its electronic structures but also calls for a deep understanding of the interaction among all the degrees of freedom at play. This Review describes how state-of-the-art ab initio computational methods, combined with data-driven approaches to materials modelling, can be integrated into a fully multiscale strategy capable of defining design rules for magnetic molecules.

Multiconfiguration Pair-Density Functional Theory for Chromium(IV) Molecular Qubits

Pseudotetrahedral organometallic complexes containing chromium(IV) and aryl ligands have been experimentally identified as promising molecular qubit candidates. Here we present a computational protocol based on multiconfiguration pair-density functional theory for computing singlet-triplet gaps and zero-field splitting (ZFS) parameters in Cr(IV) aryl complexes. We find that two multireference methods, multistate complete active space second-order perturbation theory (MS-CASPT2) and hybrid multistate pair-density functional theory (HMS-PDFT), perform better than Kohn-Sham density functional theory for singlet-triplet gaps. Despite the very small values of the ZFS parameters, both multireference methods performed qualitatively well. MS-CASPT2 and HMS-PDFT performed particularly well for predicting the trend in the ratio of the rhombic and axial ZFS parameters, |E/D|. We have also investigated the dependence and sensitivity of the calculated ZFS parameters on the active space and the molecular geometry. The methodologies outlined here can guide future prediction of ZFS parameters in molecular qubit candidates.

Antisymmetric Exchange in a Real Copper Triangular Complex

The antisymmetric exchange, also known as the Dzyaloshinskii-Moriya interaction (DMI), is an effective interaction that may be at play in isolated complexes (with transition metals or lanthanides, for instance), nanoparticles, and highly correlated materials with adequate symmetry properties. While many theoretical works have been devoted to the analysis of single-ion zero-field splitting and to a lesser extent to symmetric exchange, only a few ab initio studies deal with the DMI. Actually, it originates from a subtle interplay between weak electronic interactions and spin-orbit couplings. This article aims to highlight the origin of this interaction from theoretical grounds in a real tri-copper(II) complex, capitalizing on previous methodological studies on bi-copper(II) model complexes. By tackling this three-magnetic-center system, we will first show that the multispin model Hamiltonian is appropriate for trinuclear (and likely for higher nuclearity) complexes, then that the correct application of the permutation relationship is necessary to explain the outcomes of the ab initio calculations, and finally, that the model parameters extracted from a binuclear model transfer well to the trinuclear complex. For a more theory-oriented purpose, we will show that the use of a simplified structural model allows one to perform more demanding electronic structure calculations. On this simpler system, we will first check that the previous transferability is still valid, prior to performing more advanced calculations on the derived two-magnetic-center model system. To this end, we will explain in detail the physics of the DMI in the copper triangle of interest, before advocating further theory/experiment efforts.

Zero-Field Splitting Calculations by Multiconfiguration Pair-Density Functional Theory

Zero-field splitting (ZFS) is a fundamental molecular property that is especially relevant for single-molecule magnets (SMMs), electron paramagnetic resonance spectra, and quantum computing. Developing a method that can accurately predict ZFS parameters can be very powerful for designing new SMMs. One of the challenges is to include external correlation in an inherently multiconfigurational open-shell species for the accurate prediction of magnetic properties. Previously available methods depend on expensive multireference perturbation theory calculations to include external correlation. In this paper, we present spin-orbit-inclusive multiconfiguration and multistate pair-density functional theory (MC-PDFT) calculations of ZFSs; these calculations have a cost comparable to complete-active-space self-consistent field (CASSCF) theory, but they include correlation external to the active space. We found that combining a multistate formulation of MC-PDFT, namely, compressed-state multistate pair-density functional theory, with orbitals optimized by weighted-state-averaged CASSCF, yields reasonably accurate ZFS results.

Homochiral Mn3+ Spin-Crossover Complexes: A Structural and Spectroscopic Study

Structural, magnetic, and spectroscopic data on a Mn³⁺ spin-crossover complex with Schiff base ligand 4-OMe-Sal₂323, isolated in crystal lattices with five different counteranions, are reported. Complexes of [Mn(4-OMe-Sal₂323)]X where X = ClO₄^– (1), BF₄^– (2), NO₃^– (3), Br^– (4), and I^– (5) crystallize isotypically in the chiral orthorhombic space group P2₁2₁2 with a range of spin state preferences for the [Mn(4-OMe-Sal₂323)]⁺ complex cation over the temperature range 5–300 K. Complexes 1 and 2 are high-spin, complex 4 undergoes a gradual and complete thermal spin crossover, while complexes 3 and 5 show stepped crossovers with different ratios of spin triplet and quintet forms in the intermediate temperature range. High-field electron paramagnetic resonance was used to measure the zero-field splitting parameters associated with the spin triplet and quintet states at temperatures below 10 K for complexes 4 and 2 with respective values: D_S=1 = +23.38(1) cm^–1, E_S=1 = +2.79(1) cm^–1, and D_S=2 = +6.9(3) cm^–1, with a distribution of E parameters for the S = 2 state. Solid-state circular dichroism (CD) spectra on high-spin complex 1 at room temperature reveal a 2:1 ratio of enantiomers in the chiral conglomerate, and solution CD measurements on the same sample in methanol show that it is stable toward racemization. Solid-state UV–vis absorption spectra on high-spin complex 1 and mixed S = 1/S = 2 sample 5 reveal different intensities at higher energies, in line with the different electronic composition. The statistical prevalence of homochiral crystallization of [Mn(4-OMe-Sal₂323)]⁺ in five lattices with different achiral counterions suggests that the chirality may be directed by the 4-OMe-Sal₂323 ligand.

Zero-field splitting parameters of the spin triplet and quintet forms of a spin-crossover Mn³⁺ complex stabilized in lattices with different counterions are measured by high-field electron paramagnetic resonance at different frequencies. The homochiral crystallization of the enantiopure Δ or Λ forms of the chelate complex, despite the use of achiral anions, is attributed to the steric influence of the ligand substituent.

The Ruthenium Nitrosyl Moiety in Clusters: Trinuclear Linear μ-Hydroxido Magnesium(II)-Diruthenium(II), μ3-Oxido Trinuclear Diiron(III)-Ruthenium(II), and Tetranuclear μ4-Oxido Trigallium(III)-Ruthenium(II) Complexes

The ruthenium nitrosyl moiety, {RuNO}⁶, is important as a potential releasing agent of nitric oxide and is of inherent interest in coordination chemistry. Typically, {RuNO}⁶ is found in mononuclear complexes. Herein we describe the synthesis and characterization of several multimetal cluster complexes that contain this unit. Specifically, the heterotrinuclear μ₃-oxido clusters [Fe₂RuCl₄(μ₃-O)(μ-OMe)(μ-pz)₂(NO)(Hpz)₂] (6) and [Fe₂RuCl₃(μ₃-O)(μ-OMe)(μ-pz)₃(MeOH)(NO)(Hpz)][Fe₂RuCl₃(μ₃-O)(μ-OMe)(μ-pz)₃(DMF)(NO)(Hpz)] (7·MeOH·2H₂O) and the heterotetranuclear μ₄-oxido complex [Ga₃RuCl₃(μ₄-O)(μ-OMe)₃(μ-pz)₄(NO)] (8) were prepared from trans-[Ru(OH)(NO)(Hpz)₄]Cl₂ (5), which itself was prepared via acidic hydrolysis of the linear heterotrinuclear complex {[Ru(μ-OH)(μ-pz)₂(pz)(NO)(Hpz)]₂Mg} (4). Complex 4 was synthesized from the mononuclear Ru complexes (H₂pz)[trans-RuCl₄(Hpz)₂] (1), trans-[RuCl₂(Hpz)₄]Cl (2), and trans-[RuCl₂(Hpz)₄] (3). The new compounds 4–8 were all characterized by elemental analysis, ESI mass spectrometry, IR, UV–vis, and ¹H NMR spectroscopy, and single-crystal X-ray diffraction, with complexes 6 and 7 being characterized also by temperature-dependent magnetic susceptibility measurements and Mössbauer spectroscopy. Magnetometry indicated a strong antiferromagnetic interaction between paramagnetic centers in 6 and 7. The ability of 4 and 6–8 to form linkage isomers and release NO upon irradiation in the solid state was investigated by IR spectroscopy. A theoretical investigation of the electronic structure of 6 by DFT and ab initio CASSCF/NEVPT2 calculations indicated a redox-noninnocent behavior of the NO ancillary ligand in 6, which was also manifested in TD-DFT calculations of its electronic absorption spectrum. The electronic structure of 6 was also studied by an X-ray charge density analysis.

Mononuclear trans-[Ru(OH)NO(Hpz)₄]²⁺ proved to be a source of μ-hydroxido and μ₃- and/or μ₄-oxido bridging groups, which could be incorporated into the heterotrinuclear complexes {[Ru(μ-OH)(μ-pz)₂(pz)(NO)(Hpz)]₂Mg}, [Fe₂RuCl₄(μ₃-O)(μ-OMe)(μ-pz)₂(NO)(Hpz)₂], and [Fe₂RuCl₃(μ₃-O)(μ-OMe)(μ-pz)₃(MeOH)(NO)(Hpz)][Fe₂RuCl₃(μ₃-O)(μ-OMe)(μ-pz)₃(DMF)(NO)(Hpz)] (7·MeOH·2H₂O) and the heterotetranuclear μ₄-oxido complex [Ga₃RuCl₃(μ₄-O)(μ-OMe)₃(μ-pz)₄(NO)]. The structures obtained were all confirmed by SC-XRD, including an X-ray charge density analysis that revealed the electronic structure of the RuFe2 cluster. Two of these nitrosyl complexes underwent photoinduced isomerization with generation of the nitrosyl linkage isomers MS1 and MS2, as revealed by IR spectroscopy at 10 K.

Ultrafast processes: coordination chemistry and quantum theory

Coordination compounds, characterized by fascinating and tunable electronic properties, are capable of binding easily to proteins, polymers, wires and DNA. Upon irradiation, these molecular systems develop functions finding applications in solar cells, photocatalysis, luminescent and conformational probes, electron transfer triggers and diagnostic or therapeutic tools. The control of these functions is activated by the light wavelength, the metal/ligand cooperation and the environment within the first picoseconds (ps). After a brief summary of the theoretical background, this perspective reviews case studies, from 1st row to 3rd row transition metal complexes, that illustrate how spin-orbit, vibronic coupling and quantum effects drive the photophysics of this class of molecules at the early stage of the photoinduced elementary processes within the fs-ps time scale range.

Investigation of vanadium(III) and vanadium(IV) compounds supported by the linear diaminebis(phenolate) ligands: correlation between structures and magnetic properties

A family of oxidovanadium(iv) compounds containing linear diaminebis(phenolate (salans) L1-5 ligands (L1 = [MeNCH2CH2NMe(CH2-4-CMe2CH2CMe3-C6H3O)2]2-; L2 = [MeNCH2CH2NMe(CH2-4-CH3-C6H3O)2]2-; L3 = [MeNCH2CH2NMe(CH2-4-Cl-C6H3O)2]2-; L4 = {MeNCH2CH2NMe[CH2-4,6-(CH3)2-C6H2O]2}2-; and L5 = {MeNCH2CH2NMe[CH2-4,6-(Br)2-C6H2O]2}2-) and non-oxidovanadium(iii) with L2,4 and acac ligands has been prepared and characterized by chemical and physical techniques. Reactions of [VO(acac)2] with ligand precursors H2L2,4 in toluene or hexane afforded vanadium(iii) compounds [V(L-κ4ONNO)(acac)] (1, L2; 2, L4), while the use of acetonitrile or ethanol led to the formation of dimeric oxidovanadium(iv) [(VO)2(μ-L-κ4ONNO)2] (3, L1; 4, L2; 5, L3) and monomeric [VO(L-κ4ONNO)] (6, L4, 7, L5) compounds. As shown by X-ray crystallography, compounds 1 and 2 are monomeric, in which the chelating ligands afford octahedral cis-α geometry at the vanadium center. In the dimeric structures of 3-5, the six-coordinate vanadium centers are bridged via two oxygen atoms of the L1-3 ligands while the L4,5 ligands generate square pyramidal structures of the monomeric 6 and 7 compounds. HFEPR studies allowed the determination of the spin Hamiltonian parameters of the S = 1 spin state of the monomeric V(iii) and dimeric V(iv), and S = ½ in monomeric V(iv) compounds. Magnetic measurements of 3-5 indicated weak ferromagnetic metal-metal exchange interactions. A reaction course for the deoxygenation and reduction of vanadyl-salan compounds is proposed.

A Mononuclear and High-Spin Tetrahedral TiII Complex

A high-spin, mononuclear TiII complex, [(TptBu,Me)TiCl] [TptBu,Me- = hydridotris(3-tert-butyl-5-methylpyrazol-1-yl)borate], confined to a tetrahedral ligand-field environment, has been prepared by reduction of the precursor [(TptBu,Me)TiCl2] with KC8. Complex [(TptBu,Me)TiCl] has a 3A2 ground state (assuming C3v symmetry based on structural studies), established via a combination of high-frequency and -field electron paramagnetic resonance (HFEPR) spectroscopy, solution and solid-state magnetic studies, Ti K-edge X-ray absorption spectroscopy (XAS), and both density functional theory and ab initio (complete-active-space self-consistent-field, CASSCF) calculations. The formally and physically defined TiII complex readily binds tetrahydrofuran (THF) to form the paramagnetic adduct [(TptBu,Me)TiCl(THF)], which is impervious to N2 binding. However, in the absence of THF, the TiII complex captures N2 to produce the diamagnetic complex [(TptBu,Me)TiCl]2(η1,η1;μ2-N2), with a linear Ti═N═N═Ti topology, established by single-crystal X-ray diffraction. The N2 complex was characterized using XAS as well as IR and Raman spectroscopies, thus establishing this complex to possess two TiIII centers covalently bridged by an N22- unit. A π acid such as CNAd (Ad = 1-adamantyl) coordinates to [(TptBu,Me)TiCl] without inducing spin pairing of the d electrons, thereby forming a unique high-spin and five-coordinate TiII complex, namely, [(TptBu,Me)TiCl(CNAd)]. The reducing power of the coordinatively unsaturated TiII-containing [(ΤptBu,Me)TiCl] species, quantified by electrochemistry, provides access to a family of mononuclear TiIV complexes of the type [(TptBu,Me)Ti═E(Cl)] (with E2- = NSiMe3, N2CPh2, O, and NH) by virtue of atom- or group-transfer reactions using various small molecules such as N3SiMe3, N2CPh2, N2O, and the bicyclic amine 2,3:5,6-dibenzo-7-azabicyclo[2.2.1]hepta-2,5-diene.

Field-induced single molecule magnet behavior of a dinuclear cobalt(II) complex: a combined experimental and theoretical study

Two dinuclear cobalt(ii) complexes, [(dmso)CoIIL1(μ-(m-NO2)C6H4COO)CoII(NCS)] (1) and [(dmso)CoIIL2(μ-(m-NO2)C6H4COO)CoII(NCS)] (2) [dmso = dimethylsulfoxide, H2L1 = (2,2-dimethyl-1,3-propanediyl)bis(iminomethylene)bis(6-methoxyphenol) and H2L2 = (2,2-dimethyl-1,3-propanediyl)bis(iminomethylene)bis(6-ethoxyphenol)] have been synthesized and structurally characterized by single-crystal X-ray diffraction, magnetic-susceptibility measurements and various spectroscopic techniques. Each complex contains a cobalt(ii) center with a slightly distorted octahedral geometry and a second cobalt(ii) center with a distorted trigonal prismatic one. To obtain insight into the physical nature of weak non-covalent interactions, we have extensively used the Bader's quantum theory of atoms-in-molecules (QTAIM). In addition, the non-covalent interaction reduced density gradient (NCI-RDG) methods established the presence of such non-covalent intermolecular interactions. Variable temperature magnetic susceptibility measurements show that both cobalt centers in each complex are in the high spin state (S = 3/2) and both complexes show weak ferromagnetic couplings through the double phenoxido bridges (J = 3.36(3) cm-1 in 1 and 4.56(2) cm-1 in 2). The magnetic properties of both complexes can be fitted to a Co(ii) dimer model including similar orbital reduction factors (α = -0.94(1) for 1 and -0.85(1) for 2) although different zero field splitting parameters D(1) = 11.0(4) cm-1 and D(2) = 19.5(4) cm-1 in 1 and D(1) = 8.2(4) cm-1 and D(2) = -1.3(4) cm-1 in 2. AC magnetic measurements reveal that the CoII2 unit in complex 2 exhibits field-induced slow relaxation of the magnetization at low temperatures and high frequencies.

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.

Electronic Structure and Magnetic Properties of a Titanium(II) Coordination Complex

Stable coordination complexes of Ti^II (3d²) are relatively uncommon, but are of interest as synthons for low oxidation state titanium complexes for application as potential catalysts and reagents for organic synthesis. Specifically, high-spin Ti^II ions supported by redox-inactive ligands are still quite rare due to the reducing power of this soft ion. Among such Ti^II complexes is trans-[TiCl₂(tmeda)₂], where tmeda = N,N,N',N'-tetramethylethane-1,2-diamine. This complex was first reported by Gambarotta and co-workers almost 30 years ago, but it was not spectroscopically characterized and theoretical investigation by quantum chemical theory (QCT) was not feasible at that time. As part of our interest in low oxidation state early transition metal complexes, we have revisited this complex and report a modified synthesis and a low temperature (100 K) crystal structure that differs slightly from that originally reported at ambient temperature. We have used magnetometry, high-frequency and -field EPR (HFEPR), and variable-temperature variable-field magnetic circular dichroism (VTVH-MCD) spectroscopies to characterize trans-[TiCl₂(tmeda)₂]. These techniques yield the following S = 1 spin Hamiltonian parameters for the complex: D = -5.23(1) cm^-1, E = -0.88(1) cm^-1, (E/D = 0.17), g = [1.86(1), 1.94(2), 1.77(1)]. This information, in combination with electronic transitions from MCD, was used as input for both classical ligand-field theory (LFT) and detailed QCT studies, the latter including both density functional theory (DFT) and ab initio methods. These computational methods are seldom applied to paramagnetic early transition metal complexes, particularly those with S > 1/2. Our studies provide a complete picture of the electronic structure of this complex that can be put into context with the few other high-spin and mononuclear Ti^II species characterized to date.

Coordination bonding in dicopper and dichromium tetrakis(μ-acetato)-diaqua complexes: Nature, strength, length, and topology

Geometry optimization, energetics, electronic structure, and topology of electron density of dicopper (I) and dichromium (II) tetrakis(μ-acetato)-diaqua complexes are studied focusing on the metal-metal interactions. The performance of broken symmetry (BS) single-determinant ab initio (Hartree-Fock, Møller-Plesset perturbation theory to the second and third orders, coupled clusters singles and doubles) and density functional theory (BLYP, B3LYP, B3LYP-D3, B2PLYP, MPW2PLYP) methods is compared to multideterminant ab initio (CASSCF, NEVPT2) methods as well as to the multipole model of charge density from a single-crystal X-ray diffraction experiment (Herich et al., Acta Cryst. 2018, B74, 681-692). In vacuo DFT geometry optimizations (improper axial water ligand orientation) are compared against the periodic ones. The singlet state is found to be energetically preferred. J coupling of (I) becomes underestimated for all ab initio methods used, when compared to experiment. It is concluded that the strength of the direct M─M interactions correlates closely with the J coupling magnitude at a given level of theory. The double potential well character of (II) and of the dehydrated form of (II) are considered with respect to the Cr─Cr distance. The physical effective bond order of the metal-metal interaction is small (below 0.1 e) in (I) and moderate (0.4 e) in (II). The CASSCF results overestimate the electron density of the metal-metal bond critical point by 20% and 50% in (I) and (II), respectively, when compared to the multipole model. © 2019 Wiley Periodicals, Inc.

Advanced Paramagnetic Resonance Studies on Manganese and Iron Corroles with a Formal d4 Electron Count

Metallocorroles wherein the metal ion is Mn^III and formally Fe^IV are studied here using field- and frequency-domain electron paramagnetic resonance techniques. The Mn^III corrole, Mn(tpfc) (tpfc = 5,10,15-tris(pentafluorophenyl)corrole trianion), exhibits the following S = 2 zero-field splitting (zfs) parameters: D = -2.67(1) cm^-1, |E| = 0.023(5) cm^-1. This result and those for other Mn^III tetrapyrroles indicate that when D ≈ - 2.5 ± 0.5 cm^-1 for 4- or 5-coordinate and D ≈ - 3.5 ± 0.5 cm^-1 for 6-coordinate complexes, the ground state description is [Mn^III(Cor^3-)]⁰ or [Mn^III(P^2-)]⁺ (Cor = corrole, P = porphyrin). The situation for formally Fe^IV corroles is more complicated, and it has been shown that for Fe(Cor)X, when X = Ph (phenyl), the ground state is a spin triplet best described by [Fe^IV(Cor^3-)]⁺, but when X = halide, the ground state corresponds to [Fe^III(Cor^•2-)]⁺, wherein an intermediate spin (S = ³/₂) Fe^III is antiferromagnetically coupled to a corrole radical dianion (S = ¹/₂) to also give an S = 1 ground state. These two valence isomers can be distinguished by their zfs parameters, as determined here for Fe(tpc)X, X = Ph, Cl (tpc = 5,10,15-triphenylcorrole trianion). The complex with axial phenyl gives D = 21.1(2) cm^-1, while that with axial chloride gives D = 14.6(1) cm^-1. The D value for Fe(tpc)Ph is in rough agreement with the range of values reported for other Fe^IV complexes. In contrast, the D value for Fe(tpc)Cl is inconsistent with an Fe^IV description and represents a different type of iron center. Computational studies corroborate the zfs for the two types of iron corrole complexes. Thus, the zfs of metallocorroles can be diagnostic as to the electronic structure of a formally high oxidation state metallocorrole, and by extension to metalloporphyrins, although such studies have yet to be performed.

Three Manganese Complexes of Anionic N4-Donor Schiff-Base Macrocycles: Monomeric MnII and MnIII, and dimeric MnIV

Three manganese macrocyclic complexes of two anionic N4-donor [1+1] Schiff-base macrocycles that differ in ring size (14 versus 16 membered), HLEt and HLPr (obtained from condensation of diphenylamine-2,2′-dicarboxaldehyde and either diethylenetriamine or dipropylenetriamine), are reported. Specifically, a pair of monomeric complexes MnIILEt(NCS)(H2O) and [MnIIILPr(NCS)2]·0.5H2O, plus a dimeric complex [MnIV2LEt2(O)2](ClO4)2·3DMF have been synthesised and characterised. Single crystal structure determinations on [MnIIILPr(NCS)2]·0.5H2O and [MnIV2LEt2(O)2](ClO4)2·3DMF revealed octahedral manganese centres in both cases: N6-coordinated Jahn–Teller distorted MnIII in the former and a pair of N4O2-coordinated MnIV in the latter. UV-Vis, IR, and electron paramagnetic resonance spectroscopy as well as magnetic measurements are reported. These macrocyclic complexes feature a simple and original design, and could find future uses as models for manganese catalase or as building blocks for the assembly of larger supramolecular architectures.

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.

Rationalizing the sign and magnitude of the magnetic coupling and anisotropy in dinuclear manganese(iii) complexes

We have synthesised twelve manganese(iii) dinuclear complexes, 1-12, in order to understand the origin of magnetic exchange (J) between the metal centres and the magnetic anisotropy (D) of each metal ion using a combined experimental and theoretical approach. All twelve complexes contain the same bridging ligand environment of one μ-oxo and two μ-carboxylato, that helped us to probe how the structural parameters, such as bond distance, bond angle and especially Jahn-Teller dihedral angle affect the magnetic behaviour. Among the twelve complexes, we found ferromagnetic coupling for five and antiferromagnetic coupling for seven. DFT computed the J and ab initio methods computed the D parameter, and are in general agreement with the experimentally determined values. The dihedral angle between the two Jahn-Teller axes of the constituent MnIII ions are found to play a key role in determining the sign of the magnetic coupling. Magneto-structural correlations are developed by varying the Mn-O distance and the Mn-O-Mn angle to understand how the magnetic coupling changes upon these structural changes. Among the developed correlations, the Mn-O distance is found to be the most sensitive parameter that switches the sign of the magnetic coupling from negative to positive. The single-ion zero-field splitting of the MnIII centres is found to be negative for complexes 1-11 and positive for complex 12. However, the zero-field splitting of the S = 4 state for the ferromagnetic coupled dimers is found to be positive, revealing a significant contribution from the exchange anisotropy - a parameter which has long been ignored as being too small to be effective.

Experimental and Theoretical Identification of the Origin of Magnetic Anisotropy in Intermediate Spin Iron(III) Complexes

The complexes [FeL^N2S2X] [in which L^N2S2=2,2′‐(2,2′‐bipryridine‐6,6′‐diyl)bis(1,1′‐diphenylethanethiolate) and X=Cl, Br and I], characterized crystallographically earlier and here (Fe(L)Br), reveal a square pyramidal coordinated Fe^III ion. Unusually, all three complexes have intermediate spin ground states. Susceptibility measurements, powder cw X‐ and Q‐band EPR spectra, and zero‐field powder Mössbauer spectra show that all complexes display distinct magnetic anisotropy, which has been rationalized by DFT calculations.

Influence of the Disposition of the Anisotropy Axes into the Magnetic Properties of MnIII Dinuclear Compounds with Benzoato Derivative Bridges

The two new Mn^III dinuclear compounds [{Mn(H₂O)(phen)}₂(μ-4-CH₃C₆H₄COO)₂(μ-O)](ClO₄)₂·3CH₃CN·H₂O (1·3CH₃CN·H₂O) and [{Mn(H₂O)(phen)}(μ-O)(μ-2-BrC₆H₄COO)₂{Mn(NO₃)(phen)}]NO₃ (2) have been synthesized. Their structural data reveal significant differences in the shape of the coordination octahedron around the Mn^III ions in both compounds. The different distortions from ideal geometry incite a very different magnetic behavior, affecting both the zero-field splitting parameters of the Mn^III ions (D_Mn and E_Mn) and the magnetic interaction between them. Compound 1, with elongation in the monodentate ligand direction, shows antiferromagnetic coupling (ground state S = 0) and local D_Mn < 0, while compound 2, with compression in the oxo bridge direction, displays a ferromagnetic interaction (ground state S = 4) and local D_Mn > 0. Theoretical CASSCF and DFT calculations corroborate the different magnetic anisotropy and exchange coupling found in both compounds. Moreover, with the help of theoretical calculations, some interesting magneto-structural correlations have been found between the degree of distortion of the coordination octahedra and the magnetic coupling; it becomes more antiferromagnetic when the elongation parameter, Δ, in absolute value is increased.

Spectroscopic and Computational Studies of Spin States of Iron(IV) Nitrido and Imido Complexes

High-oxidation-state metal complexes with multiply bonded ligands are of great interest for both their reactivity as well as their fundamental bonding properties. This paper reports a combined spectroscopic and theoretical investigation into the effect of the apical multiply bonded ligand on the spin-state preferences of threefold symmetric iron(IV) complexes with tris(carbene) donor ligands. Specifically, singlet (S = 0) nitrido [{PhB(Im^R)₃}FeN], R = ^tBu (1), Mes (mesityl, 2) and the related triplet (S = 1) imido complexes, [{PhB(Im^R)₃}Fe(NR')]⁺, R = Mes, R' = 1-adamantyl (3), ^tBu (4), were investigated by electronic absorption and Mössbauer effect spectroscopies. For comparison, two other Fe(IV) nitrido complexes, [(TIMEN^Ar)FeN]⁺ (TIMEN^Ar = tris[2-(3-aryl-imidazol-2-ylidene)ethyl]amine; Ar = Xyl (xylyl), Mes), were investigated by ⁵⁷Fe Mössbauer spectroscopy, including applied-field measurements. The paramagnetic imido complexes 3 and 4 were also studied by magnetic susceptibility measurements (for 3) and paramagnetic resonance spectroscopy: high-frequency and -field electron paramagnetic resonance (for 3 and 4) and frequency-domain Fourier-transform (FD-FT) terahertz electron paramagnetic resonance (for 3), which reveal their zero-field splitting parameters. Experimentally correlated theoretical studies comprising ligand-field theory and quantum chemical theory, the latter including both density functional theory and ab initio methods, reveal the key role played by the Fe 3d_z² (a₁) orbital in these systems: the nature of its interaction with the nitrido or imido ligand dictates the spin-state preference of the complex. The ability to tune the spin state through the energy and nature of a single orbital has general relevance to the factors controlling spin states in complexes with applicability as single molecule devices.

A five-coordinate manganese(iii) complex of a salen type ligand with a positive axial anisotropy parameter D

Quantum chemical calculations reproduced well the electronic absorption spectrum and spin Hamiltonian parameters for MnL(NCS).

Three novel mononuclear Mn(iii)-based magnetic materials with square pyramidal versus octahedral geometries

Single crystal X-ray diffraction studies reveal that complexes 1 and 2 have square pyramidal geometry and 3 has octahedral geometry, which showed a dependence of negative anisotropy (D) values on the electronic, geometry and packing effects.

Behaviour of DFT-based approaches to the spin–orbit term of zero-field splitting tensors: a case study of metallocomplexes, MIII(acac)3 (M = V, Cr, Mn, Fe and Mo)

Zero-field splitting tensors of M^III(acac)₃ complexes are calculated using ab initio and DFT methods.

Singlet ground states in compounds with a [MnIII4O2]8+ core due to broken degeneration

Energy distribution of spin states depending on the distinction between the magnetic interactions. Singlet ground states due to broken degeneration of S_T ≠ 0 states. Attempt to assign spin states to a particular spin configuration.

Slow magnetic relaxation in a dimeric Mn2Ca2 complex enabled by the large Mn(iii) rhombicity

A large single-ion transverse anisotropy at Mn(iii) sites induces slow magnetic relaxation at zero magnetic field of the ferromagnetic Mn dimers in a singular Mn₂Ca₂ complex.

New insights into the comprehension of the magnetic properties of dinuclear Mn(III) compounds with the general formula [{MnL(NN)}2(μ-O)(μ-n-RC6H4COO)2]X2

Five new dinuclear Mn(iii) compounds with benzoato derivative bridges [{Mn(bpy)L}2(μ-O)(μ-n-RC6H4COO)2]X2 (n-R = 3-MeO, 4-MeO and 4-tBu, X = NO3(-) and ClO4(-)) were synthesised and characterised. According to X-ray diffraction, the X anions tend to be coordinated to the Mn ions and may occupy the place of the monodentate ligand L. Two structural isomers that only differ in one of their monodentate ligands have been obtained with the 3-MeOC6H4COO(-) bridges. For all compounds, the Mn(iii) ions display elongated octahedra with a pronounced rhombic distortion. To quantify these distortions separately, the elongation and rhombicity parameters Δ and ρ have been defined. The magnetic study shows a good relationship between the distortion of the coordination polyhedra and the zero field splitting parameters (DMn and EMn). From the magnetic data of a powder sample, it is possible to determine the sign and magnitude of DMn for ferromagnetic systems or weak antiferromagnetic systems with DMn < 0. For this kind of dinuclear compound, the R group at the meta position, the rhombic distortion of the octahedra, and large torsion angles between the Jahn-Teller axes lead to ferromagnetic interactions.

Spectroscopic and Computational Investigation of Low-Spin Mn(III) Bis(scorpionate) Complexes

Six-coordinate MnIII complexes are typically high-spin (S = 2), however, the scorpionate ligand, both in its traditional, hydridotris(pyrazolyl)borate form, Tp- and Tp*- (the latter with 3,5-dimethylpyrazole substituents) and in an aryltris(carbene)borate (i.e., N-heterocyclic carbene, NHC) form, [Ph(MeIm)3B]-, (MeIm = 3-methylimidazole) lead to formation of bis(scorpionate) complexes of MnIII with spin triplet ground states; three of which were investigated herein: [Tp2Mn]SbF6 (1SBF6), [Tp*2Mn]SbF6 (2SBF6), and [{Ph(MeIm)3B}2Mn]CF3SO3 (3CF3SO3). These trigonally symmetric complexes were studied experimentally by magnetic circular dichroism (MCD) spectroscopy (the propensity of 3 to oxidize to MnIV precluded collection of useful MCD data) including variable temperatures and fields (VTVH-MCD) and computationally by ab initio CASSCF/NEVPT2 methods. These combined experimental and theoretical techniques establish the 3A2g electronic ground state for the three complexes, and provide information on the energy of the "conventional" high-spin excited state (5Eg) and other, triplet excited states. These results show the electronic effect of pyrazole ring substituents in comparing 1 and 2. The tunability of the scorpionate ligand, even by perhaps the simplest change (from pyrazole in 1 to 3,5-dimethylpyrazole in 2) is quantitatively manifested through perturbations in ligand-field excited-state energies that impact ground-state zero-field splittings. The comparison with the NHC donor is much more dramatic. In 3, the stronger σ-donor properties of the NHC lead to a quantitatively different electronic structure, so that the lowest lying spin triplet excited state, 3Eg, is much closer in energy to the ground state than in 1 or 2. The zero-field splitting (zfs) parameters of the three complexes were calculated and in the case of 1 and 2 compare closely to experiment (lower by < 10%, < 2 cm-1 in absolute terms); for 3 the large magnitude zfs is reproduced, although there is ambiguity about its sign. The comprehensive picture obtained for these bis(scorpionate) MnIII complexes provides quantitative insight into the role played by the scorpionate ligand in stabilizing unusual electronic structures.

Construction of Giant-Spin Hamiltonians from Many-Spin Hamiltonians by Third-Order Perturbation Theory and Application to an Fe3 Cr Single-Molecule Magnet

A general giant-spin Hamiltonian (GSH) describing an effective spin multiplet of an exchange-coupled metal cluster with dominant Heisenberg interactions was derived from a many-spin Hamiltonian (MSH) by treating anisotropic interactions at the third order of perturbation theory. Going beyond the existing second-order perturbation treatment allows irreducible tensor operators of rank six (or corresponding Stevens operator equivalents) in the GSH to be obtained. Such terms were found to be of crucial importance for the fitting of high-field EPR spectra of a number of single-molecule magnets (SMMs). Also, recent magnetization measurements on trigonal and tetragonal SMMs have found the inclusion of such high-rank axial and transverse terms to be necessary to account for experimental data in terms of giant-spin models. While mixing of spin multiplets by local zero-field splitting interactions was identified as the major origin of these contributions to the GSH, a direct and efficient microscopic explanation had been lacking. The third-order approach developed in this work is used to illustrate the mapping of an MSH onto a GSH for an S=6 trigonal Fe3 Cr complex that was recently investigated by high-field EPR spectroscopy. Comparisons between MSH and GSH consider the simulation of EPR data with both Hamiltonians, as well as locations of diabolical points (conical intersections) in magnetic-field space. The results question the ability of present high-field EPR techniques to determine high-rank zero-field splitting terms uniquely, and lead to a revision of the experimental GSH parameters of the Fe3 Cr SMM. Indeed, a bidirectional mapping between MSH and GSH effectively constrains the number of free parameters in the GSH. This notion may in the future facilitate spectral fitting for highly symmetric SMMs.

HFEPR and Computational Studies on the Electronic Structure of a High-Spin Oxidoiron(IV) Complex in Solution

Nonheme iron enzymes perform diverse and important functions in biochemistry. The active form of these enzymes comprises the ferryl, oxidoiron(IV), [FeO](2+) unit. In enzymes, this unit is in the high-spin, quintet, S = 2, ground state, while many synthetic model compounds exist in the spin triplet, S = 1, ground state. Recently, however, Que and co-workers reported an oxidoiron(IV) complex with a quintet ground state, [FeO(TMG3tren)](OTf)2, where TMG3tren = 1,1,1-tris{2-[N2-(1,1,3,3-tetramethylguanidino)]ethyl}amine and OTf = CF3SO3(-). The trigonal geometry imposed by this ligand, as opposed to the tetragonal geometry of earlier model complexes, favors the high-spin ground state. Although [FeO(TMG3tren)](2+) has been earlier probed by magnetic circular dichroism (MCD) and Mössbauer spectroscopies, the technique of high-frequency and -field electron paramagnetic resonance (HFEPR) is superior for describing the electronic structure of the iron(IV) center because of its ability to establish directly the spin-Hamiltonian parameters of high-spin metal centers with high precision. Herein we describe HFEPR studies on [FeO(TMG3tren)](OTf)2 generated in situ and confirm the S = 2 ground state with the following parameters: D = +4.940(5) cm(-1), E = 0.000(5), B4(0) = -14(1) × 10(-4) cm(-1), g⊥ = 2.006(2), and g∥ = 2.03(2). Extraction of a fourth-order spin-Hamiltonian parameter is unusual for HFEPR and impossible by other techniques. These experimental results are combined with state-of-the-art computational studies along with previous structural and spectroscopic results to provide a complete picture of the electronic structure of this biomimetic complex. Specifically, the calculations reproduce well the spin-Hamiltonian parameters of the complex, provide a satisfying geometrical picture of the S = 2 oxidoiron(IV) moiety, and demonstrate that the TMG3tren is an "innocent" ligand.

X-Band Electron Paramagnetic Resonance Comparison of Mononuclear Mn(IV)-oxo and Mn(IV)-hydroxo Complexes and Quantum Chemical Investigation of Mn(IV) Zero-Field Splitting

X-band electron paramagnetic resonance (EPR) spectroscopy was used to probe the ground-state electronic structures of mononuclear Mn(IV) complexes [Mn(IV)(OH)2(Me2EBC)](2+) and [Mn(IV)(O)(OH)(Me2EBC)](+). These compounds are known to effect C-H bond oxidation reactions by a hydrogen-atom transfer mechanism. They provide an ideal system for comparing Mn(IV)-hydroxo versus Mn(IV)-oxo motifs, as they differ by only a proton. Simulations of 5 K EPR data, along with analysis of variable-temperature EPR signal intensities, allowed for the estimation of ground-state zero-field splitting (ZFS) and (55)Mn hyperfine parameters for both complexes. From this analysis, it was concluded that the Mn(IV)-oxo complex [Mn(IV)(O)(OH)(Me2EBC)](+) has an axial ZFS parameter D (D = +1.2(0.4) cm(-1)) and rhombicity (E/D = 0.22(1)) perturbed relative to the Mn(IV)-hydroxo analogue [Mn(IV)(OH)2(Me2EBC)](2+) (|D| = 0.75(0.25) cm(-1); E/D = 0.15(2)), although the complexes have similar (55)Mn values (a = 7.7 and 7.5 mT, respectively). The ZFS parameters for [Mn(IV)(OH)2(Me2EBC)](2+) were compared with values obtained previously through variable-temperature, variable-field magnetic circular dichroism (VTVH MCD) experiments. While the VTVH MCD analysis can provide a reasonable estimate of the magnitude of D, the E/D values were poorly defined. Using the ZFS parameters reported for these complexes and five other mononuclear Mn(IV) complexes, we employed coupled-perturbed density functional theory (CP-DFT) and complete active space self-consistent field (CASSCF) calculations with second-order n-electron valence-state perturbation theory (NEVPT2) correction, to compare the ability of these two quantum chemical methods for reproducing experimental ZFS parameters for Mn(IV) centers. The CP-DFT approach was found to provide reasonably acceptable values for D, whereas the CASSCF/NEVPT2 method fared worse, considerably overestimating the magnitude of D in several cases. Both methods were poor in reproducing experimental E/D values. Overall, this work adds to the limited investigations of Mn(IV) ground-state properties and provides an initial assessment for calculating Mn(IV) ZFS parameters with quantum chemical methods.

Formation of Hexacoordinate Mn(III) in Bacillus subtilis Oxalate Decarboxylase Requires Catalytic Turnover

Oxalate decarboxylase (OxDC) catalyzes the disproportionation of oxalic acid monoanion into CO2 and formate. The enzyme has long been hypothesized to utilize dioxygen to form mononuclear Mn(III) or Mn(IV) in the catalytic site during turnover. Recombinant OxDC, however, contains only tightly bound Mn(II), and direct spectroscopic detection of the metal in higher oxidation states under optimal catalytic conditions (pH 4.2) has not yet been reported. Using parallel mode electron paramagnetic resonance spectroscopy, we now show that substantial amounts of Mn(III) are indeed formed in OxDC, but only in the presence of oxalate and dioxygen under acidic conditions. These observations provide the first direct support for proposals in which Mn(III) removes an electron from the substrate to yield a radical intermediate in which the barrier to C-C bond cleavage is significantly decreased. Thus, OxDC joins a small list of enzymes capable of stabilizing and controlling the reactivity of the powerful oxidizing species Mn(III).