Magnetic exchange and valence delocalization in a mixed valence [Fe2+Fe3+Te2]+ complex: insights from theory and interpretations of magnetic and spectroscopic data.

A mixed valence binuclear Fe2.5+-Fe2.5+ (Robin-Day Class III) transition metal complex, [Fe2.5+µTe2Fe2.5+]1-, composed of two FeN2Te2 pseudo-tetrahedral units with µ-bridging Te2- ligands was reported to exist in an unprecedented S = 3/2 ground state (Nature Chemistry, https://doi.org/10.1038/s41557-021-00853-5). For this and the homologous complexes containing Se2- and S2-, the Anderson-Hasegawa double exchange spin-Hamiltonian was broadly used to interpret the corresponding structural, spectroscopic and magnetic data. First principles multireference ab initio calculations are used here to simulate magnetic and spectroscopic EPR data; analysis of the results affords a rationale for the stabilization of the S = 3/2 ground state of the Fe2 pair. Complete Active Space Self-Consistent Field (CASSCF) calculations and dynamical correlation accounted for by means of N-Electron Valence Perturbation Theory to Second Order (NEVPT2) reproduce well the g-factors determined from simulations of X-band EPR spectra. A crucial technical tool to achieve these results is: (i) use of a localized orbital formulation of the many-particle problem at the scalar-relativistic CASSCF step; (ii) choice of state averaging over states of a given spin (at the CASCI/NEVPT2 step); and (iii) accounting for spin-orbit coupling within the non-relativistic Born-Oppenheimer (BO) many-particle basis using Quasi-Degenerate Perturbation Theory (QDPT). The inclusion of the S = 5/2 spin manifold reproduced the observed increase in the magnetic susceptibility (χT) in the high temperature range (T > 100 K), which is explained by thermal population of the S = 5/2 excited state at energy 160 cm-1 above the S = 3/2 ground state. Theoretical values of χT from experimentally reported data points in the temperature range from 3 to 30 K were further computed and analyzed using a model which takes spin-phonon coupling into account. The model considerations and the computational protocols of this study are generally applicable to any Class I/II mixed valence dimer. The work can potentially stimulate further experimental and theoretical work on bi- and oligonuclear transition metal complexes of importance to bioinorganic chemistry and life sciences.

Double-hybrid density functional theory for g-tensor calculations using gauge including atomic orbitals.

An efficient implementation for calculations of the electronic g-tensor at the level of second-order Møller-Plesset perturbation theory (MP2) is presented. The resolution of identity (RI) approximation is applied for the efficient treatment of two-electron integrals, and gauge including atomic orbitals are used to circumvent the gauge problem present in all magnetic property calculations. Furthermore, given that MP2 is an ingredient in double-hybrid density functional theory (DHDFT), the latter is also featured in the implementation. Calculated g-shifts with RI-MP2 and DHDFT using the double-hybrid density functionals B2PLYP and DSD-PBEP86 are compared to experimental data and published data from other methods including coupled cluster singles doubles. Additionally, the computational performance for medium to large size molecular systems was studied using the RIJK and RIJCOSX approximations for the two-electron integral treatment in the formation of Fock and Fock-like matrices necessary for the calculation of analytic second derivatives.

One-electron contributions to the g-tensor for second-order Douglas-Kroll-Hess theory.

The electric g-tensor is a central quantity for the interpretation of electron paramagnetic resonance spectra. In this paper, a detailed derivation of the 1-electron contributions to the g-tensor is presented in the framework of linear response theory and the second-order Douglas-Kroll-Hess (DKH) transformation. Importantly, the DKH transformation in the presence of a magnetic field is not unique. Whether or not the magnetic field is included in the required Foldy-Wouthuysen transformation, different transformation matrices and, consequently, Hamiltonians result. In this paper, a detailed comparison of both approaches is presented, paying particular attention to the mathematical properties of the resulting Hamiltonians. In contrast to previous studies that address the g-tensor in the framework of DKH theory, the resulting terms are compared to those of the conventional Pauli theory and are given a physical interpretation. Based on these mathematical and physical arguments, we establish that the proper DKH transformation for systems with constant magnetic fields is based on a gauge-invariant Foldy-Wouthuysen transformation, i.e., a Foldy-Wouthuysen transformation including the magnetic field. Calculations using density functional theory (DFT) are carried out on a set of heavy, diatomic molecules, and a set of transition-metal complexes. Based on these calculations, the performance of the relativistic calculation with and without inclusion of picture-change effects is compared. Additionally, the g-tensor is calculated for the Lanthanide dihydrides. Together with the results from the other two molecular test sets, these calculations serve to quantify the magnitude of picture-change effects and elucidate trends across the periodic table.

Theoretical insights into the magnetostructural correlations in Mn3-based single-molecule magnets.

Density functional theory (DFT) and the valence bond configuration interaction (VBCI) model have been applied to the oximato-based Mn(III)(3)O single-molecule magnets (SMMs), allowing one to correlate the Mn(III)-Mn(III) exchange coupling energy (J) with the bridging geometry in terms of two structural angles: the Mn-O-N-Mn torsion angle (γ) and the Mn(3) out-of-plane shift of O (angle δθ). Using DFT, a two-dimensional (γ, δθ) energy surface of J is derived and shown to yield essentially good agreement with the reported J values deduced from magnetic susceptibility data on trigonal oximato-bridged Mn(3) SMMs. VBCI is used to understand and analyze the DFT results. It is shown that the exchange coupling in these systems is governed by a spin-polarization mechanism inducing a pronounced and dominating ferromagnetic exchange via the oximato bridge as opposed to kinetic exchange, which favors a weaker and antiferromagnetic exchange via the bridging oxide. In the light of these results, a discussion of the exchange coupling in the Mn(6) family of the SMM with a record demagnetization barrier is given.

Zero field splitting of the chalcogen diatomics using relativistic correlated wave-function methods.

The spectrum arising from the (π*)(2) configuration of the chalcogen dimers, namely, the X(2)1, a2, and b0(+) states, is calculated using wave-function theory based methods. Two-component (2c) and four-component (4c) multireference configuration interaction (MRCI) and Fock-space coupled cluster (FSCC) methods are used as well as two-step methods spin-orbit complete active space perturbation theory at 2nd order (SO-CASPT2) and spin-orbit difference dedicated configuration interaction (SO-DDCI). The energy of the X(2)1 state corresponds to the zero-field splitting of the ground state spin triplet. It is described with high accuracy by the 2- and 4-component methods in comparison with experiment, whereas the two-step methods give about 80% of the experimental values. The b0(+) state is well described by 4c-MRCI, SO-CASPT2, and SO-DDCI, but FSCC fails to describe this state and an intermediate Hamiltonian FSCC ansatz is required. The results are readily rationalized by a two-parameter model; Δε, the π* spinor splitting by spin-orbit coupling and K, the exchange integral between the π(1)* and the π(-1)* spinors with, respectively, angular momenta 1 and -1. This model holds for all systems under study with the exception of Po(2).

Spin interaction in octahedral zinc complexes of mono- and diradical Schiff and mannich bases.

The four Schiff bases 2-tert-butyl-4-methoxy-6-[(pyridin-2-ylmethylimino)methyl]phenol, 2,4-di-tert-butyl-6-[(pyridin-2-ylmethylimino)methyl]phenol, 2-tert-butyl-4-methoxy-6-(quinolin-8-yliminomethyl)phenol, and 2,4-di-tert-butyl-6-(quinolin-8-yliminomethyl)phenol) as well as one Mannich base, N,N',N,N'-bis[(2-hydroxy-3,5-di-tert-butylbenzyl)(2-pyridylmethyl)]ethylenediamine, and their zinc bis-phenolate complexes 1-5, respectively, have been prepared. The complexes 4 and 5 have been characterized by X-ray diffraction crystallography, showing a zinc ion within an octahedral environment, with a cis orientation of the phenolate moieties. 1-5 exhibit in their cyclic voltammetry curves two anodic reversible waves attributable to the successive oxidation of the phenolates into phenoxyl radicals. Bulk electrolysis at ca. +0.1 V affords the zinc-coordinated monophenoxyl radical species (1(*))(+)-(5(*))(+) characterized by UV-vis absorption bands at 400-440 nm. The more stable radicals are (3(*))(+) and (4(*))(+) (half-life higher than 90 min at 298 K), likely due to the increased charge delocalization within the quinoline moieties. These species exhibit a significant additional near-IR band (epsilon > 1650 M(-1) cm(-1)) attributed to a CT transition. In the two-electron-oxidized species (1(**))(2+)-(5(**))(2+) the radical spins present a weak magnetic coupling. EPR reveals an antiferromagnetic exchange interaction for (1(**))(2+)-(4(**))(2+), whereas an unusual ferromagnetic exchange coupling is operative in (5(**))(2+). The weak magnitude of experimental |J| values (within the 1-5 cm(-1) range) as well as their sign could be well reproduced by DFT calculations at the B3LYP level. The small energy gap between the ground and the first excited spin states allows us to investigate the zero-field splitting (ZFS) of the triplet by EPR spectroscopy. This parameter is found to be axial for all systems, with |D| values of 0.0163 cm(-1) for (1(**))(2+), 0.0182 cm(-1) for (2(**))(2+), 0.0144 cm(-1) for (3(**))(2+), 0.0160 cm(-1) for (4(**))(2+), and 0.0115 cm(-1) for (5(**))(2+). The trend between experimental ZFS is confirmed by DFT calculations, which give further insight regarding its sign (negative for all the compounds). Lower ZFS values are obtained for (2(**))(2+) compared to (1(**))(2+) (and also for (4(**))(2+) compared to (3(**))(2+)), which can be interpreted by an increased delocalization of the spin density over the methoxy para substituent. Significant spin population on the quinoline also contributes to a lowering of the |D| value, as observed when (3(**))(2+) is compared to (1(**))(2+) (and also when (4(**))(2+) is compared to (2(**))(2+)).

New insights from spectroscopy into the structure/function relationships of lipoxygenases.

Spectroscopic properties of the redox-active iron in the active site of plant and mammalian lipoxygenases can now be combined with recent crystal structure determinations to obtain new insights into lipoxygenase reaction mechanisms.

Calculating absorption shifts for retinal proteins: computational challenges.

Rhodopsins can modulate the optical properties of their chromophores over a wide range of wavelengths. The mechanism for this spectral tuning is based on the response of the retinal chromophore to external stress and the interaction with the charged, polar, and polarizable amino acids of the protein environment and is connected to its large change in dipole moment upon excitation, its large electronic polarizability, and its structural flexibility. In this work, we investigate the accuracy of computational approaches for modeling changes in absorption energies with respect to changes in geometry and applied external electric fields. We illustrate the high sensitivity of absorption energies on the ground-state structure of retinal, which varies significantly with the computational method used for geometry optimization. The response to external fields, in particular to point charges which model the protein environment in combined quantum mechanical/molecular mechanical (QM/MM) applications, is a crucial feature, which is not properly represented by previously used methods, such as time-dependent density functional theory (TDDFT), complete active space self-consistent field (CASSCF), and Hartree-Fock (HF) or semiempirical configuration interaction singles (CIS). This is discussed in detail for bacteriorhodopsin (bR), a protein which blue-shifts retinal gas-phase excitation energy by about 0.5 eV. As a result of this study, we propose a procedure which combines structure optimization or molecular dynamics simulation using DFT methods with a semiempirical or ab initio multireference configuration interaction treatment of the excitation energies. Using a conventional QM/MM point charge representation of the protein environment, we obtain an absorption energy for bR of 2.34 eV. This result is already close to the experimental value of 2.18 eV, even without considering the effects of protein polarization, differential dispersion, and conformational sampling.

Mössbauer and computational investigation of a functional [NiFe] hydrogenase model complex.

Developing biomimetic complexes that model the active site of [NiFe] hydrogenase enzymes in order to catalyze the activation of H2 is a topic of major interest. A functional [NiFe] hydrogenase model complex has recently been described by Ogo et al. (Science, 2013, 339, 682-683). Here, we report a Mössbauer and computational investigation of this model complex. This study affords deeper understanding of the electronic structure, the reactivity and the mechanism of H2 activation by this complex.

Reactions of nitric oxide with nitronyl nitroxides and oxygen: prediction of nitrite and nitrate formation by kinetic simulation.

Nitric oxide reacts with nitronyl nitroxides (NNO) to form imino nitroxides (INO) and this transformation can be monitored using electron spin resonance spectroscopy. Recently, Akaike et al., reported that NNO such as 2-phenyl-4,4,5,5-tetramethylimidazoline-3-oxide-1-oxyl (PTIO) and its derivatives (e.g., carboxy-PTIO) react with nitric oxide (.NO) in a 1:1 stoichiometry forming 2-phenyl-4,4,5,5-tetramethylimidazoline-1-oxyl (PTI) or the respective product (e.g., carboxy-PTI) together with nitrite and nitrate (Akaike et al., Biochemistry 32, 827-332, 1993). In this paper, we reevaluate their results and show that the stoichiometry of the reaction between PTIO and .NO is 0.63 +/- 0.06:1.0. The reason for this discrepancy is due to an erroneous assumption by Akaike et al., that the stoichiometry for the reaction between .NO and O2 is 2:1 in aqueous solution. If the data reported by Akaike et al., were recalculated using a 4:1 stoichiometry established for the aqueous oxidation of .NO, the reaction between .NO and PTIO would give a stoichiometry of 0.5:1.0 in closer agreement with our data. We propose mechanism for the reaction between PTIO and .NO in aqueous solution. This mechanism predicts that the stoichiometry between carboxy-PTIO and .NO is dependent on the rate of generation of .NO and is 1:1 only at low rates of .NO generation (i.e., 10(-13) M/s). However the stoichiometry approaches 0.5:1.0 at higher rates of .NO production or when it is added as a bolus. The ratio between nitrite and nitrate also varies as a function of the rate of generation of .NO. The model agrees with previous experimental observations that the aqueous oxidation of .NO in air saturated solutions will exclusively form nitrite and predicts that .NO will only generate substantial amounts of nitrate if it is released at a rate less than 10(-17) M/s. This may have important consequences in cellular systems where the concentration of .NO is typically measured from nitrite production.

Trapping of nitric oxide formed during photolysis of sodium nitroprusside in aqueous and lipid phases: an electron spin resonance study.

Photolytic decomposition of sodium nitroprusside (SNP), a widely used nitrovasodilator, produced nitric oxide (.NO), which was continuously monitored by electron spin resonance (ESR) spectroscopy. The .NO present in the aqueous or the lipid phase was trapped by either a hydrophilic or a hydrophobic nitronyl nitroxide, respectively, to form the corresponding imino nitroxide. The conversion of nitronyl nitroxide to imino nitroxide was monitored by ESR spectrometry. The quantum yield for the generation of .NO from SNP, measured from the rate of decay of nitronyl nitroxide, was 0.201 +/- 0.007 and 0.324 +/- 0.01 (mean +/- SD, n = 3) at 420 nm and 320 nm, respectively. The action spectrum for .NO generation was found to overlap the optical absorption spectrum of SNP closely. A mechanism for the reaction between SNP and nitronyl nitroxide in the presence of light is proposed and computer-aided simulation of this mechanism using published rate constants agreed well with experimental data. The methodology described here may be used to assay .NO production continuously during photoactivation of .NO donors in aqueous and lipid environments. Biological implications of this methodology are discussed.

EPR experiments to elucidate the structure of the ready and unready states of the [NiFe] hydrogenase of Desulfovibrio vulgaris Miyazaki F.

Isolation and purification of the [NiFe] hydrogenase of Desulfovibrio vulgaris Miyazaki F under aerobic conditions leads to a mixture of two states, Ni-A (unready) and Ni-B (ready). The two states are distinguished by different activation times and different EPR spectra. HYSCORE and ENDOR data and DFT calculations show that both states have an exchangeable proton, albeit with a different (1)H hyperfine coupling. This proton is assigned to the bridging ligand between Ni and Fe. For Ni-B, a hydroxo ligand is found. For Ni-A, either a hydroxo in a different orientation or a hydroperoxo-bridging ligand is present.

Molecular and electronic structure of [Mn(V)N(cyclam-acetato)]PF6. A combined experimental and DFT study.

From the reaction of Li(cyclam-acetate), MnCl(2).4H(2)O, and KPF(6) in methanol brown microcrystals of [Mn(III)Cl(cyclam-acetato)]PF(6) (1) were obtained in the presence of air (cyclam-acetic acid = 1,4,8,11-tetraazacyclotetradecane-1-acetic acid). The reaction of 1 in aqueous NH(3) solution with NaOCl produced blue crystals of [Mn(V)N(cyclam-acetato)]PF(6) (2). Complexes 1 and 2 were characterized by single-crystal X-ray crystallography, IR and Raman, electronic absorption, and (1)H, (13)C, and (15)N NMR spectroscopies. Their magnetochemistry as well as their electrochemistry have been investigated. The complexes [MnN(cyclam-acetato)](+/2+) were studied by theoretical calculations at the DFT and semiempirical levels in order to obtain more insight into the ground and excited states of the Mn(V)(triple bond)N unit. Structural and spectroscopic parameters were successfully calculated and compared to experiment. A pictorial description of the bonding has been developed.

Pentahaem cytochrome c nitrite reductase: reaction with hydroxylamine, a potential reaction intermediate and substrate.

The pentahaem enzyme cytochrome c nitrite reductase catalyses the reduction of nitrite to ammonia, a key reaction in the biological nitrogen cycle. The enzyme can also transform nitrogen monoxide and hydroxylamine, two potential bound reaction intermediates, into ammonia. Structural and mechanistic aspects of the multihaem enzyme are discussed in comparison with hydroxylamine oxidoreductase, a trimeric protein with eight haem molecules per subunit.

Structural investigations of the CuA centre of nitrous oxide reductase from Pseudomonas stutzeri by site-directed mutagenesis and X-ray absorption spectroscopy.

Nitrous oxide reductase is the terminal component of a respiratory chain that utilizes N2O in lieu of oxygen. It is a homodimer carrying in each subunit the electron transfer site, CuA, and the substrate-reducing catalytic centre, CuZ. Spectroscopic data have provided robust evidence for CuA as a binuclear, mixed-valence metal site. To provide further structural information on the CuA centre of N2O reductase, site directed mutagenesis and Cu K-edge X-ray absorption spectroscopic investigation have been undertaken. Candidate amino acids as ligands for the CuA centre of the enzyme from Pseudomonas stutzeri ATCC14405 were substituted by evolutionary conserved residues or amino acids similar to the wild-type residues. The mutations identified the amino acids His583, Cys618, Cys622 and Met629 as ligands of Cu1, and Cys618, Cys622 and His626 as the minimal set of ligands for Cu2 of the CuA centre. Other amino acid substitutions indicated His494 as a likely ligand of CuZ, and an indirect role for Asp580, compatible with a docking function for the electron donor. Cu binding and spectroscopic properties of recombinant N2O reductase proteins point at intersubunit or interdomain interaction of CuA and CuZ. Cu K-edge X-ray absorption spectra have been recorded to investigate the local environment of the Cu centres in N2O reductase. Cu K-edge Extended X-ray Absorption Fine Structure (EXAFS) for binuclear Cu chemical systems show clear evidence for Cu backscattering at approximately 2.5 A. The Cu K-edge EXAFS of the CuA centre of N2O reductase is very similar to that of the CuA centre of cytochrome c oxidase and the optimum simulation of the experimental data involves backscattering from a histidine group with Cu-N of 1.92 A, two sulfur atoms at 2.24 A and a Cu atom at 2. 43 A, and allows for the presence of a further light atom (oxygen or nitrogen) at 2.05 A. The interpretation of the CuA EXAFS is in line with ligands assigned by site-directed mutagenesis. By a difference spectrum approach, using the Cu K-edge EXAFS of the holoenzyme and that of the CuA-only form, histidine was identified as a major contributor to the backscattering. A structural model for the CuA centre of N2O reductase has been generated on the basis of the atomic coordinates for the homologous domain of cytochrome c oxidase and incorporating our current results and previous spectroscopic data.