Broken-symmetry Density Research Articles

Structural and Magnetic Investigations of a Heterospin System Composed of High-spin Mn(II) and Pyridyl-containing Triarylmethyl Radicals

A novel molecular heterospin system composed of high-spin MnII (S = 5/2) and (3,5-dichloro-4-pyridyl)bis(2,4,6-trichlorophenyl)methyl radical (PyBTM; S = 1/2) was developed. The MnII ion formed distorted octahedral coordination geometry with two PyBTM radicals coordinated in the trans configuration. Magnetic studies disclosed an intramolecular antiferromagnetic exchange interaction between the spins on PyBTM and MnII with JR–Mn/kB of −9.7 K. The antiferromagnetic interaction was confirmed by broken-symmetry density functional theory calculations. This study reveals the definite intramolecular exchange interaction in the MnII–triarylmethyl radical system for the first time.

Understanding Thermodynamic and Spectroscopic Properties of Tetragonal Mn12 Single-Molecule Magnets from Combined Density Functional Theory/Spin-Hamiltonian Calculations.

We apply broken-symmetry density functional theory to determine isotropic exchange-coupling constants and local zero-field splitting (ZFS) tensors for the tetragonal Mn12(t)BuAc single-molecule magnet. The obtained parametrization of the many-spin Hamiltonian (MSH), taking into account all 12 spin centers, is assessed by comparing theoretical predictions for thermodynamic and spectroscopic properties with available experimental data. The magnetic susceptibility (calculated by the finite-temperature Lanczos method) is well approximated, and the intermultiplet excitation spectrum from inelastic neutron scattering (INS) experiments is correctly reproduced. In these respects, the present parametrization of the 12-spin model represents a significant improvement over previous theoretical estimates of exchange-coupling constants in Mn12, and additionally offers a refined interpretation of INS spectra. Treating anisotropic interactions at the third order of perturbation theory, the MSH is mapped onto the giant-spin Hamiltonian describing the S = 10 ground multiplet. Although the agreement with high-field EPR experiments is not perfect, the results clearly point in the right direction and for the first time rationalize the angular dependence of the transverse-field spectra from a fully microscopic viewpoint. Importantly, transverse anisotropy of the effective S = 10 manifold is explicitly shown to arise largely from the ZFS-induced mixing of exchange multiplets. This effect is given a thorough analysis in the approximate D2d spin-permutational symmetry group of the exchange Hamiltonian.

Synthesis, structure, electrochemistry, and magnetic properties of face-sharing bioctahedral nickel complexes containing a N3Ni(μ-S2)(μ-X)NiN3 core (X = F−, Cl−, Br−, N3−, OH−)

A series of isostructural dinickel complexes of the type [Ni2(LMe2H4)][X]2 (where (LMe2H4)2− represents a 28-membered macrocyclic N6S2 donor ligand, X = ClO4− (1a), I− (1b)) and [Ni2(LMe2H4)(μ-L′)][X] (X = ClO4−, L′ = F− (2a), Cl− (3a), OH− (5a), N3− (6a), X = BPh4–, L′ = F− (2b), Cl− (3b), OH− (5b), N3− (6b), X = Br−, L′ = Br− (4)) have been synthesized and characterized by IR, ESI-MS, UV–vis, cyclic voltammetry, SQUID magnetometry, and X-ray crystallography. The dications in 1a and 1b feature an edge sharing bis(square-pyramidal) N3Ni(μ-S2)NiN3 core, while the monocations of 2a-6b comprise a face-sharing bioctahedral N3Ni(μ-S)2(μ-L′)NiN3 core. The variation of the coordination geometry has a strong impact on the magnetic properties of the Ni complexes. 3a, 4, and 5a have an S = 2 ground state with a value for the magnetic exchange coupling constant J of +10.06 cm−1, (3a), J = +12.13 cm−1 (4) and J = +2.9(1) cm−1 (5a), while 1a, 1b, and 2a have an S = 0 ground state with J = −13.4 cm−1 (1a), −22.8 cm−1 (1b) and J = −0.56 cm−1 (2a) (H = – 2JS1S2). Broken symmetry density functional theory calculations have been performed to study the individual contributions of the coligand and thiolato-bridges to the overall magnetic behavior. The capability to propagate exchange interactions was found to increase in the order Br− < Cl− < N3− < OH− ∼ F−.

Manganese Oxidation State Assignment for Manganese Catalase.

The oxidation state assignment of the manganese ions present in the superoxidized manganese (III/IV) catalase active site is determined by comparing experimental and broken symmetry density functional theory calculated (14)N, (17)O, and (1)H hyperfine couplings. Experimental results have been interpreted to indicate that the substrate water is coordinated to the Mn(III) ion. However, by calculating hyperfine couplings for both scenarios we show that water is coordinated to the Mn(IV) ion and that the assigned oxidation states of the two manganese ions present in the site are the opposite of that previously proposed based on experimental measurements alone.

A broken-symmetry density functional study of structures, energies, and protonation states along the catalytic O-O bond cleavage pathway in ba3 cytochrome c oxidase from Thermus thermophilus.

Broken-symmetry density functional calculations have been performed on the [Fea3, CuB] dinuclear center (DNC) of ba3 cytochrome c oxidase from Thermus thermophilus in the states of [Fea3(3+)-(HO2)(-)-CuB(2+), Tyr237(-)] and [Fea3(4+)[double bond, length as m-dash]O(2-), OH(-)-CuB(2+), Tyr237˙], using both PW91-D3 and OLYP-D3 functionals. Tyr237 is a special tyrosine cross-linked to His233, a ligand of CuB. The calculations have shown that the DNC in these states strongly favors the protonation of His376, which is above propionate-A, but not of the carboxylate group of propionate-A. The energies of the structures obtained by constrained geometry optimizations along the O-O bond cleavage pathway between [Fea3(3+)-(O-OH)(-)-CuB(2+), Tyr237(-)] and [Fea3(4+)[double bond, length as m-dash]O(2-)HO(-)-CuB(2+), Tyr237˙] have also been calculated. The transition of [Fea3(3+)-(O-OH)(-)-CuB(2+), Tyr237(-)] → [Fea3(4+)[double bond, length as m-dash]O(2-)HO(-)-CuB(2+), Tyr237˙] shows a very small barrier, which is less than 3.0/2.0 kcal mol(-1) in PW91-D3/OLYP-D3 calculations. The protonation state of His376 does not affect this O-O cleavage barrier. The rate limiting step of the transition from state A (in which O2 binds to Fea3(2+)) to state PM ([Fea3(4+)[double bond, length as m-dash]O(2-), OH(-)-CuB(2+), Tyr237˙], where the O-O bond is cleaved) in the catalytic cycle is, therefore, the proton transfer originating from Tyr237 to O-O to form the hydroperoxo [Fea3(3+)-(O-OH)(-)-CuB(2+), Tyr237(-)] state. The importance of His376 in proton uptake and the function of propionate-A/neutral-Asp372 as a gate to prevent the proton from back-flowing to the DNC are also shown.

Characterization of Oxygen Bridged Manganese Model Complexes Using Multifrequency (17)O-Hyperfine EPR Spectroscopies and Density Functional Theory.

Multifrequency pulsed EPR data are reported for a series of oxygen bridged (μ-oxo/μ-hydroxo) bimetallic manganese complexes where the oxygen is labeled with the magnetically active isotope (17)O (I = 5/2). Two synthetic complexes and two biological metallocofactors are examined: a planar bis-μ-oxo bridged complex and a bent, bis-μ-oxo-μ-carboxylato bridge complex; the dimanganese catalase, which catalyzes the dismutation of H2O2 to H2O and O2, and the recently identified manganese/iron cofactor of the R2lox protein, a homologue of the small subunit of the ribonuclotide reductase enzyme (class 1c). High field (W-band) hyperfine EPR spectroscopies are demonstrated to be ideal methods to characterize the (17)O magnetic interactions, allowing a magnetic fingerprint for the bridging oxygen ligand to be developed. It is shown that the μ-oxo bridge motif displays a small positive isotropic hyperfine coupling constant of about +5 to +7 MHz and an anisotropic/dipolar coupling of -9 MHz. In addition, protonation of the bridge is correlated with an increase of the hyperfine coupling constant. Broken symmetry density functional theory is evaluated as a predictive tool for estimating hyperfine coupling of bridging species. Experimental and theoretical results provide a framework for the characterization of the oxygen bridge in Mn metallocofactor systems, including the water oxidizing cofactor of photosystem II, allowing the substrate/solvent interface to be examined throughout its catalytic cycle.

Modeling the Photoelectron Spectra of MoNbO2(-) Accounting for Spin Contamination in Density Functional Theory.

Spin contamination in density functional studies has been identified as a cause of discrepancies between theoretical and experimental spectra of metal oxide clusters such as MoNbO2. We perform calculations to simulate the photoelectron spectra of the MoNbO2 anion using broken-symmetry density functional theory incorporating recently developed approximate projection methods. These calculations are able to account for the presence of contaminating spin states at single-reference computational cost. Results using these new tools demonstrate the significant effect of spin-contamination on geometries and force constants and show that the related errors in simulated spectra may be largely overcome by using an approximate projection model.

Heisenberg coupling constant predicted for molecular magnets with pairwise spin-contamination correction

New method to eliminate the spin-contamination in broken symmetry density functional theory (BS DFT) calculations is introduced. Unlike conventional spin-purification correction, this method is based on canonical Natural Orbitals (NO) for each high/low spin coupled electron pair. We derive an expression to extract the energy of the pure singlet state given in terms of energy of BS DFT solution, the occupation number of the bonding NO, and the energy of the higher spin state built on these bonding and antibonding NOs (not self-consistent Kohn–Sham orbitals of the high spin state). Compared to the other spin-contamination correction schemes, spin-correction is applied to each correlated electron pair individually. We investigate two binuclear Mn(IV) molecular magnets using this pairwise correction. While one of the molecules is described by magnetic orbitals strongly localized on the metal centers, and spin gap is accurately predicted by Noodleman and Yamaguchi schemes, for the other one the gap is predicted poorly by these schemes due to strong delocalization of the magnetic orbitals onto the ligands. We show our new correction to yield more accurate results in both cases.

Broken-Symmetry DFT Computations for the Reaction Pathway of IspH, an Iron–Sulfur Enzyme in Pathogenic Bacteria

The recently discovered methylerythritol phosphate (MEP) pathway provides new targets for the development of antibacterial and antimalarial drugs. In the final step of the MEP pathway, the [4Fe–4S] IspH protein catalyzes the 2e–/2H+ reductive dehydroxylation of (E)-4-hydroxy-3-methyl-but-2-enyl diphosphate (HMBPP) to afford the isoprenoid precursors isopentenyl pyrophosphate (IPP) and dimethylallyl pyrophosphate (DMAPP). Recent experiments have attempted to elucidate the IspH catalytic mechanism to drive inhibitor development. Two competing mechanisms have recently emerged, differentiated by their proposed HMBPP binding modes upon 1e– reduction of the [4Fe–4S] cluster: (1) a Birch reduction mechanism, in which HMBPP remains bound to the [4Fe–4S] cluster through its terminal C4–OH group (ROH-bound) until the −OH is cleaved as water; and (2) an organometallic mechanism, in which the C4–OH group rotates away from the [4Fe–4S] cluster, allowing the HMBPP olefin group to form a metallacycle complex with the apical iron (η2-bound). We perform broken-symmetry density functional theory computations to assess the energies and reduction potentials associated with the ROH- and η2-bound states implicated by these competing mechanisms. Reduction potentials obtained for ROH-bound states are more negative (−1.4 to −1.0 V) than what is typically expected of [4Fe–4S] ferredoxin proteins. Instead, we find that η2-bound states are lower in energy than ROH-bound states when the [4Fe–4S] cluster is 1e– reduced. Furthermore, η2-bound states can already be generated in the oxidized state, yielding reduction potentials of ca. −700 mV when electron addition occurs after rotation of the HMBPP C4–OH group. We demonstrate that such η2-bound states are kinetically accessible both when the IspH [4Fe–4S] cluster is oxidized and 1e– reduced. The energetically preferred pathway gives 1e– reduction of the cluster after substrate conformational change, generating the 1e– reduced intermediate proposed in the organometallic mechanism.

Molecular and Electronic Structures of Mononuclear and Dinuclear Titanium Complexes Containing π-Radical Anions of 2,2'-Bipyridine and 1,10-Phenanthroline: An Experimental and DFT Computational Study.

Whereas reaction of [(η(5)-Cp*)Ti(IV)Cl3](0) (1) with 2 equiv of neutral 2,2'-bipyridine (bpy) and 1.5 equiv of magnesium in tetrahydrofuran affords the mononuclear complex [(η(5)-Cp*)Ti(III)(bpy(•))2](0) (2), performing the same reaction with only 1 equiv each of magnesium and bpy provides the dinuclear complex [{(η(5)-Cp*)Ti(μ-Cl)(bpy(•))}2](0) (3). Conducting the latter reaction using 1,10-phenanthroline (phen) in place of bpy resulted in formation of dinuclear [{(η(5)-Cp*)Ti(μ-Cl)(phen(•))}2](0) (4). The structures of 2, 3, and 4 have all been determined by high-resolution X-ray crystallography at 153 K; the Cpy-Cpy distances of 1.420(3) and 1.431(4) Å in the N,N'-coordinated bpy ligands of 2 and 3, respectively, are indicative of the presence of (bpy(•))(1-) ligands, rather than neutral (bpy(0)). The electronic spectra (300-1600 nm) of these two complexes are similar in form, and contain intense π → π* transitions associated with the (bpy(•))(1-) radical anion. Temperature dependent magnetic susceptibility measurements (4-300 K) show that mononuclear 2 possesses a temperature independent magnetic moment of 1.73 μB, which is indicative of an S = (1)/2 ground state. Broken symmetry density functional theory (BS-DFT) calculations yield a picture consistent with the experimental findings, in which the central Ti atom possesses a +3 oxidation state and is coordinated by a η(5)-Cp* ligand and two (bpy(•))(1-). Strong intramolecular antiferromagnetic coupling of these three unpaired spins, one each on the Ti(III) center and on the two (bpy(•))(1-) ligands, affords the experimentally observed doublet ground state. The magnetic susceptibility measurements for dinuclear 3 and 4 display weak but significant ferromagnetic coupling, and indicate that these complexes possess S = 1 ground states. The mechanism of the spin coupling phenomenon that yields the observed behavior was analyzed using BS-DFT calculations, and it was discovered that the tight π-stacking of the N,N'-coordinated (bpy(•))(1-)/(phen(•))(1-) ligands in these two complexes results from direct overlap of their SOMOs and formation of a two-electron multicentered bond. This yields a diamagnetic {(bpy)2}(2-)/{(phen)2}(2-) bridging unit whose doubly occupied HOMO is spread equally over both ligands. The two remaining unpaired electrons, one at each Ti(III) center, couple weakly in a ferromagnetic fashion to yield the experimentally observed S = 1 ground states.

Structure and magnetic properties of an unusual homoleptic iron(III) thiocyanate dimer.

We describe the structural and variable temperature magnetic susceptibility properties of an unusual homoleptic bimetallic iron(III) thiocyanate tetraanion. This work represents the first structurally characterized bis(μ-1,3-thiocyanato) dimer of iron(III). A weak antiferromagnetic exchange interaction is observed between the two iron(III) ions, which is supported by broken symmetry density functional theory (DFT) calculations.

Spin decontamination of broken-symmetry density functional theory calculations: deeper insight and new formulations.

This work re-examines the problem of the broken-symmetry Density-Functional Theory (DFT) solutions in diradical systems, in particular for the calculation of magnetic couplings. The Ms = 0 solution is not an eigenfunction of the S(2) spin operator and the evaluation of the singlet state energy requires a spin-decontamination. A popular approximation is provided by the so-called Yamaguchi formula, which operates using the expectation values of S(2) relative to both Ms = 1 and Ms =0 solutions. Referring to a previous decomposition of the magnetic coupling in terms of direct exchange, kinetic exchange and core polarization, it is shown that this expression will lead to unreliable values of the singlet-triplet energy gap when the spin polarization of the core orbitals becomes large. The here-proposed method of spin-decontamination is based on the Effective Hamiltonian Theory and uses the overlap between the two degenerate Ms = 0 solutions. An approximate and convenient formula, which uses the expectation values of S(2) of the Ms = 0 solutions before and after core polarization is proposed, which is free from the Yamaguchi's formula artefact, as illustrated on an organic diradical presenting a very high value of 〈S(2)〉 for the Ms = 0 solution, the antiferromagnetic coupling being due to the spin polarization mechanism.

Theoretical study on diradical characters and nonlinear optical properties of 1,3-diradical compounds.

We investigate the relationships between the diradical character (y) and nonlinear optical (NLO) properties of open-shell 1,3-diradical compounds using the broken-symmetry density functional theory method. The 2,2-substituent effects on the structure-property relationship are clarified for several 1,3-diphenylcyclopentane-1,3-diyl derivatives, which are known as the systems with weak or intermediate π-single-bonding characters. The parent 1,3-diphenylcyclopentane-1,3-diyl (1a: X = H) is found to be almost pure diradical (y ∼ 1) owing to the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). The energy gap is determined by the balance of the through-space coupling with the through bond coupling effect. On the other hand, the introduction of the electron-withdrawing substituents X at the C2 position of cyclopentane-1,3-diyls (1b: X = OH, 1c: X = F) is found to decrease the y-value owing to the effects of additional through-bond interactions. As a result, 1b and 1c are found to have intermediate y. Static second hyperpolarizabilities (γ) of 1b and 1c are found to be enhanced by a factor of ∼4.5 and ∼6.4, respectively, compared with those of the pure singlet diradical 1a and those of the triplet 1a-1c. From the analysis of the third-order responses of electron density, the introduction of the 2,2-substituents is found to enhance the field-induced third-order polarizations over the whole system. We also investigate the effects of asymmetric donor/acceptor substitutions at the para positions of phenyl rings on the response properties. Although the asymmetric donor/acceptor substitutions have no significant impact on y in the present systems, they are found to provide the increase of γ from the corresponding nonsubstituted analogues. The present results have revealed strong correlation between the π-bonding character (diradical character) and third-order NLO properties in the real 1,3-diradical compounds. On the basis of the theoretically predicted correlation in the real systems, NLO measurements are speculated to be utilized as a new probe of the unique chemical bonding nature in such localized diradical compounds, which is one of the fundamental subjects in chemistry.

Computational quantum chemistry for single Heisenberg spin couplings made simple: just one spin flip required.

We highlight a simple strategy for computing the magnetic coupling constants, J, for a complex containing two multiradical centers. On the assumption that the system follows Heisenberg Hamiltonian physics, J is obtained from a spin-flip electronic structure calculation where only a single electron is excited (and spin-flipped), from the single reference with maximum Ŝz, M, to the M - 1 manifold, regardless of the number of unpaired electrons, 2M, on the radical centers. In an active space picture involving 2M orbitals, only one β electron is required, together with only one α hole. While this observation is extremely simple, the reduction in the number of essential configurations from exponential in M to only linear provides dramatic computational benefits. This (M, M - 1) strategy for evaluating J is an unambiguous, spin-pure, wave function theory counterpart of the various projected broken symmetry density functional theory schemes, and likewise gives explicit energies for each possible spin-state that enable evaluation of properties. The approach is illustrated on five complexes with varying numbers of unpaired electrons, for which one spin-flip calculations are used to compute J. Some implications for further development of spin-flip methods are discussed.

Use of Broken-Symmetry Density Functional Theory To Characterize the IspH Oxidized State: Implications for IspH Mechanism and Inhibition.

With current therapies becoming less efficacious due to increased drug resistance, new inhibitors of both bacterial and malarial targets are desperately needed. The recently discovered methylerythritol phosphate (MEP) pathway for isoprenoid synthesis provides novel targets for the development of such drugs. Particular attention has focused on the IspH protein, the final enzyme in the MEP pathway, which uses its [4Fe–4S] cluster to catalyze the formation of the isoprenoid precursors IPP and DMAPP from HMBPP. IspH catalysis is achieved via a 2e–/2H+ reductive dehydroxylation of HMBPP; the mechanism by which catalysis is achieved, however, is highly controversial. The work presented herein provides the first step in assessing different routes to catalysis by using computational methods. By performing broken-symmetry density functional theory (BS–DFT) calculations that employ both the conductor-like screening solvation model (DFT/COSMO) and a finite-difference Poisson–Boltzmann self-consistent reaction field methodology (DFT/SCRF), we evaluate geometries, energies, and Mössbauer signatures of the different protonation states that may exist in the oxidized state of the IspH catalytic cycle. From DFT/SCRF computations performed on the oxidized state, we find a state where the substrate, HMBPP, coordinates the apical iron in the [4Fe–4S] cluster as an alcohol group (ROH) to be one of two, isoenergetic, lowest-energy states. In this state, the HMBPP pyrophosphate moiety and an adjacent glutamate residue (E126) are both fully deprotonated, making the active site highly anionic. Our findings that this low-energy state also matches the experimental geometry of the active site and that its computed isomer shifts agree with experiment validate the use of the DFT/SCRF method to assess relative energies along the IspH reaction pathway. Additional studies of IspH catalytic intermediates are currently being pursued.

On ammonia binding to the oxygen-evolving complex of photosystem II: a quantum chemical study.

A recent EPR study (M. Perrez Navarro et al., Proc. Natl. Acad. Sci. 2013, 110, 15561) provided evidence that ammonia binding to the oxygen-evolving complex (OEC) of photosystem II in its S2 state takes place at a terminal-water binding position (W1) on the "dangler" manganese center MnA. This contradicted earlier interpretations of (14)N electron-spin-echo envelope modulation (ESEEM) and extended X-ray absorption fine-structure (EXAFS) data, which were taken to indicate replacement of a bridging oxo ligand by an NH2 unit. Here we have used systematic broken-symmetry density functional theory calculations on large (ca. 200 atom) model clusters of an extensive variety of substitution patterns and core geometries to examine these contradictory pieces of evidence. Computed relative energies clearly favor the terminal substitution pattern over bridging-ligand arrangements (by about 20-30 kcal mol(-1)) and support W1 as the preferred binding site. Computed (14)N EPR nuclear-quadrupole coupling tensors confirm previous assumptions that the appreciable asymmetry may be accounted for by strong, asymmetric hydrogen bonding to the bound terminal NH3 ligand (mainly by Asp61). Indeed, bridging NH2 substitution would lead to exaggerated asymmetries. Although our computed structures confirm that the reported elongation of an Mn-Mn distance by about 0.15 Å inferred from EXAFS experiments may only be reproduced by bridging NH2 substitution, it seems possible that the underlying EXAFS data were skewed by problems due to radiation damage. Overall, the present data clearly support the suggested terminal NH3 coordination at the W1 site. The finding is significant for the proposed mechanistic scenarios of OEC catalysis, as this is not a water substrate site, and effects of this ammonia binding on catalysis thus must be due to more indirect influences on the likely substrate binding site at the O5 bridging-oxygen position.

Quantum mechanics/molecular mechanics study of oxygen binding in hemocyanin.

We report a combined quantum mechanics/molecular mechanics (QM/MM) study on the mechanism of reversible dioxygen binding in the active site of hemocyanin (Hc). The QM region is treated by broken-symmetry density functional theory (DFT) with spin projection corrections. The X-ray structures of deoxygenated (deoxyHc) and oxygenated (oxyHc) hemocyanin are well reproduced by QM/MM geometry optimizations. The computed relative energies strongly depend on the chosen density functional. They are consistent with the available thermodynamic data for oxygen binding in hemocyanin and in synthetic model complexes when the BH&HLYP hybrid functional with 50% Hartree-Fock exchange is used. According to the QM(BH&HLYP)/MM results, the reaction proceeds stepwise with two sequential electron transfer (ET) processes in the triplet state followed by an intersystem crossing to the singlet product. The first ET step leads to a nonbridged superoxo CuB(II)-O2(•-) intermediate via a low-barrier transition state. The second ET step is even more facile and yields a side-on oxyHc complex with the characteristic Cu2O2 butterfly core, accompanied by triplet-singlet intersystem crossing. The computed barriers are very small so that the two ET processes are expected to very rapid and nearly simultaneous.

Asymmetry within the Fe(NO)2 moiety of dithiolate dinitrosyl iron complexes

Dinitrosyl iron complexes have earned attention due to their applications as nitric oxide donors as well as their interesting electronic structures. Typical Fe–NO electromerism issues are complicated in this case by the presence of a second nitrosyl ligand. Each of the formal oxidation states of iron in such complexes – from Fe(III) to Fe(0) – have been shown to be subject to electromerism. Here, broken-symmetry density functional theory data are shown, that reveal asymmetry within iron dithiolate dinitrosyl models in several formal oxidation states. CASSCF calculations on selected models confirm the multiconfigurational character of the Fe(NO)2 moiety, with the largest contributor at only 44% of the total weight of the wave function. This asymmetry is most noticeable in the excited states; it is further enhanced by solvation and reveals itself even in the ground state in dynamics calculations as well as in reaction pathways connecting the dinitrosyl state to a putative hyponitrite adduct.

Theoretical and computational investigation of meta-phenylene as ferromagnetic coupler in nitronyl nitroxide diradicals

We predict the magnetic exchange coupling constant (J) for 27 m-phenylene-based nitronyl nitroxide (NN) diradicals with nine different substituents in three unique (common ortho, ortho–meta and common meta) positions on the coupler unit by using the broken-symmetry density functional methodology. For all investigated diradicals, J values are computed using B3LYP, B3LYP-D3 and M06-2X functionals with 6–311+G(d,p) basis set. The JM06-2X value is larger than JB3LYP and closer to the observed value for the unsubstituted species. Substitutions at common ortho position always produce a greater angle of twist between the spin source and the coupler units. When the twist angle is very large, the nature of intramolecular magnetic interaction changes from ferromagnetic to antiferromagnetic. In these cases, the coupler–NN bond order becomes small. Substitution at the common meta position of m-phenylene in the diradical has little steric and hydrogen-bonding effects. Electron-withdrawing groups reveal a specific trend for single-atom substitution. An ortho substitution generally decreases J and a meta substitution always increases J with a decreasing −I effect. Variation of J with planarity as well as Hammett constant is investigated. The nucleus-independent chemical shift value is found to decrease from the corresponding mono-substituted phenyl derivatives. The dependence of J on these factors is explored.

Oxo-Bridged Dinuclear Chromium(III) Complexes: Correlation between the Optical and Magnetic Properties and the Basicity of the Oxo Bridge

The synthesis and X-ray structure of a new member of the series of oxo-bridged, dinuclear chromium(III) complexes, the methyl isocyanide complex [(CH3NC)5CrOCr(CNCH3)5](PF6)4·2CH3CN, is reported. This constitutes only the third oxo-bridged, dinuclear chromium(III) complex with a homoleptic auxillay ligand sphere. Experimentally, the system shows unshifted narrow nuclear magnetic resonance (NMR) spectra that are consistent with calculations using broken symmetry density functional theory (DFT), which suggests it to be the strongest coupled, dinuclear chromium(III) complex known. Furthermore, we report the crystal structure and computed magnetic properties for [(bpy)2(SCN)CrOCr(NCS)(bpy)2](ClO4)2·2H2O (bpy = 2,2'-bipyridine), which differs from other reported oxo-bridged species by featuring a bent CrOCr(4+) core. We also interpret the spectacular 10-orders-of-magnitude variation in acid dissociation constant of the bridging hydroxo ligand in mono hydroxo-bridged dinuclear chromium(III) complexes, in terms of a valence bond model parametrized by metal-to-metal charge transfer (MMCT) and ligand-to-metal charge transfer (LMCT) energies.