Broken Symmetry Approach Research Articles

The role of non-covalent interaction in the hexadentate coordination environment on the magnetic behavior of binuclear helical complex [Ni2(L)2]4+: A broken-symmetry approach

The nature of bonds in coordination environments of a homobimetallic supramolecular helicate complex has been studied using Quantum Theory of Atom in Molecule (QTAIM) and the electron localization function (ELF) analysis. The topological parameters at critical points (CPs) indicate that all bonds between nickel ions and ligand donors have non-covalent nature. The lack of any disynaptic basins in coordination environments confirms the QTAIM results. The broken-symmetry (BS) approach has been employed to predict properties of the complex using B3LYP functional and different basis sets for metal ions. The calculated magnetic exchange coupling constants (J) are 2683.34 and 2897.87cm−1 for different metal basis sets. The NBO analysis has been performed to explain the role of coordination bonds nature in strong ferromagnetic behavior of the complex.

Geometries of low spin states of multi-centre transition metal complexes through extended broken symmetry variational Monte Carlo.

The correct description of the ground state electronic and geometrical properties of multi-centre transition metal complexes necessitates of a high-level description of both dynamical and static correlation effects. In di-metallic complexes, the ground state low spin properties can be computed starting from single-determinants High-Spin (HS) and Broken Symmetry (BS) states by reconstructing an approximated low spin potential energy surface through the extended broken symmetry approach, based on the Heisenberg Hamiltonian. In the present work, we first apply this approach within the variational Monte Carlo method to tackle the geometry optimization of a Fe2S2(SH)42- model complex. To describe the HS and BS wavefunctions, we use a fully optimized unrestricted single determinant with a correlated Jastrow factor able to recover a large amount of dynamical correlation. We compared our results with those obtained by density functional theory and other multiconfigurational approaches, discussing the role of the nodal surface on the structural parameters.

Magnetic exchange coupling of chalcogen-centered radicals mediated via the 2D curved π-network: A broken-symmetry approach

DFT broken-symmetry calculations framework at the B3LYP/6-31G(d) level were carried out to evaluate the magnetic exchange coupling constants of four chalcogen-centered radical-C60 diadducts. The interactions of radicals, including ȮH, ṠH, ṠCH3, ṠC6H5 occurred in different relative positions. The calculated exchange coupling constants indicate that the coupling interaction regime changes when the radical centers and the relative distance of binding sites on C60 coupler change. In fact, the most intense ferromagnetic interaction occurs when radicals form a right-angle with the fullerene center. The shapes of singly occupied molecular orbital (SOMO) and spin density distribution of structures have also been studied. The energy splitting of the singly occupied molecular orbitals (ΔESS) confirm the broken symmetry results. The calculated isotropic hyperfine coupling constants (hfccs) show some differences in diradical-coupler complexes that can be employed in the experimental electron paramagnetic resonance (EPR) spectroscopy.

Quantum chemical calculation of exchange interactions in supramolecularly arrangedN,N′-dioxy-2,6-diazaadamantane organic biradical

Quantum mechanical exchange effects in purely organic N,N′-dioxy-2,6-diazaadamantane biradical derivatives with promesogenic substituents have been studied. To determine intermolecular exchange energies, packing conditions of the radical core units in layered liquid crystalline phases are simulated using the Gaussian 09 program. The broken symmetry approach gives J ≈ 7 cm−1 for intramolecular ferromagnetic exchange interactions between nitroxyl radical centers in one molecule. Both ferromagnetic and antiferromagnetic intermolecular interactions are possible in this kind of systems according to the obtained calculation results. Depending on the mutual positioning and orientation of molecules, the intermolecular antiferromagnetic exchange constant can reach a value of −50 cm−1, and the intermolecular ferromagnetic constant a value of 10 cm−1. The simultaneous presence of intramolecular and intermolecular exchange between spin-carrying centers in this kind of supramolecularly ordered multispin systems is favorable for the formation of magnetically interacting chains and two-dimensional networks. © 2016 Wiley Periodicals, Inc.

Electronic Structure and Magnetic Properties of Dioxo-Bridged Diuranium Complexes with Diamond-Core Structural Motifs: A Relativistic DFT Study.

Electronic structures and magnetic properties of the binuclear bis(μ-oxo) U(IV)/U(IV) K2[{(((nP,Me)ArO)3tacn)U(IV)}2(μ-O)2] and U(V)/U(V) [{(((nP,Me)ArO)3tacn)U(V)}2(μ-O)2] (tacn = triazacyclononane, nP = neopentyl) complexes, exhibiting [U(μ-O)2U] diamond-core structural motifs, have been investigated computationally using scalar relativistic Density Functional Theory (DFT) combined with the Broken Symmetry (BS) approach for their magnetic properties. Using the B3LYP hybrid functional, the BS ground state of the pentavalent [U(V)(μ-O)2U(V)] 5f(1)-5f(1) complex has been found of lower energy than the high spin (HS) triplet state, thus confirming the antiferromagnetic character in agreement with experimental magnetic susceptibility measurements. The nonmagnetic character observed for the tetravalent K2[U(IV)(μ-O)2U(IV)] 5f(2)-5f(2) species is also predicted by our DFT calculations, which led practically to the same energy for the HS and BS states. As reported for related dioxo diuranium(V) systems, superexchange is likely to be responsible for the antiferromagnetic coupling through the π-network orbital pathway within the (μ-O)2 bridge, the dissymmetrical structure of the U2O2 core playing a determining role. In the case of the U(IV) species, our computations indicate that the K(+) counterions are likely to play a role for the observed magnetic property. Finally, the MO analysis, in conjunction with NPA and QTAIM analyses, clarify the electronic structures of the studied complexes. In particular, the fact that the experimentally attempted chemical oxidation of the U(V) species does not lead straightforwardly to binuclear complexes U(VI) is clarified by the MO analysis.

Crystal structure and magnetic properties of binuclear copper(II) complex with 2-N-(phenylhydrazono)-3-((ethyl-2-olato)imino)-1-phenyl-1,2,3-butanetrione

The binuclear copper(II) complex based on azomethine, being a condensation product of 2-aminoethanol with 1-phenyl-1,2,3-butanetrione phenylhydrazone, is structurally characterized (CIF file CCDC 1059996). The structure is compared with the structure of an analog containing the axially coordinated pyridine molecule. The influence of the axial coordination of pyridine on the magnetic exchange interaction is studied by the DFT method in the broken symmetry approach.

Density functional theory of the CuA -like Cu2 S2 diamond core in Cu 2II(NGuaS)2 Cl2.

Density functional theory (DFT) calculations with localized as well as plane-wave basis functions are performed for the recently reported dicopper thiolate species Cu2 (NGuaS)2 Cl2 [NGuaS = 2-(1,1,3,3-tetramethylguanidino) benzenethiolate, C11 H16 N3 S] and its bromo derivative [Neuba et al., Angew. Chem. Int. Ed. 2012, 51, 1714.]. For both hybrid and semilocal functionals, the neutral complexes are found to have broken symmetry (BS) character, with electron paramagnetic resonance silent, antiferromagnetically coupled [Cu(2+) …Cu(2+) ] site in which the coupling is driven by super exchange interaction within the Cu2 S2 diamond core. The accurate theoretical description of the geometric structure, however, provides a major challenge for DFT: (i) the multideterminant character of the ground state wave function has to be covered by the BS approach. It requires (ii) metageneralized gradient approximations, that is hybrid functionals with an explicit dependence on the kinetic energy of the individual orbitals: In combination with a dispersion correction, the metafunctional TPSSh results in a CuCu distance close to the experimentally observed value of 2.7 Å. For the negative charge state of the complex, a mixed-valent [Cu(1.5+) …Cu(1.5+) ] electronic structure with a smaller CuCu distance of 2.6 Å is predicted, similar to the value of the CuA site of cytochrome c oxidase.

Iron(iii) bis(pyrazol-1-yl)acetate based decanuclear metallacycles: synthesis, structure, magnetic properties and DFT calculations.

The synthesis, structural aspects, magnetic interpretation and theoretical rationalizations for a new member of the ferric wheel family, a decanuclear iron(iii) complex with the formula [Fe10(bdtbpza)10(μ2-OCH3)20] (1), featuring the N,N,O tridentate bis(3,5-di-tert-butylpyrazol-1-yl)acetate ligand, are reported. The influence of the steric effect on both the core geometry and coordination mode is observed. Temperature dependent (2.0-300 K range) magnetic susceptibility studies carried out on complexes 1 established unequivocally antiferromagnetic (AF) interactions between high-spin iron(iii) centers (S = 5/2), leading to a ground state S = 0. The mechanism of AF intramolecular coupling was proved using a broken-symmetry approach within the density functional method at the B3LYP/def2-TZVP(-f)/def2-SVP level of theory.

The Cu2O2 torture track for a real-life system: [Cu2(btmgp)2O2](2+) oxo and peroxo species in density functional calculations.

Density functional theory (DFT) calculations of the equilibrium geometry, vibrational modes, ionization energies, electron affinities, and optical response of [Cu2(btmgp)2(μ-O)2](2+) (oxo) and [Cu2(btmgp)2(μ-η(2):η(2)-O2)](2+) (peroxo) are presented. Comprehensive benchmarking shows that the description of the oxo-peroxo energetics is still a torture track for DFT, but finds the molecular geometry to be comparatively robust with respect to changes in the exchange-correlation functionals and basis sets. Pure functionals favor the oxo core found experimentally, whereas hybrid functionals shift the bias toward the peroxo core. Further stabilization of peroxo core results from relaxing the spin degrees of freedom using the broken-symmetry (BS) approach. Dispersion effects, conversely, tend to favor the oxo configuration. Triple-zeta basis sets are found to represent a sensible compromise between numerical accuracy and computational effort. Particular attention is paid to the modification of the electronic structure, optical transitions, and excited-state energies along the transition path between the oxo and peroxo species. The excited-state potential energy surface calculations indicate that two triplet states are involved in the transition that stabilize the BS solution. Charge decomposition and natural transition orbital analyses are used for obtaining microscopic insight into the molecular orbital interactions. Here, the crucial role of guanidine π-interactions is highlighted for the stabilization of the Cu2O2 core.

Synthesis and Properties of the Heterospin (S1 = S2 = (1)/2) Radical-Ion Salt Bis(mesitylene)molybdenum(I) [1,2,5]Thiadiazolo[3,4-c][1,2,5]thiadiazolidyl.

Low-temperature interaction of [1,2,5]thiadiazolo[3,4-c][1,2,5]thiadiazole (1) with MoMes2 (Mes = mesitylene/1,3,5-trimethylbenzene) in tetrahydrofuran gave the heterospin (S1 = S2 = (1)/2) radical-ion salt [MoMes2](+)[1](-) (2) whose structure was confirmed by single-crystal X-ray diffraction (XRD). The structure revealed alternating layers of the cations and anions with the Mes ligands perpendicular, and the anions tilted by 45°, to the layer plane. At 300 K the effective magnetic moment of 2 is equal to 2.40 μB (theoretically expected 2.45 μB) and monotonically decreases with lowering of the temperature. In the temperature range 2-300 K, the molar magnetic susceptibility of 2 is well-described by the Curie-Weiss law with parameters C and θ equal to 0.78 cm(3) K mol(-1) and -31.2 K, respectively. Overall, the magnetic behavior of 2 is similar to that of [CrTol2](+)[1](-) and [CrCp*2](+)[1](-), i.e., changing the cation [MAr2](+) 3d atom M = Cr (Z = 24) with weak spin-orbit coupling (SOC) to a 4d atom M = Mo (Z = 42) with stronger SOC does not affect macroscopic magnetic properties of the salts. For the XRD structure of salt 2, parameters of the Heisenberg spin-Hamiltonian were calculated using the broken-symmetry DFT and CASSCF approaches, and the complex 3D magnetic structure with both the ferromagnetic (FM) and antiferromagnetic (AF) exchange interactions was revealed with the latter as dominating. Salt 2 is thermally unstable and slowly loses the Mes ligands upon storage at ambient temperature. Under the same reaction conditions, interaction of 1 with MoTol2 (Tol = toluene) proceeded with partial loss of the Tol ligands to afford diamagnetic product.

Density Functional Theory Calculations for the Structural, Electronic, and Magnetic Properties of (Gd2O3)n0,±1 Clusters with n = 1–10

The structural stability and electronic and magnetic properties of stoichiometric (Gd2O3)n clusters with n = 1–10 were investigated using spin-polarized density functional theory through the broken-symmetry approach. Size-induced changes in the point symmetry of these clusters were observed. A large coordination number led to elongation of Gd–O bonding. Either adding an electron to or removing an electron from the ground state of a neutral cluster brought significant changes in the van der Waals volume for clusters n = 1–3. Binding energy increased with cluster size. However, the highest occupied molecular orbital–lowest unoccupied molecular orbital gap, ionization, and electron affinity fluctuated when n increased from 1 to 10. Natural population analysis and partial density of states revealed that the Gd-4f orbital hardly participated in bonding and that the Gd-5d/6s/6p orbitals were hybrid with the O-2p orbitals. The competition between Ruderman–Kittel–Kasuya–Yosida-type and superexchange-type interact...

Density Functional Theory Modeling and Time-of-Flight Secondary Ion Mass Spectrometric and X-ray Photoelectron Spectroscopic Investigations into Mechanistic Key Events of Coronene Oxidation: Toward Molecular Understanding of Soot Combustion

Density functional [revised Perdew–Burke–Ernzerhof (rPBE)/double-numerical basis set with polarization functions (DNP)] molecular modeling of the mechanistic steps of coronene oxidation was performed together with X-ray photoelectron spectroscopic (XPS) and time-of-flight secondary ion mass spectrometric (ToF-SIMS) identification of the reaction intermediates. For the reaction steps involving singlet–triplet crossing, transition states were located within the broken-symmetry approach by use of a Becke three-parameter Lee–Yang–Parr (B3LYP)/triple-ζ plus polarization (TZVP) calculation scheme. For the conceivable attack by O2 molecule, topologically different in-plane, free edge, zigzag, bay, armchair, and C–H sites of the coronene molecule and its derivatives were considered. Energetic profiles of the oxidation cascade revealed that the reaction occurs by a sequence of oxidation and fragmentation steps. For the key steps, the influence of the evolution of free energy with temperature was assessed and discu...

Spin Adapted versus Broken Symmetry Approaches in the Description of Magnetic Coupling in Heterodinuclear Complexes

The performance of a series of wave function and density functional theory based methods in predicting the magnetic coupling constant of a family of heterodinuclear magnetic complexes has been studied. For the former, the accuracy is similar to other simple cases involving homodinuclear complexes, the main limitation being a sufficient inclusion of dynamical correlation effects. Nevertheless, these series of calculations provide an appropriate benchmark for density functional theory based methods. Here, the usual broken symmetry approach provides a convenient framework to predict the magnetic coupling constants but requires deriving the appropriate mapping. At variance with simple dinuclear complexes, spin projection based techniques cannot recover the corresponding (approximate) spin adapted solution. Present results also show that current implementation of spin flip techniques leads to unphysical results.

Magnetostructural dynamics of Rieske versus ferredoxin iron-sulfur cofactors.

The local chemical environment of the [2Fe-2S] cofactor hosted by ferredoxin and Rieske-type proteins is fundamentally different due to the presence of distinct ligands at the two iron centers in the case of Rieske proteins, whereas they are identical in ferredoxins. This renders Rieske [2Fe-2S] cores chemically asymmetric and results in more complex vibrational spectra as compared to ferredoxin. Likewise, one would expect other properties, for instance the dynamics of the magnetic exchange coupling constant J, to be also more complex. Applying ab initio molecular dynamics using our recently introduced spin-constrained two-determinant extended broken symmetry (CEBS) approach to Rieske and ferredoxin model complexes at 300 K, we extract the molecular fluctuations and the resulting magnetostructural cross-correlations involving the antiferromagnetic exchange interaction J(t). This analysis demonstrates that the details of the magnetostructural dynamics are indeed distinctly different for Rieske and ferredoxin cofactors, while the time averages of 〈J〉 are shown to be essentially identical. In particular, the frequency window between about 200 and 350 cm(-1), is a "fingerprint region" that allows one to distinguish chemically asymmetric from symmetric cofactors and thus Rieske proteins from ferredoxins.

Theoretical Study of Electronic Properties of Phenalenyl Radical and Zethrene Diradical Species: Possibility of Triplet Oxygen Adsorption onto Graphene Surface

Abstract Phenalenyl, zethrene, and extended zethrene molecules were employed to study the change in electronic properties of graphene surfaces upon exposure to oxygen atmosphere. These hydrocarbons are the smallest systems that can be used to evaluate intermolecular interaction with triplet oxygen molecules. The phenalenyl radical can simulate the radical nature of an edge structure and defect site of graphene sheets. Zethrene and extended zethrene molecules (n = 0, 1, 2, 3, and 4), which possess open-singlet diradical character, are also good models for studying chemisorption phenomena. From the calculated results for phenalenyl, the reaction path from the dissociation limit to the final products was found with chemisorbed structures (SS1 and SS2) and transition states (TS1, TS2, and TS3). Calculated adsorption energies were 7.72 (SS1) and 6.58 (SS2) kcal mol−1. An oxygen molecule can form a contact with phenalenyl radical in a weak chemisorption process, which is endothermic and has very low energy barriers to transition states. For the zethrene series, the diradical character index y, used to describe coupling between two radical spins, was evaluated using the broken symmetry approach. The values were 0.00, 0.01, 0.10, 0.23, and 0.32, for n = 0, 1, 2, 3, and 4, respectively. Although diradical nature was absent in ordinary zethrene, other extended zethrene molecules exhibited diradical character. The radical spin induced in phenalenyl unit A can contribute to the chemisorption of triplet oxygen molecules. The calculated adsorption energy for the first O2 adsorption onto heptazethrene was 5.38 kcal mol−1. Concomitantly, the radical electron on unit B revived and played an important role in the radical activity. The required adsorption energy for the second O2 adsorption became lower at −0.64 kcal mol−1.

Computational study of exchange coupling in homo- and heterometallic oxo- and carboxylato bridged trinuclear complexes with triangular {FeIII2M(μ3-O)} (M = FeIII, NiII, CoII) core

Using broken symmetry approach (DFT-BS, 6-311G(d)/B3LYP level of theory) the structure and magnetic exchange interactions in homo- and heterometallic oxo-centered trinuclear carboxylate complexes [Fe2M(μ3-O)(RCO2)6(H2O)3]n+ (M=FeIII, n=1; NiII, CoII, n=0; R=C(CH3)3, CH3, CCl3, CF3) were evaluated. The influence of metal ion and the nature of the carboxylate bridging ligand on the structure and magnetic properties of trinuclear complex is discussed. It was shown, that antiferromagnetic exchange interactions in both FeIII–FeIII and FeIII–MII (M=Ni, Co) pairs weakens in the row trimethylacetate>acetate>trichloroacetate≈trifluoroacetate.

Syntheses, crystal structures and magnetic properties of two halogen bridged dinuclear copper(II) complexes [(4,4′-diethylester-2,2′-biquinoline)2Cu2(μ-X)2X2] (X− = Cl−, Br−)

Two dinuclear Cu2+ complexes, [(deebq)2Cu2(μ-X)2X2] (deebq=4,4′-diethylester-2,2′-biquinoline, X−=Cl− for 1 and Br− for 2), were prepared and structurally characterized. The isostructural 1 and 2 crystallize in monoclinic space group P21/c, with quite similar unit cell parameters and packing structures. Two Cu2+ ions related to each other via an inversion center are connected by two halogen anions in a μ2-bridge mode, and each Cu2+ ion is coordinated by two N atoms form one deebq ligand and three X− anions to form distorted trigonal bipyramidal coordination geometry in dinuclear Cu2+ complex. The neighboring dinuclear units are held together through intermolecular van der Waals forces. Two complexes show antiferromagnetic (AFM) coupling nature with J/kB=−73.4K for 1 and −83.7K for 2 within the dinuclear unit. The theoretical analyses utilizing broken-symmetry approach disclosed that the AFM coupling is achieved via orbital overlap in the dinuclear unit for two complexes.

Computational design of the magnetism-tunable oligobenzylic carbanion complexes

Unrestricted density functional theory calculations in combination with the broken symmetry approach have been employed to study several benzylic carbanions. As a free anion, 2-(3,5-dinitrophenyl)-1,3-dithiane carbanion has near-degenerate singlet and triplet states and appears to be a promising magnetism-tunable species. In this work, we computationally design some of its derivatives in two ways: expanding the π-conjugated structures and introducing Lewis acids (Li+, Na+, and K+, and polar molecules are considered here) with different acidities. Calculations reveal that ring expansion does not change its open-shell broken symmetry singlet diradical ground state and antiferromagnetic character, but decreases its magnetism, whereas introduction of Lewis acids can lead to different ground states (triplet vs. singlet) and different magnetism, depending on the binding sites of the Lewis acid. That is, they show closed-shell singlet ground states without magnetism when a cation locates near the anionic center of the 1,3-dithiane ring, but convert to triplet as their ground states with ferromagnetic character when the cation moves to one nitro group of the 3,5-dinitrophenyl-based π-conjugation-expanded fragment. These findings regarding modulation through ring expansion and Lewis acid-binding ways make the magnetisms of 2-(3,5-dinitrophenyl)-1,3-dithiane-based carbanions tunable, and thus provide prospects of a new extension of the results from the previous study for designing magnetism-tunable building blocks for novel electromagnetic materials.

Broken symmetry approach to density functional calculation of zero field splittings including anisotropic exchange interactions

The broken symmetry approach to the calculation of zero field splittings (or magnetic anisotropies) of multinuclear transition metal complexes is further developed. A procedure is suggested how to extract spin Hamiltonian parameters for anisotropic exchange from a set of broken symmetry density functional calculations. For isotropic exchange coupling constants Jij, the established procedure is retrieved, and anisotropic (or pseudodipolar) exchange coupling tensors Dij are obtained analogously. This procedure only yields the sum of the individual single-ion zero field splitting tensors Di. Therefore, a procedure based on localized orbitals has been developed to extract the individual single-ion contributions. With spin Hamiltonian parameters at hand, the zero field splittings of the individual spin multiplets are calculated by an exact diagonalization of the isotropic part, followed by a spin projection done numerically. The method is applied to the binuclear cation [LCr(OH)3CrL](3 +) (L = 1,4,7-trimethyl-1,4,7-triazanonane) for which experimental zero field splittings for all low-energy spin states are known, and to the single-molecule magnet [Fe4(CH3C(CH2O)3)2(dpm)6] (Hdpm = 2,2,6,6-tetramethylheptane-3,5-dione). In both these 3d compounds, the single-ion tensors mainly come from the spin-orbit interaction. Anisotropic exchange is dominated by the spin-dipolar interaction only for the chromium compound. Despite the rather small isotropic exchange couplings in the iron compound, spin-orbit and spin-dipolar contributions to anisotropic exchange are of similar size here.

Microbial hydrogen splitting in the presence of oxygen

The origin of the tolerance of a subclass of [NiFe]-hydrogenases to the presence of oxygen was unclear for a long time. Recent spectroscopic studies showed a conserved active site between oxygen-sensitive and oxygen-tolerant hydrogenases, and modifications in the vicinity of the active site in the large subunit could be excluded as the origin of catalytic activity even in the presence of molecular oxygen. A combination of bioinformatics and protein structural modelling revealed an unusual co-ordination motif in the vicinity of the proximal Fe-S cluster in the small subunit. Mutational experiments confirmed the relevance of two additional cysteine residues for the oxygen-tolerance. This new binding motif can be used to classify sequences from [NiFe]-hydrogenases according to their potential oxygen-tolerance. The X-ray structural analysis of the reduced form of the enzyme displayed a new typeof [4Fe-3S] cluster co-ordinated by six surrounding cysteine residues in a distorted cubanoid geometry. The unusual electronic structure of the proximal Fe-S cluster can be analysed using the broken-symmetry approach and gave results in agreement with experimental Mößbauer studies. An electronic effect of the proximal Fe-S cluster on the remote active site can be detected and quantified. In the oxygen-tolerant hydrogenases, the hydride occupies an asymmetric binding position in the Ni-C state. This may rationalize the more facile activation and catalytic turnover in this subclass of enzymes.