Theory of chemical bonds in metalloenzymes IV: Hybrid‐DFT study of Rieske‐type [2Fe?2S] clusters

The Rieske‐type [2Fe? 2S] cores of electron‐transfer (ET) proteins in the mitochondrial respiratory chain have unusual properties, such as redox potentials and spectroscopy. In this study, part IV of a series, the inherent molecular structures and characteristic electronic structures of the Rieske‐type [2Fe? 2S] clusters are investigated using broken‐symmetry hybrid density functional theory (BS‐HDFT). Geometry optimizations for the oxidized and reduced states were performed and their characteristic vibrational modes are assigned. Magnetic properties are investigated using model Hamiltonians to describe the electron delocalization and the unsymmetric property. The parameters of the model Hamiltonian, such as exchange coupling J, valence delocalization B, and potential energy difference Δ, are evaluated from the BS‐HDFT calculations. The valence localization and excitation energy (ΔE) of the Rieske‐type [2Fe? 2S] cluster are discussed. The chemical bond nature is characterized by chemical indices from natural orbital analysis. Our theoretical results are reasonably consistent with experimental results. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

A Two‐in‐one Pincer Ligand and its Diiron(II) Complex Showing Spin State Switching in Solution through Reversible Ligand Exchange

A novel pyrazolate‐bridged ligand providing two {PNN} pincer‐type compartments has been synthesized. Its diiron(II) complex LFe₂(OTf)₃(CH₃CN) ( 1 ; Tf=triflate) features, in solid state, two bridging triflate ligands, with a terminal triflate and a MeCN ligand completing the octahedral coordination spheres of the two high‐spin metal ions. In MeCN solution, 1 is shown to undergo a sequential, reversible, and complete spin transition to the low‐spin state upon cooling. Detailed UV/Vis and ¹⁹F NMR spectroscopic studies as well as magnetic measurements have unraveled that spin state switching correlates with a rapid multistep triflate/MeCN ligand exchange equilibrium. The spin transition temperature can be continuously tuned by varying the triflate concentration in solution.     

异双核X-M之间的磁耦合交换作用: Keggin型杂多酸衍生物[M(H2O)XW11O39]7-(X=FeⅢ, CoⅢ; M=CoⅡ)的密度泛函研究

采用DFT-BS方法研究异双核的Keggin型杂多酸衍生物[M(H2O)XW11O39]7-(Ⅰ: X=FeⅢ, M=CoⅡ; Ⅱ: X=CoⅢ, M=CoⅡ)的磁耦合作用, 计算得到耦合常数(J)为负值, 表明所研究体系具有反铁磁性; J值大小顺序为|J(Ⅰ)|<|J(Ⅱ)|, 说明磁耦合作用增强; 体系Ⅰ与Ⅱ相比, X由FeⅢ变成CoⅢ, M不变, 桥氧原子Ob和Ob2(O′b2)上的自旋密度增大, 进一步从相关BS态的磁轨道比较得出, 体系Ⅱ中轨道重叠程度大于体系Ⅰ, 结果使X-M之间的反铁磁耦合作用加强.     

O deficiency in the rutile TiO2 (110) surface: Ab initio quantum chemical investigation of the electronic properties

The (110) surface of rutile TiO₂ (110) has been modeled using a density functional theory (DFT) plane‐wave pseudo‐potential method (CASTEP). In this study, 6 and 9 atomic‐layer slabs have been examined. The stoichiometric surface converges to a low‐spin solution in both cases with a density of states (DOS) similar to that for the bulk. O deficiencies are introduced by the removal of neutral O atoms thus leaving a neutral model with a surfeit of 2 e^? per vacancy. This results in the partial filling of the Ti t_2g conduction band orbitals and a compensatory shift in the Fermi level. The reduced surface converges to a high‐spin solution in all cases, with the excess spin located within the previously unoccupied Ti t_2g orbitals. Removal of the bridging surface O atoms results in an excess spin of 2 electrons per unit cell with approximately one‐half that for removal of in‐plane surface O atoms and subsurface O atoms. The removal of O atoms from the surface leads to an increase of the band gap, with the largest increase due to the removal of in‐plane 3‐fold coordinated surface O atoms, and the smallest one due to the removal of subsurface O atoms. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Magnetic exchange interactions in cyano‐bridged MoIII binuclear complexes: Broken‐symmetry and density functional theory calculations

Molecular magnetism in cyano‐bridged Mo^III binuclear complexes [Mo₂(CN)₁₁]^5? and [(Me₃tacn)₂Mo₂(CN)₅]⁺ (Me₃tacn?N, N′, N″‐trimethyl‐1,4,7‐triazacyclononane) has been calculated using Becke's three‐parameter exchange functional and the gradient‐corrected functional of Lee, Yang, and Parr (B3LYP), a hybrid density functional theory (DFT), combined with a modified broken symmetry (BS) approach and the post–Hartree‐Fock (post‐HF) method difference‐dedicated configuration interaction (DDCI). We find B3LYP combined with broken‐symmetry approach (DFT‐BS) give the similar J values to those calculated by DDCI. So we use B3LYP combined with BS approach to investigate the magnetism above two molecules. Through calculations, we find that the absolute J values decrease with the increase of r (the Mo(2)‐C_brid and Mo(1)‐N_brid distances) and are linearly related to the differences of the squared spin populations [(ρ ? ρ)] on Mo^III atoms between the highest‐spin (HS) state and the broken symmetry (BS) state. Moreover, the absolute J values are linearly related to the sum of the square of the difference in energy of the unpaired electrons (ξ) with a limited variation of the r distance. We conclude that ξ can be used to scale the degree of the antiferromagnetic coupling interactions. At the end of the paper, the spin density distributions and the mechanisms of magnetic coupling interactions are analyzed by us. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Does the Sign of the Cu–Gd Magnetic Interaction Depend on the Number of Atoms in the Bridge?

Several theoretical investigations with CASSCF methods confirm that the magnetic behavior of Cu–Gd complexes can only be reproduced if the 5d Gd orbitals are included in the active space. These orbitals, expected to be unoccupied, do present a low spin density, which is mainly due to a spin polarization effect. This theory is strengthened by the experimental results reported herein. We demonstrate that Cu–Gd complexes characterized by Cu–Gd interactions through single‐oxygen and three‐atom bridges consisting of oxygen, carbon, and nitrogen atoms, present weak ferromagnetic exchange interactions, whereas complexes with bridges made of two atoms, such as the nitrogen–oxygen oximato bridge, are subject to weak antiferromagnetic exchange interactions. Therefore, a bridge with an odd number of atoms induces a weak ferromagnetic exchange interaction, whereas a bridge with an even number of atoms supports a weak antiferromagnetic exchange interaction, as observed in pure organic compounds and also, as in this case, in metal–organic compounds with an active spin polarization effect.     

Experimental Determination of Magnetic Anisotropy in Exchange‐Bias Dysprosium Metallocene Single‐Molecule Magnets

We investigate a family of dinuclear dysprosium metallocene single‐molecule magnets (SMMs) bridged by methyl and halogen groups [Cp′₂Dy(μ‐X)]₂ (Cp′=cyclopentadienyltrimethylsilane anion; 1 : X=CH₃^?; 2 : X=Cl^?; 3 : X=Br^?; 4 : X=I^?). For the first time, the magnetic easy axes of dysprosium metallocene SMMs are experimentally determined, confirming that the orientation of them are perpendicular to the equatorial plane which is made up of dysprosium and bridging atoms. The orientation of the magnetic easy axis for 1 deviates from the normal direction (by 10.3°) due to the stronger equatorial interactions between Dy^III and methyl groups. Moreover, its magnetic axes show a temperature‐dependent shifting, which is caused by the competition between exchange interactions and Zeeman interactions. Studies of fluorescence and specific heat as well as ab initio calculations reveal the significant influences of the bridging ligands on their low‐lying exchange‐based energy levels and, consequently, low‐temperature magnetic properties.     

Unconventional Magnetic and Resistive Hysteresis in an Iodine‐Bonded Molecular Conductor

Simultaneous manipulation of both spin and charge is a crucial issue in magnetic conductors. We report on a strong correlation between magnetism and conductivity in the iodine‐bonded molecular conductor (DIETSe)₂FeBr₂Cl₂ [DIETSe=diiodo(ethylenedithio)tetraselenafulvalene], which is the first molecular conductor showing a large hysteresis in both magnetic moment and magnetoresistance associated with a spin‐flop transition. Utilizing a mixed‐anion approach and iodine bonding interactions, we tailored a molecular conductor with random exchange interactions exhibiting unforeseen physical properties.     

Theoretical investigation of the magnetic interactions of Ni9 complexes

On the basis of density-functional theory (DFT) calculations, a theoretical analysis of the exchange interactions in Ni9L2(O2CMe)8{(2-py)2CO2}4, was performed, where L is a bridging ligand, OH- (1) or N3- (2). Each magnetic interaction between the Ni spin centers is analyzed for 1 and 2 in terms of exchange integrals (J values), orbital overlap integrals (T values) and natural orbitals. It was found that a J3 interaction, which is a magnetic interaction via the bridging ligand orbitals, mainly controls the whole magnetic properties, and the dominant interaction is a sigma-type orbital interaction between Ni dz2 orbitals. Further investigations on the magnetostructural correlations are performed on the J3 interactions using simplest Ni-L-Ni models. These models reproduced the magnetic interactions qualitatively well not only for the Ni9 complexes but also for other inorganic complexes. Strong correlations have been found between the magnetic orbital overlaps (T values) and the Ni-L-Ni angle. These results revealed that the difference of the magnetic properties between OH- and N3- is caused by the orbital overlap integral (T values) of the sigma-type J3 interaction pathway. The magnetic interactions are also discussed from a Hubbard model by evaluating the transfer integral (t) and on-site Coulomb integrals (U), in relation to the Heisenberg picture.     

Exchange and Delocalization Effects in [Fe6S6]2+ Superclusters

A theoretical study of Heisenberg exchange and double exchange (delocalization) effects in the iron-sulphur supercluster is presented. Such clusters can play important role in biological systems (proteins and enzymes) acting as so-called active centres. The cluster with valence 2+ can be modelled by two Fe(III) and four Fe(II) ions. An idealized structure of double cubane has been considered instead of a more realistic defected double cubane structure of lower symmetry. Energies of the lowest spin states have been calculated numerically depending on the Heisenberg exchange J _i and double exchange b parameters. Possible spin ground states (S=0, 1, 2, 3, 4, 5) have been predicted. The ground state of a given total spin Sis usually achieved for the intermediate spin value of S ₅₆=4 in the case of fully antiferromagnetic as well as partially ferromagnetic spin interactions. In the case of no double exchange, the ground state with the total spin S=3 should always be observed, while a nonzero hopping effect results in narrowing a parameter region of the ground state. If the double exchange is taken into account, then the spin values depend on the Heisenberg integrals. The model results can be applied in order to interpret many structural and magnetic properties of proteins and enzymes possessing the Fe-S active centres.     

Maximum Spin Polarization in Chromium Dimer Cations as Demonstrated by X‐ray Magnetic Circular Dichroism Spectroscopy

X‐ray magnetic circular dichroism spectroscopy has been used to characterize the electronic structure and magnetic moment of Cr₂⁺. Our results indicate that the removal of a single electron from the 4sσ_g bonding orbital of Cr₂ drastically changes the preferred coupling of the 3d electronic spins. While the neutral molecule has a zero‐spin ground state with a very short bond length, the molecular cation exhibits a ferromagnetically coupled ground state with the highest possible spin of S=11/2, and almost twice the bond length of the neutral molecule. This spin configuration can be interpreted as a result of indirect exchange coupling between the 3d electrons of the two atoms that is mediated by the single 4s electron through a strong intraatomic 3d‐4s exchange interaction. Our finding allows an estimate of the relative energies of two states that are often discussed as ground‐state candidates, the ferromagnetically coupled ¹²Σ and the low‐spin ²Σ state.     

A Theoretical Account of the Coupling between Metal- and Ligand-centred Spins

This study addresses the magnetic interaction between paramagnetic metal ions and the radical ligands taking the [Cu^II(hfac)₂(imVDZ)] and [M^II(hfac)₂(pyDTDA)] (imVDZ=1,5-dimethyl-3-(1-methyl-2-imidazolyl)-6-oxoverdazyl; hfac=(1,1,1,5,5,5)hexafluroacetylacetonate; pyDTDA=4-(2′-pyridyl)-1,2,3,5-dithiadiazolyl), (M=Cu, Ni, Co, Fe, Mn) compounds as reference systems. The coupling between the metal and ligand spins is quantified in terms of the exchange coupling constant (J) in the platform of density functional theory (DFT) and the wave function-based complete active space self-consistent field (CASSCF) method. Application of DFT and broken symmetry (BS) formalism results ferromagnetic coupling for all the transition metal complexes except the Mn(II) complex. This DFT-BS prediction of magnetic nature matches with the experimental finding for all the complexes other than the Fe(II)-pyDTDA complex, for which an antiferromagnetic coupling between high spin iron and the thiazyl ligand has been reported. However, evaluation of spin state energetics through the multiconfigurational wave function-based method produces the S=3/2 ground spin state for the iron-thiazyl in parity with experiment. Electronic structure analyses find the overlap between the metal- and ligand-based singly occupied molecular orbitals (SOMOs) to be one of the major reasons attributing to different extent of exchange coupling in the systems under investigation.     

Spin exchange interactions and magnetic structures of extended magnetic solids with localized spins: theoretical descriptions on formal, quantitative and qualitative levels

Low-energy excitation energies of a magnetic solid with localized spins are probed by magnetic susceptibility, neutron scattering and Raman scattering measurements, and are analyzed using a spin Hamiltonian with a set of spin exchange parameters. The nature and values of the spin exchange parameters deduced from this analysis depend on what spin exchange paths one includes in the spin Hamiltonian. In this article, we review how spin exchange interactions of magnetic solids with localized spins are described on formal, quantitative and qualitative theoretical levels, investigate antisymmetric and anisotropic interactions for general spin dimers, and discuss the spin exchange interactions and magnetic structures of various extended magnetic solids on the basis of spin dimer analysis. Strongly interacting spin exchange paths of a magnetic solid are determined by the overlap between its magnetic orbitals, so that the strongly interacting spin unit of a magnetic solid does not necessarily have the same geometrical feature as does the arrangement of its magnetic ions or spin-carrying molecules. Therefore, in interpreting results of magnetic susceptibility, inelastic neutron scattering or Raman scattering measurements, it is essential to employ a set of spin exchange parameters chosen on the basis of proper electronic structure considerations. Spin dimer analyses based on extended Hückel tight binding calculations provide a reliable and expedient means to study the relative strengths of superexchange and super-superexchange spin exchange interactions.     

Unraveling σ and π Effects on Magnetic Anisotropy in cis‐NiA4B2 Complexes: Magnetization,HF‐HFEPR Studies,First‐Principles Calculations,and Orbital Modeling

By using complementary experimental techniques and first‐principles theoretical calculations, magnetic anisotropy in a series of five hexacoordinated nickel(II) complexes possessing a symmetry close to C_2v, has been investigated. Four complexes have the general formula [Ni(bpy)X₂]ⁿ⁺ (bpy=2,2′‐bipyridine; X₂=bpy ( 1 ), (NCS^?)₂ ( 2 ), C₂O₄^2? ( 3 ), NO₃^? ( 4 )). In the fifth complex, [Ni(HIM₂‐py)₂(NO₃)]⁺ ( 5 ; HIM₂‐py=2‐(2‐pyridyl)‐4,4,5,5‐tetramethyl‐4,5‐dihydro‐1H‐imidazolyl‐1‐hydroxy), which was reported previously, the two bpy bidentate ligands were replaced by HIM₂‐py. Analysis of the high‐field, high‐frequency electronic paramagnetic resonance (HF‐HFEPR) spectra and magnetization data leads to the determination of the spin Hamiltonian parameters. The D parameter, corresponding to the axial magnetic anisotropy, was negative (Ising type) for the five compounds and ranged from ?1 to ?10 cm^?1. First‐principles SO‐CASPT2 calculations have been performed to estimate these parameters and rationalize the experimental values. From calculations, the easy axis of magnetization is in two different directions for complexes 2 and 3 , on one hand, and 4 and 5 , on the other hand. A new method is proposed to calculate the g tensor for systems with S=1. The spin Hamiltonian parameters (D (axial), E (rhombic), and g_i) are rationalized in terms of ordering of the 3 d orbitals. According to this orbital model, it can be shown that 1) the large magnetic anisotropy of 4 and 5 arises from splitting of the e_g‐like orbitals and is due to the difference in the σ‐donor strength of NO₃^? and bpy or HIM₂‐py, whereas the difference in anisotropy between the two compounds is due to splitting of the t_2g‐like orbitals; and 2) the anisotropy of complexes 1 – 3 arises from the small splitting of the t_2g‐like orbitals. The direction of the anisotropy axis can be rationalized by the proposed orbital model.     

2,6‐Bis(pyrazol‐3‐yl)pyridine as Meridional Capping Ligand: Synthesis,Characterization, and Crystal Structure of the First Corresponding Hexanuclear Iron(III) Complex

Based on the 2,6‐bis(pyrazol‐3‐yl)pyridine ligand (H₂bpp) the hexanuclear iron(III) complex [Fe₆(bpp)₄(μ₃‐O)₂(μ‐OMe)₃(μ‐OH)Cl₂] ( 1 ) was synthesized. The reaction with iron(II) chloride and additional pyridine leads to the exclusive formation of the complex through self‐assembly process. Six octahedrally coordinated iron atoms are linked through the pyrazolido groups of four H₂bpp ligands. These are further linked through bridging hydroxido, methoxido, and oxido groups. The complex has been characterized by IR spectroscopy, ESI mass spectrometry, elemental analysis and X‐ray crystallography. Temperature‐dependent magnetic measurements indicate strong antiferromagnetic exchange interaction between the high‐spin iron(III) ions within the complex, which leads to an S = 0 spin ground state. As a result of the two Fe3(μ₃‐O) fragments two frustrated exchange pathways are present. In addition the properties of H₂bpp as a potential capping ligand for the synthesis of heteroleptic trinuclear complexes based on the triaminoguanidine core is investigated.     

A New Hydroxo‐bridged Chromium(III) Dimer [Cr(saltn)OH]2·4H2O: Synthesis,Crystal Structure and Magnetic Properties

A new hydroxo‐bridged dimeric Cr(III) complex [Cr(saltn)OH]₂·4H₂O [H₂saltn=N,N′‐bis(salicylidene)trimethylenediamine] has been synthesized and its structural and magnetic properties have been investigated. The complex crystallizes in the triclinic space group P‐1 with one dimeric formula unit in a cell of dimensions a=0.95828(19) nm, b=0.95926(19) nm, c=1.0437(2) nm, α=86.77(3)°, β=82.48(3)°, and γ=64.93(3)°. The geometry around each chromium(III) center is six‐coordinate, distorted‐octahedral. The bridging Cr₂O₂ unit is strictly planar, as required by the crystallographic symmetry. The Cr? O? Cr′ bridging angle is 99.94(16)°, and the distance between Cr…Cr′ is 0.3019 nm. The magnetic susceptibility of the complex has been examined in the range of 2‐300 K. By using the spin‐spin coupled model for an S₁=S₂=3/2 dimeric system , the magnetic data were fitted to give the parameters of g=2.01(1), J=‐0.85(2) cm^‐1, and zJ' =0.18(3)cm^‐1, indicating the presence of a weak antiferromagnetic spin‐exchange interaction between the Cr(III) ions in the binuclear complex.     

A Redox‐Active Bridging Ligand to Promote Spin Delocalization,High‐Spin Complexes,and Magnetic Multi‐Switchability

A dinuclear Co^II complex, [Co₂(tphz)(tpy)₂]ⁿ⁺ (n=4, 3 or 2; tphz: tetrapyridophenazine; tpy: terpyridine), has been assembled using the redox‐active and strongly complexing tphz bridging ligand. The magnetic properties of this complex can be tuned from spin‐crossover with T_1/2≈470 K for the pristine compound (n=4) to single‐molecule magnet with an S_T=5/2 spin ground state when once reduced (n=3) to finally a diamagnetic species when twice reduced (n=2). The two successive and reversible reductions are concomitant with an increase of the spin delocalization within the complex, promoting remarkably large magnetic exchange couplings and high‐spin species even at room temperature.     

A Redox‐Active Bridging Ligand to Promote Spin Delocalization,High‐Spin Complexes,and Magnetic Multi‐Switchability

A dinuclear Co^II complex, [Co₂(tphz)(tpy)₂]ⁿ⁺ (n=4, 3 or 2; tphz: tetrapyridophenazine; tpy: terpyridine), has been assembled using the redox‐active and strongly complexing tphz bridging ligand. The magnetic properties of this complex can be tuned from spin‐crossover with T_1/2≈470 K for the pristine compound (n=4) to single‐molecule magnet with an S_T=5/2 spin ground state when once reduced (n=3) to finally a diamagnetic species when twice reduced (n=2). The two successive and reversible reductions are concomitant with an increase of the spin delocalization within the complex, promoting remarkably large magnetic exchange couplings and high‐spin species even at room temperature.     

Synthesis,Structure, and Magnetic Studies of a New Wheel‐Shaped [LiMnIII6] Cluster

The synthesis, crystal structure, and magnetic properties of a new hexanuclear manganese(III) complex are reported. The complex [LiMn₆(L)₆]OH · 2MeCN · 4MeOH · 1.5H₂O (LiH₂L = lithium 2‐{[bis(2‐hydroxyethyl)amino]methyl}‐4‐methylphenate) ( 1 ), was obtained from the reaction of one equivalent of LiH₂L with Mn(OAc)₂ in MeCN/MeOH (v:v/1:1). Single‐crystal X‐ray diffraction shows that six octahedrally coordinated manganese(III) ions define a ring and are linked by twelve bridging oxygen atoms from alkoxo groups. The resulting [Mn₆(OCH₂)₁₂] skeleton has the remarkable property of acting as a host for a octahedrally coordinated lithium ion in the center of the ring. Variable‐temperature solid‐state magnetic susceptibility studies of 1 in the temperature range 2.0–300 K reveal that the complex has a S = 12 ground state spin, showing ferromagnetic exchange interactions between the constituent manganese(III) ions.     

Broken-symmetry density functional theory investigation on bis-nitronyl nitroxide diradicals: influence of length and aromaticity of couplers

A series of nitronyl nitroxide (NN) diradicals with linear conjugated couplers and another series with aromatic couplers have been investigated by the broken-symmetry (BS) DFT approach. The overlap integral between the magnetically active orbitals in the BS state has been explicitly computed and used for the evaluation of the magnetic exchange coupling constant (J). The calculated J values are in very good agreement with the observed values in the literature. The magnitude of J depends on the length of the coupler as well as the conformation of the radical units. The aromaticity of the spacer decreases the strength of the exchange coupling constant. The SOMO-SOMO energy splitting analysis, where SOMO stands for the singly occupied molecular orbital, and the calculation of electron paramagnetic resonance (EPR) parameters have also been carried out. The computed hyperfine coupling constants support the intramolecular magnetic interactions. The nature of magnetic exchange coupling constant can also be predicted from the shape of the SOMOs as well as the spin alternation rule in the unrestricted Hartree-Fock (UHF) treatment. It is found that pi-conjugation along with the spin-polarization plays the major role in controlling the magnitude and sign of the coupling constant.