两个典型氧桥三核铁(Ⅲ)配合物[Fe3O(O2CCH2OC6H5)6(3H2O)]和[Fe3O(TIEO)2(O2CPh)2Cl3]的局域自旋和磁性质的理论探讨

用从头算波函数(UHF或UDFT波函数)代替ZILSH方法中的半经验波函数得到了ABLSH方法，接着用该方法研究了两个典型氧桥三核铁(Ⅲ)配合物[Fe₃O(O₂CCH₂OC₆H₅)₆(3H₂O)]和[Fe₃O(TIEO)₂(O₂CPh)₂Cl₃]的局域自旋和磁性质。通过计算得到的局域自旋结果和前人的具有可比性，同时所得的磁交换耦合常数和实验值很吻合。该方法可作为研究海森堡型磁性系统(HM)的新工具。     

A local spin evaluation into the active site models of [2Fe2S] ferrodoxin [Fe<Subscript>2</Subscript>S<Subscript>2</Subscript>(SR)<Subscript>4</Subscript>]<Superscript>2−</Superscript> (R=—H, —CH<Subscript>3</Subscript>)

To test the feasibility of local spin theory of Davidson and Clark for ferrodoxin clusters, the models [Fe₂S₂(SR)₄]²⁻ (R=—H, —CH₃) are chosen for evaluation. This purpose is realized by calculating the local spin expectation values 〈S _A·S _B〉, 〈S _A ² 〉, and m _A and discussing the connection between these expected values and the Heisenberg spin model (HSM) and the Noodleman broken-symmetry approach. In practical calculation, the spin-unrestricted Hartree-Fock (UHF) and spin-polarized density functional theory (DFT) are used and the calculational qualities of these two methods are also discussed. In addition, the theoretical magnetic coupling constants J _AB of these models are calculated by various computational schemes for comparison with both theoretical and experimental results previously reported. Supported by the Doctorial Initial Foundations of Hainan Normal University (Grant No. 13140252)     

Theoretical study of the exchange coupling interactions in a polyoxometalate Fe9W12 complex

Theoretical methods based on density functional theory have been employed to analyze the exchange interactions in a Fe₉W₁₂ polyoxometalate complex. The calculated values of the seven exchange coupling constants required by the molecular structure agree well with those reported previously for other Fe^III polynuclear complexes and give an S = 15/2 single determinant ground state, with a first excited state that has S = 5/2.     

Magnetic Coupling Constants of Self‐Assembled CuII [3×3] Grids: Alternative Spin Model from Theoretical Calculations

This paper reports a theoretical analysis of the electronic structure and magnetic properties of a ferromagnetic Cu^II [3×3] grid. A two‐step strategy, combining calculations on the whole grid and on binuclear fragments, has been employed to evaluate all the magnetic interactions in the grid. The calculations confirm an S=7/2 ground state, which is in accordance with the magnetisation versus field curve and the thermal dependence of the magnetic moment data. Only the first‐neighbour coupling terms present non‐negligible amplitudes, all of them in agreement with the structure and arrangement of the Cu 3d magnetic orbitals. The results indicate that the dominant interaction in the system is the antiferromagnetic coupling between the ring and the central Cu sites (J₃=J₄≈?31 cm^?1). In the ring two different interactions can be distinguished, J₁=4.6 cm^?1 and J₂=?0.1 cm^?1, in contrast to the single J model employed in the magnetic data fit. The calculated J values have been used to determine the energy level distribution of the Heisenberg magnetic states. The effective magnetic moment versus temperature plot resulting from this ab initio energy profile is in good agreement with the experimental curve and the fitting obtained with the simplified spin model, despite the differences between these two spin models. This study underlines the role that the theoretical evaluations of the coupling constants can play on the rationalisation of the magnetic properties of these complex polynuclear systems.     

A quantum algorithm for spin chemistry: a Bayesian exchange coupling parameter calculator with broken-symmetry wave functions

The Heisenberg exchange coupling parameter J (H = −2JS_i · S_j) characterises the isotropic magnetic interaction between unpaired electrons, and it is one of the most important spin Hamiltonian parameters of multi-spin open shell systems. The J value is related to the energy difference between high-spin and low-spin states, and thus computing the energies of individual spin states are necessary to obtain the J values from quantum chemical calculations. Here, we propose a quantum algorithm, B̲ayesian ex̲change coupling parameter calculator with b̲roken-symmetry wave functions (BxB), which is capable of computing the J value directly, without calculating the energies of individual spin states. The BxB algorithm is composed of the quantum simulations of the time evolution of a broken-symmetry wave function under the Hamiltonian with an additional term jS², the wave function overlap estimation with the SWAP test, and Bayesian optimisation of the parameter j. Numerical quantum circuit simulations for H₂ under a covalent bond dissociation, C, O, Si, NH, OH⁺, CH₂, NF, O₂, and triple bond dissociated N₂ molecule revealed that the BxB can compute the J value within 1 kcal mol⁻¹ of errors with less computational costs than conventional quantum phase estimation-based approaches.

A quantum algorithm “Bayesian exchange coupling parameter calculator with broken-symmetry wave function (BxB)” enables us to calculate Heisenberg exchange coupling parameter J without inspecting total energies of individual spin states, within 1 kcal mol⁻¹ of energy tolerance.     

Redox potential of iron–sulfur clusters as a model of the Desulfovibrio vulgaris center

A theoretical study of Heisenberg exchange and double exchange effects in clusters with four and six iron ions has been performed for [Fe₄ S₃ O] ^m+, [Fe₄ S₄]^m+ (where m = 3, 2), and [Fe₆ S₆] ⁿ⁺ (where n = 5, 4) ions as models of the Desulfovibrio vulgaris iron–sulfur centers. Assuming that the redox potential mostly depends on the Heisenberg spin coupling and the resonance delocalization, we performed an analysis of the reduction process for the [Fe₄ S₃ O] ^3+/2+, [Fe₄ S₄] ^3+/2+, and [Fe₆ S₆] ^5+/4+ ions and showed that the redox potential can be calculated as a difference between average spin energies of the tetravalent and pentavalent double cubane superclusters. For the Heisenberg parameter of J₁ = 20 cm^-1, the redox potential amounts to about 0.03 V.It complies with close to zero experimental values of the redox potential.Electronic Supplementary Material: Supplementary material is available in the online version of this article at     

Spin-projected coupled-cluster theory with single and double excitations

Coupled-cluster (CC) theory including single (S) and double (D) excitations and carried out with a spin-unrestricted Hartree–Fock (UHF) reference wave function is free from S + 1 spin contamination as can be confirmed by an analysis of the expectation value of the spin operator, Ŝ ². Contamination by the S + 2 contaminant can be projected out by an approximate procedure (APCCSD) with a projection operator, P^, represented by the product of the spin annihilation operators ? _{s+ 1} and ?_s+2. The computational cost of such a projection scales with O(M ⁶) (M is the number of basis functions). The APCCSD energy obtained after annihilation of the S + 2 contaminant can be improved by adding triple (T) excitations in a perturbative way, thus leading to APCCSD(T) energies. For the 17 examples studied, the deviation of the UHF-CCSD(T) energies from the corresponding full configuaration interaction values is reduced from 4.0 to 2.3 mhartree on the average as a result of annihilating the S + 2 contaminant in an approximate way. In the case of single-bond cleavage, APCSSD leads to a significant improvement of the energy in the region where the bonding electrons recouple from a closed shell to an open shell singlet electron pair. Received: 13 April 2000 / Accepted: 12 July 2000 / Published online: 24 October 2000     

Ab initio Hartree–Fock and multiple-scattering Xα calculation of the g factors for CuF2

Ab initio Hartree–Fock and multiple-scattering wave functions are calculated for linear CuF₂. These wave functions are used to calculate the spin–orbit coupling in a new way where the neglect of two- and many-center terms is avoided and where experimental or calculated spin–orbit coupling constants for the atomic ions are used. The calculated value of g is too small by the MS Xα method and too large by the ab initio method, indicating too much 3d–L interaction in the MS Xα case and too little in the ab initio case.     

Electronic Structure of Thiolate‐bridged Diiron Complexes and a Single‐electron Oxidation Reaction: A Combination of Experimental and Computational Studies

Single‐electron oxidation of a diiron‐sulfur complex [Cp*Fe(μ‐bdt)FeCp*] ( 1 , Cp*=η⁵‐C₅Me₅; bdt=benzene‐1,2‐dithiolate) to [Cp*Fe(μ‐bdt)FeCp*]⁺ ( 2 ) has been experimentally conducted. The bdt ligand with redox‐active character has been computationally proposed to be a dianion (bdt^2?) rather than previously proposed monoanion (bdt^·?) radical in 1 though it has un‐equidistant aromatic C? C bond lengths. The ground state of 1 is predicted to be two low‐spin ferrous ions (S_Fe=0) and 2 has a medium‐spin ferric ion (S_Fe=1/2) and a low‐spin ferrous center (S_Fe=0), and the oxidation of 1 to 2 is calculated to be a single‐metal‐based process. Both complexes have no significant antiferromagnetic coupling character.     

Diagrammatic valence-bond theory for finite model Hamiltonians

Valence bond (VB ) diagrams form a complete basis for model Hamiltonians that conserve total spin, S, and have one valence state, ?_p, per site. Hubbard and Pariser–Parr–Pople (PPP ) models illustrate ionic problems, with zero, one, or two electrons in each ?_p, while isotropic Heisenberg models illustrate spin problems, with only purely covalent VB diagrams. The difficulty of nonorthogonal VB diagrams is by-passed by exploiting the finite dimensionality of the complete basis and working with unsymmetric sparse matrices. We introduce efficient bit manipulations for generating, storing, and handling VB diagrams as integers and describe a new coordinate relaxation method for the ground and lowest excited states of unsymmetric sparse matrices. Antiferromagnetic spin-½ Heisenberg rings and chains of N ? 20 spins, or 2^N spin functions, are solved in C₂ symmetry as illustrative examples. The lowest S = 1 and 0 excitations are related to domain walls, or spin solitons, and studied for alternations corresponding to polyacetylene. VB diagrams with arbitrary S and nonneighbor interactions are constructed for both spin and ionic problems, thus extending diagrammatic VB theory to other topologies.     

Unexpected Luminescence Behavior of Coinage Metal π‐Diborene Complexes

A number of unprecedented photophysical phenomena were observed in the study of luminescent π‐diborene complexes of Cu and Ag. These observations included unusually high fluorescence quantum yields (up to 100%) in solution for complexes of these metals. This result indicates that very little or no intersystem crossing between S₁ and T_n occurs in the complexes, despite the strong spin–orbit coupling of the metal atoms. The replacement of carbon with boron thus yields luminescent isolobal analogues of otherwise non‐emissive olefin complexes of Cu and Ag.     

Quantum Monte Carlo Simulations and High‐Field Magnetization Studies of Antiferromagnetic Interactions in a Giant Hetero‐Spin Ring

Chromium lanthanide heterometallic wheel complexes {Cr₈Ln₈} (Ln=Gd, Dy and Y) with alternating metal centres are presented. Quantum Monte Carlo simulations reveal antiferromagnetic exchange‐coupling constants with an average of 2.1 K within the {Cr₈Gd₈} wheel, which leads to a large ground spin state (S _T=16) that is confirmed by magnetization studies up to 20 Tesla. The {Cr₈Dy₈} wheel is a single‐molecule magnet.     

Determination of heisenberg exchange coupling constants in clusters with magnetic sites: A local spin approach

This work studies the ability of the two‐center local spin quantities, provided by the partitioning of the expectation value of the spin‐squared operator corresponding to N‐electron systems, for determining spin‐exchange coupling constants within the Heisenberg spin Hamiltonian model. The spin‐exchange parameters, which characterize this Hamiltonian for a determined system, have been evaluated in the HeH₂ aggregate and in several clusters (n = 2, 3, 4) with different geometrical arrangements, using internuclear distances larger than the equilibrium ones (beyond the bonding regions). The results found have been analyzed and compared with those arising from other approaches, showing the feasibility of our methodology. © 2014 Wiley Periodicals, Inc.     

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.     

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.     

Inclusion of hydrogen p orbitals in the semiempirical calculation of NMR parameters. III: INDO CHF calculations of orbital and dipolar contributions to spin–spin coupling constants involving protons

The self-consistent perturbation theory is used to calculate noncontract contributions to spin–spin coupling constants involving protons. Molecular wave functions were obtained with a modified version of the INDO method which includes hydrogen 2p orbitals in its basis set. It is found that in many cases the orbital and dipolar terms are by no means negligible, being particularly important in geminal H? H couplings. Results reported in this paper for this type of coupling, reproduce experimental trends in the series CH₄, NH₃, and OH₂. In general, noncontact terms are found to decrease as the number of bonds separating the interacting nuclei increases.     

Theoretical study of the relationship between the nearest-neighbor exchange coupling interactions and the number of peripheral complexes in the cyano-bridged CrMn6(CN)6 and CrMn2(CN)2 clusters

A theoretical density functional study of the relationship between the nearest-neighbor constants and the number of peripheral complexes in the cyano-bridged [Cr[CNMn(salen)(H2O)]6]3+ and [(5-Brsalen)2(H2O)2Mn2Cr(CN)6] clusters is presented. Two approaches show that the antiferromagnetic coupling interactions between nearest neighbors decrease with the increase of the number of peripheral complexes, although the second approach provides better results using several exchange-correlation functionals. The first approach consisted of evaluating the exchange coupling constant J(ij) between two paramagnetic metal centers i and j in the hexanuclear molecule by calculating the energy differences between the highest and broken-symmetry spin states of a model molecule in which metal atoms except for i and j are substituted by diamagnetic Zn(II) cations, while the second consisted of calculating the different spin-state energies of hexanuclear complexes and using the Heisenberg Hamiltonian to obtain the exchange coupling constants between different metal centers. Moreover, Kahn's qualitative theory succeeded in being applied to interpret the trend.