Structure distortion effects in the spectrum of tunnel-exchange states of tetrahedral mixed-valence tetramers

Tunnel-exchange states of a tetrameric mixed-valence (MV) d₁–d₁–d₁–d₂ cluster are considered. Energy levels of distorted pseudotetrahedral conjiprations with rhombic and trigonal symmetry are calculated. It is demonstrated that the correlation diagrams of planar systems are symmetric with respect to the sign of the double exchange parameter. A strong double exchange always results in the ferromagnetic ground state of planar systems. The following types of spectrum defamations of the d₁–d₁–d₁–d₂ tetramer from tetrahedral to planar systems have been found: a) with a weak positive double exchange, deformation of a tetrahedral system does not lead to any change of spin of the antiferromagnetic ground state of the cluster; b) with a strong positive double exchange, the defonnation alters the antiferromagnetic ground (S = 1/2) state of the tetrahedral system to the ferromagnetic (S = 5/2) state of the planar system, or to an intermediate (S = 3/2) state; c) with a negative double exchange, irrespective of its absolute value, the tetrahedral system deformation does not alter the spin of the ground state. With a weak double exchange, this ground state remains antiferromagnetic, and with a strong double exchange, it is ferromagnetic or intermediate.Moldova State University. Translated fromZhurnal Strukturnoi Khimii, Vol. 34, No. 5, pp. 33–46, September–October, 1993.Translated by L. Chernomorskaya     

Hole-type mixed-valence tetrahedral cluster: Exchange-tunnel states and magnetic properties

The paper deals with the exchange-tunnel states of a tetrahedral tetrameric hole-type cluster d¹-d²-d²-d² used as a model of metal core of vrious protiens. A new method for group-theoretic classification ofthe quantum states of mixed-valence clusters is suggested. The nature ofthe ground spin state of the above systems has been investigated. The effect of partial spin alignment depending on the double exchange parameter value is discussed.Moldova State University. Translated fromZhumal Strukturnoi Khimii, Vol. 34, No. 3, pp. 14–25, May–June 1993.Translated by L. Smolina     

Double exchange in polynuclear mixed-valence clusters. 1. General solution of the electronic problem

The problem of calculating the electronic energy spectra of mixed-valence clusters with one “extra” electron (dⁿ-dⁿ...dⁿ⁺¹) or hole (dⁿ⁺¹-dⁿ⁺¹...dⁿ) delocalized in the paramagnetic cores of transition metals is solved. Unlike the available particular solutions, which are restricted to small numbers of ions and electrons, the solution proposed in this work is general and is suitable for many-electron systems of arbitrary numbers of nuclei and arbitrary symmetries. The new microscopic approach to the double exchange problem is based on the combination of the sequential (“chain”) scheme of spin coupling and angular momentum method. In terms of this approach, an analytical dependence of the matrix elements of the double exchange, Heisenberg exchange, and vibronic interaction on all spin quantum numbers is obtained. The final equations contain only the 6j symbols and are free of the higher-order nj symbols, which obstructed the solution of the double exchange problem in previous works. Valencia University, Spain. Bordeaux University, France. Moldova State University. Institute of Chemistry, Academy of Sciences, Moldova Republic. Translated fromZhurnal Strukturnoi Khimii, Vol. 37, No. 5, pp. 805–815, September–October, 1996. Translated by I. Izvekova     

Magnetic moments of multielectron mixed-valency dimer clusters in a dynamic intermediate vibronic coupling approach

The vibronic aspect of the Jahn-Teller effect is considered for multielectron mixed-valency dimer clusters. A basic intermediate-coupling set is used in the numerical diagonalization of the vibronic Hamiltonian. The temperature dependence of the vibronic magnetic moment is derived for symmetrical and distorted mixed-valency dimer clusters. Strong vibronic interaction can suppress double exchange and lead to an antiferromagnetic ground state for the cluster. Distortions that eliminate the inversion center localize the surplus electron and suppress the ferromagnetic effect caused by double exchange.Chemical Institute, Moldovian Academy of Sciences. Moldovian State University. Translated from Zhurnal Strukturnoi Khimii, Vol. 34, No. 2, pp. 11–19, March–April, 1993.     

Effect of magnetic exchange,double exchange,vibronic coupling,and asymmetry on magnetic properties in d2–d3 mixed‐valence dimers

The effect of magnetic exchange, double exchange, vibronic coupling, and asymmetry on magnetic properties of d²–d³ systems is discussed. The temperature‐dependent magnetic moment was calculated with the semiclassical adiabatic approach. The results show that the vibronic coupling from the out‐of‐phase breathing vibration on the metal sites (Piepho, Krausz, and Schatz [PKS] model) and the vibronic coupling from the stretching vibration between the metal sites (P model) favor the localization and delocalization of the “extra” electron in mixed‐valence dimers, respectively. The magnetic properties are determined by the interplay among magnetic exchange, double exchange, and vibronic coupling. The results obtained by analyzing d²–d³ systems can be generalized to other full delocalized dinuclear mixed valence systems with a unique transferable electron. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Electronic and vibronic states of an asymmetric trimeric mixed-valence cluster

Electronic and adiabatic vibronic states of d¹-d¹-d² trimeric clusters are considered in terms of the many-electron theory of mixed-valence states. The initial model includes two d-orbitals on each center and allows for Heisenberg and double exchange, asymmetry of the system, and vibronic coupling with local shifts of ligands. Influence of distortions in the trimers on the structure of tunnel-exchange states, on ferro-or antiferromagnetism of the clusters, and on the form of the adiabatic potential is examined. State University, Moldova Republic. Valencia University, Spain. Institute of Chemistry, Academy of Sciences, Moldova Republic. Translated fromZhurnal Strukturnoi Khimii, Vol. 35, No. 4, pp. 35–45, July–August, 1994. Translated by L. Smolina     

Vibronic reduction of Heisenberg and double exchange in multielectron mixed-valency clusters

Vibronic reduction is considered for Coulomb interaction between centers for Heisenberg and double exchange in multielectron mixed-valency d²-d³ clusters. A simplified multimode vibration model indicates how effects arise via vibrations from the correlation interaction between electron shells. Vibronic reduction in double exchange can alter the magnetic parameters for the cluster's ground state.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 28, No. 2, pp. 114–121, March–April, 1992.     

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.     

Geometric and Electronic Structure of WSiN(N = 1–6, 12) Clusters

Geometry optimizations of WSi _N (n = 1–6, 12) clusters are performed using the B3LYP/ LanL2DZ method for a sequence of different spin states, changing from spin singlet to spin septet conditions. The resulting equilibrium structures are discussed under the aspects of geometric features, cluster internal charge transfer and magnetic properties. It is shown that the W impurity in the Si _N environment generally acts as an electron acceptor. However, the charge on the W atom, as obtained by natural population analysis, can be sensitively tuned through the variation of the spin constraint from S = 0 to S = 3. The resulting geometries of WSi _n (N = 3–6) are compared with the known ground state structures of Si _N+1 (N = 3–6), and substitutional geometries are identified for N = 3 and N = 5. The nonzero spin states of WSi _N are shown to display different patterns of magnetic order, corresponding to uniform and to alternating atomic spin orientations within the cluster. Highly compact O _h and D _6h structures are identified as stable geometries of WSi₆ and of the experimentally detected unit WSi₁₂, respectively. Comparison is made with the cluster series MoSi_N(N = 1–6) and CuSi _N (N = 1–6,12).     

Magnetic properties of d–d–d MV trimers with partial electron delocalization in the generalized vibronic model

The effects of magnetic exchange, double exchange and vibronic coupling on magnetic properties of the d¹–d¹–d² trimer with C_2V symmetry are discussed in the generalized vibronic model. The magnetic moments are calculated with the semiclassical adiabatic approach. The results show that the PKS vibronic coupling and the P vibronic coupling favor the localization and the delocalization of the ‘extra’ electron, respectively. The magnetic properties are determined by the interplay among magnetic exchange, double exchange and vibronic coupling.     

Vibronic coupling to T1 and T2 vibrations and the Jahn-Teller effect in transition-metal exchange tetraclusters

A study has been made on the four-center Jahn-Teller effect in tetrahedral transition-metal tetraclusters of M₄X₄L₄ and M₄OX₆L₄ types (M metal, X and L ligands) for twofold orbital degeneracy at each of the four centers and strong coupling between the electronic states there and the cluster vibrations. An analytic expression is derived for the adiabatic potential in the space of all active vibrations. The features of the adiabatic-potential sheets in the T₁ and T₂ vibration space are examined, and the spectrum is derived for the lowest vibronic states. There is a qualitative discussion of the system dynamics.Translated from Teoreti-cheskaya i Éksperimental'naya Khimiya, Vol. 23, No. 6, pp. 657–665, November–December, 1987.     

Laser and radiofrequency spectroscopy of the 5d 4 6s 6 D multiplet in Ta I

The hyperfine structure (hfs) of¹⁸¹Ta has been investigated using laser radio-frequency double resonance and high resolution laser spectroscopy on collimated atomic beams. The magnetic dipole and electric quadrupole hyperfine structure coupling constants of the 5d ^{4 6} s 6D _{3/2, 5/2, 7/2, 9/2} metastable states have been determined using radio-frequency spectroscopy. In the 5d ⁴ 6s ⁶ D _1/2 metastable state and the excited 5d ³ 6s 6p ⁴ D _3/2,⁶ D _{5/2, 9/2} as well as the unidentified 28 182.6 cm^–1 and 30 021.2 cm^–1 states, hfs constants have been obtained from high resolution laser spectroscopy. A radio-frequency converter has been developed in order to reach the frequency region 2.7–10 GHz.     

Jahn-Teller effect in tetraclusters of transition metals,taking into account vibronic coupling with E-vibrations

Conclusion From the results obtained it follows that the shape of the surface for the lower sheet of the adiabatic potential for the cluster in the E vibration space is similar to the surface for the E-e problem both in the linear and in the quadratic cases. Taking into account the extra modes of the E vibration which were discarded in this treatment does not qualitatively change the shape of the adiabatic potential surface (the number of minima and saddle points), which is a consequence of its symmetry [4]. The deformation pattern of the cluster corresponding to movement of the system along the bottom of the channel of one of the lower sheets is analogous to the case of the E-e problem for an octahedral and tetrahedral environment of a Jahn-Teller ion [10]. The average values of the pseudospin operators in the vibronic ground states are the same for all centers, which is evidence (taking into account the equality of the Jahn-Teller distortions at all centers) for ferrodistortion ordering of all the distortions, both in the linear and in the quadratic cases. If each vibronic center has spin s=1/2, all vibronic levels of the cluster have additional 16-fold spin degeneracy. Taking into account the effect of spin-orbit coupling on the shape of the adiabatic potential using perturbation theory shows that removal of spin degeneracy for the lower sheet does not occur, that the adiabatic potential does not change its shape but rather is only reduced in energy by , where is the spin-orbit coupling constant.The high orbital degeneracy of sheets 2, 3, 4 (Fig. 2a, b) is not removed by taking into account the quadratic vibronic coupling and is accidental. The indicated orbital and spin accidental degeneracy of the sheets is removed by taking into account the intercenter interaction.Translated from Teoreticheskaya i Éksperimental' naya Khimiya, Vol. 20, No. 1, pp. 1–9, January–February, 1984.     

Vibronic interactions in {6} and {18}hetero(A,B)annulenes

The vibronic (vibrational–electronic) interactions and the Jahn–Teller effects in the monoanions and trianions of {6}hetero(B,N), (C,N), and (B,O)annulenes and {18}hetero(B,N), (C,N), and (B,O)annulenes are discussed. All the heteroannulenes have threefold axis of symmetry and the twofold degenerate lowest unoccupied molecular orbital (LUMOs), and the E^′ or E vibrational modes can cause Jahn–Teller distortions in their monoanions and trianions. State vibronic coupling constants of the monoanions and trianions and orbital vibronic coupling constants concerning the LUMOs are calculated for each Jahn–Teller active vibrational mode at the B3LYP/6-31G* level of theory. Vibrational modes near 1500 cm⁻¹ of the {6}hetero(A,B)annulenes and low-frequency modes (<500 cm⁻¹) of the {18}hetero(A,B)annulenes give large coupling constants, and therefore, these modes are essential in the Jahn–Teller distortions and the vibronic interactions. The coupling constants are qualitatively analyzed by looking at the nuclear motions of the Jahn–Teller active modes and the shapes of the LUMOs on the basis of one-electron approximation.     

Subduced selection rules for vibronic transitions ind 3 octahedral complexes

Forbidden electronic transitions are often weakly allowed through vibronic coupling to normal modes of the molecule. In transition metal complexes, the first order strong coupling appears in many cases to select specifically one of the available asymmetric modes. In this work the Intermediate Ligand Field model has been extended to vibronic coupling. The basis functions and tensor operators are described as species subduced from the vibronic generative group SU(3) which results from the diagonal restriction of the direct product of the electronic generative group SU(2) with the three dimensional harmonic oscillator group SU(3). This model implies that transitions between strongly coupled bases are permitted only through an overall octupole operator. All lower multipoles are forbidden and in particular the dipole is eliminated by the requirement for a translationally invariant centre of mass. The model permits any combination of multipole operators for separate electronic and vibrational transitions which result in the overall octupole. This theory is applied to two cases ofd ³ complex spectra. It provides an unambiguous assignment of the⁴ A _2g -⁴ T _2g transition in the absorption spectrum of solid [MnF₆]^4– and of the MCD spectrum of the⁴ A _2g -(² T _1g ,⁴ T _2g ) region in [Cr(H₂O)₆]³⁺. In the latter complex, the observed exclusive coupling of the² T _1g state tot _1u (stretch) and the⁴ T _2g state tot _1u (twist) is predicted by the model.     

The heisenberg exchange integral in a non-orthogonal basis for antiferromagnetic and ferromagnetic systems

The Dirac-Van Vleck-Serber permutation degeneracy method is used to demonstrate that the Heisenberg spin exchange Hamiltonian, –2J ₁₂s₁·s₂, is a good approximate Hamiltonian for the theoretical interpretation of antiferromagnetic and ferromagnetic systems. The approach does not neglect double or higher-order permutations and covers the general case of a singleN-electron configuration as well as that of configuration interaction. An analogy between antiferromagnetic and hydrogen-molecule-like systems is established, and a formula for the estimation of the Heisenberg exchange integral is derived.     

Magnetic Properties of (C5H6N)5[Fe13O4F24(OCH3)12] · CH3OH · 4H2O

The static magnetic susceptibility of Fe(III) complex [Fe₁₃O₄F₂₄(OCH₃)₁₂]^5– was measured in the temperature range 2–300 K. The structure of the complex consists of four triangular Fe₃ fragments interacting with a central Fe atom. By disregarding weak exchange interactions through F bridges, an analytical solution of the exchange Hamiltonian was obtained with Nf 1.3 × 10¹⁰ levels. This made it possible to perform quantitative interpretation of the temperature dependence of the magnetic susceptibility. The obtained exchange parameters of the best approximation are –2J ₁ = 43 cm^–1, –2J ₂ 30 cm^–1. The ratio J ₂/J ₁ 0.70 suggests that the Fe₁₃ ground state has the spin of the ground state 23/2 or 15/2.     

Ab initio calculations of vibronic activity in phosphorescence microwave double resonance spectra of p-dichlorobenzene

The phosphorescence spectrum of p-dichlorobenzene has been calculated using multiconfiguration self-consistent-field wave functions and the quadratic response technique. Attention has been paid to the intensity distribution of the singlet–triplet (³B_1u¹A_g) transition through a number of vibronic subbands. The second order spin–orbit coupling (SOC) contribution to the spin splitting of the ³B_1u (^3*) state is found to be almost negligible, and the calculations therefore provide a good estimate for the zero-field splitting (ZFS) parameters based only on the electron spin–spin coupling expectation values. Nuclear quadrupole resonance constants for the different Cl isotopes are also calculated to accomplish the ZFS assignment. The electric dipole activity of the spin sublevels in the triplet–singlet transitions to the ground-state vibrational levels is estimated by calculations of derivatives using distorted geometries which are shifted from the equilibrium position along different vibrational modes. A vibrational analysis of the phosphorescence spectrum, based on the SOC-induced mixing of the singlet and triplet states calculated along different vibrational modes, provides reasonable agreement with experimental data.Acknowledgment O. R.-P. would like to thank the European MOLPROP network for support. The authors thank Alexander Baev for fruitful discussions. This work was supported by the Swedish Royal Academy of Science (KVA).     

Oxygen reduction in acid media at the amorphous Mo–Os–Se carbonyl cluster coated glassy carbon electrodes

An amorphous Mo–Os–Se carbonyl cluster compound has been synthesized in 1,2-dichlorobenzene (b.p.≈180°C) to be tested as an electrocatalyst for molecular oxygen reduction in 0.5 M H₂SO₄. Scanning electron microscopy (SEM) and high-resolution transmission electron microscopy (HRTEM) performed for the powder supported on pyrolytic carbon show a distribution of nanometer-scale amorphous particles with agglomerations in cluster forms. The catalytic activity was studied by the rotating disc electrode technique. Kinetic studies show a first-order reaction with a Tafel slope of −0.118 V dec⁻¹ and dα/dT=1.55×10⁻³ K⁻¹. In the temperature range 298–343 K, an activation energy of 32 kJ mol⁻¹ was determined.