A pseudo-Jahn–Teller model of the photochromic effect in sodium nitroprusside

Abstract A new model for the photochromic effect in sodium nitroprusside Na2[Fe(CN)5(NO)]·2H2O based on the concept of the pseudo-Jahn–Teller effect is proposed. The model takes into account the electron transfer from the Fe2+ ion to the π* orbitals of the NO-ligand as well as the vibronic mixing of three electronic states of the Fe NO fragment through the non-symmetric and full-symmetric modes. The problem is solved within the adiabatic approximation. Under certain conditions the lower sheet of the adiabatic potential is shown to possess three minima with the increasing energies that correspond to the N-bound, sideways bound and O-bound NO group. The barriers between the minima are estimat…

Mixed-Valence Molecular Unit for Quantum Cellular Automata: Beyond the Born-Oppenheimer Paradigm through the Symmetry-Assisted Vibronic Approach.

In this article, we focus on the electron-vibrational problem of the tetrameric mixed-valence (MV) complexes proposed for implementation as four-dot molecular quantum cellular automata (mQCA).1 Although the adiabatic approximation explored in ref 2 is an appropriate tool for the qualitative analysis of the basic characteristics of mQCA, like vibronic trapping of the electrons encoding binary information and cell-cell response, it loses its accuracy providing moderate vibronic coupling and fails in the description of the discrete pattern of the vibronic levels. Therefore, a precise solution of the quantum-mechanical vibronic problem is of primary importance for the evaluation of the shapes o…

Magnetic mixed-valence d2-d1-d1 trimers with partial electron delocalization: vibronic coupling and magnetic properties

Abstract The energy levels and magnetic properties of a triangular mixed-valence cluster d1-d1-d2 with electron delocalization in a pair of sites are examined from a model that takes into account electron transfer, magnetic exchange, and vibronic coupling. We show that the electron transfer process involves besides the usual double-exchange parameter, and additional parameter referred to as exchange transfer. This last parameter accounts for the interaction between the moving electron of the mixed valence pair and the electron localized in the third side. We notice that the role of double exchange is to stabilize a ferromagnetic alignment of the spins on the mixed-valence pair. A comparison…

Can the Double Exchange Cause Antiferromagnetic Spin Alignment?

The effect of the double exchange in a square-planar mixed-valence dn+1&minus

MAGPACK1A package to calculate the energy levels, bulk magnetic properties, and inelastic neutron scattering spectra of high nuclearity spin clusters

Anisotropic double exchange in orbitally degenerate mixed valence systems

Abstract The problem of the double exchange is considered for the mixed valence dimers in which one or both transition metal ions possess orbitally degenerate ground states. In the pseudo-angular momentum representation, the general formula is deduced for the matrix elements of double exchange involving the transfer integrals and all spin and orbital quantum numbers. The pairs 3 T 1 t 2 2 – 2 T 2 t 2 1 and 3 T 1 t 2 2 – 4 A 2 t 2 3 are considered in three high-symmetric topologies: edge-shared D2h, corner-shared D4h, and face-shared D3h bioctahedra. The double exchange in orbitally degenerate systems is shown to produce strong magnetic anisotropy of an orbital nature. The character of the a…

Problem of the magnetic anisotropy in orbitally degenerate exchange and mixed-valence clusters

Abstract This contribution summarizes the results obtained in the problem of orbital degeneracy of the metal ions in exchange coupled and mixed-valence (MV) clusters. The theory of the double exchange is generalized and the orbitally degenerate systems are considered. The orbitally dependent double exchange parameter is deduced for the singlet–triplet and triplet–triplet transition metal pairs in three high-symmetric topologies. A new effective Hamiltonian of the magnetic exchange between the ions with unquenched orbital angular momenta is discussed. The technique of the irreducible tensor operators is applied to the problem of the kinetic exchange in these kind of metal clusters. Strong ma…

Jahn-Teller effect in molecular electronics: quantum cellular automata

The article summarizes the main results of application of the theory of the Jahn-Teller (JT) and pseudo JT effects to the description of molecular quantum dot cellular automata (QCA), a new paradigm of quantum computing. The following issues are discussed: 1) QCA as a new paradigm of quantum computing, principles and advantages; 2) molecular implementation of QCA; 3) role of the JT effect in charge trapping, encoding of binary information in the quantum cell and non-linear cell-cell response; 4) spin-switching in molecular QCA based on mixed-valence cell; 5) intervalence optical absorption in tetrameric molecular mixed-valence cell through the symmetry assisted approach to the multimode/mul…

Mixed-valence molecular four-dot unit for quantum cellular automata: Vibronic self-trapping and cell-cell response

Our interest in this article is prompted by the vibronic problem of charge polarized states in the four-dot molecular quantum cellular automata (mQCA), a paradigm for nanoelectronics, in which binary information is encoded in charge configuration of the mQCA cell. Here, we report the evaluation of the electronic levels and adiabatic potentials of mixed-valence (MV) tetra-ruthenium (2Ru(ii) + 2Ru(iii)) derivatives (assembled as two coupled Creutz-Taube complexes) for which molecular implementations of quantum cellular automata (QCA) was proposed. The cell based on this molecule includes two holes shared among four spinless sites and correspondingly we employ the model which takes into accoun…

Electric Field Control of Spin-Dependent Dissipative Electron Transfer Dynamics in Mixed-Valence Molecules

We demonstrate that the borderline class II/III magnetic MV dimers, which can be referred to as single molecule multiferroics, provide a unique possibility to achieve electric field control of the electron transfer (ET) dynamics. As an example, we consider a MV dimer d2-d1 in which an extra electron is delocalized over two spin-cores (s0 = 1/2), and the ET is spin-dependent due to the double exchange mechanism. It is assumed that the “extra” electron is coupled to the only intramolecular vibration, and a weak coupling to the dissipative subsystem (thermal bath) is taken into account. The vibronic energy levels and the wave functions of the isolated dimer (quantum part of the system) are num…

Self-trapping of charge polarized states in four-dot molecular quantum cellular automata: bi-electronic tetrameric mixed-valence species

Abstract Our interest in this article is prompted by the problem of the vibronic self-trapping of charge polarized states in the four-dot molecular quantum cellular automata (mQCA), a paradigm for nanoelectronics, in which binary information is encoded in charge configuration of the mQCA cell. We report the evaluation of the electronic states and the adiabatic potentials of mixed-valence (MV) systems in which two electrons (or holes) are shared among four sites. These systems are exemplified by the two kinds of tetra–ruthenium (2Ru(II)+ 2Ru(III)) clusters (assembled as two coupled Creutz–Taube dimers) for which molecular implementation of mQCA was proposed. The tetra–ruthenium clusters incl…

ChemInform Abstract: Magnetic Exchange Between Metal Ions with Unquenched Orbital Angular Momenta: Basic Concepts and Relevance to Molecular Magnetism

This review article is a first attempt to give a systematic and comprehensive description (in the framework of the unified theoretical approach) of the exchange interactions in polynuclear systems based on orbitally degenerate metal ions in the context of their relevance to the modern molecular magnetism. Interest in these systems is related to the fundamental problems of magnetism and at the same time steered by a number of impressive potential applications of molecular magnets, like high-density memory storage units, nanoscale qubits, spintronics and photoswitchable devices. In the presence of orbital degeneracy, the conventional spin Hamiltonian (Heisenberg–Dirac–van Vleck model) becomes…

Exchange transfer in high-nuclearity mixed valence magnetic clusters: Theoretical approach and expected manifestations

Abstract We report here a general solution of the exchange transfer problem in the high-nuclearity mixed valence clusters containing arbitrary number of itinerant electrons. The concept of two kinds of exchange transfer, namely kinetic and potential, is introduced by analogy with basic Anderson's mechanisms of the magnetic exchange. The kinetic exchange transfer is treated as a second order transfer process between two centres through the excited state of a third centre. The potential exchange transfer is also considered as a three-centre interaction but in this case only the ground states of the constituent ions are involved. The actual parameters of the exchange transfer are expected to b…

MVPACK: a package to calculate energy levels and magnetic properties of high nuclearity mixed valence clusters.

We present a FORTRAN code based on a new powerful and efficient computational approach to solve the double exchange problem for high-nuclearity MV clusters containing arbitrary number of localized spins and itinerant electrons. We also report some examples in order to show the possibilities of the program.

Insight Into The Spin-Vibronic Problem of a Mixed Valence Magnetic Molecular Cell for Quantum Cellular Automata.

The effects of the vibronic coupling in quantum cellular automata (QCA) based on the square planar mixed valence (MV) molecular cells comprising four paramagnetic centers (spin cores) and two excess mobile electrons are analyzed in the important particular case when the Coulomb energy gap between the ground antipodal diagonal-type two-electron configurations and the excited side-type configurations considerably exceeds both the one-electron transfer parameter (strong U-limit) and the vibronic stabilization energy. Under such conditions the developed model involves the second-order double exchange, the Heisenberg-Dirac-Van Vleck (HDVV) exchange and the vibronic coupling of the excess electro…

Pseudo-Jahn–Teller Origin of the Metastable States in Sodium Nitroprusside

Abstract A new model for the photochromic effect in sodium nitroprusside Na 2 [Fe(CN) 5 (NO)]·2H 2 O based on the concept of the pseudo-Jahn–Teller effect is proposed. The model takes into account the electron transfer from the Fe 2+ ion to the π ∗ orbitals of the NO-ligand as well as the vibronic mixing of three electronic states of the Fe–NO fragment through the non-symmetric and full symmetric modes. The problem is solved within the adiabatic approximation. Under certain conditions, the lower sheet of the adiabatic potential is shown to possess three minima with the increasing energies that correspond to the N-bound, sideways bound, and O-bound NO group. The barriers between the minima a…

Beyond the spin model: exchange coupling in molecular magnets with unquenched orbital angular momenta.

In this critical review we review the problem of exchange interactions in polynuclear metal complexes involving orbitally degenerate metal ions. The key feature of these systems is that, in general, they carry an unquenched orbital angular momentum that manifests itself in all their magnetic properties. Thus, interest in degenerate systems involves fundamental problems related to basic models in magnetism. In particular, the conventional Heisenberg-Dirac-Van Vleck model becomes inapplicable even as an approximation. In the first part we attempt to answer two key questions, namely which theoretical tools are to be used in the case of degeneracy, and how these tools can be employed. We demons…

A general approach for the calculation of the energy levels and the inelastic neutron scattering cross-section of highly nuclear magnetic clusters

Abstract We develop here a general approach to calculate in an efficient way the spin levels as well as the spin eigenfunctions and the INS intensities of clusters formed by large numbers of exchange-coupled magnetic metal ions. The approach is based on the successive use of the irreducible tensor operator techniques and takes into account all kinds of magnetic exchange interactions between the metal ions. The potentialities of this approach are illustrated from an example comprising nine exchange-coupled Ni (II) ions.

VIBPACK: A package to treat multidimensional electron-vibrational molecular problems with application to magnetic and optical properties

We present a FORTRAN code based on a new powerful and efficient computational approach to solve multidimensional dynamic Jahn-Teller and pseudo Jahn-Teller problems. This symmetry-assisted approach constituting a theoretical core of the program is based on the full exploration of the point symmetry of the electronic and vibrational states. We also report some selected examples of increasing complexity aimed to display the theoretical background as well as the advantages and capabilities of the program to evaluate of the energy pattern, magnetic and optical properties of large multimode vibronic systems. © 2018 Wiley Periodicals, Inc.

Localization vs. Delocalization in Molecules and Clusters: Electronic and Vibronic Interactions in Mixed Valence Systems

The interplay between electron delocalization and magnetic interactions play a key role in areas as diverse as solid state chemistry (bulk magnetic materials, superconductors,...) [1] and biology (iron-sulfur proteins, manganese-oxo clusters ...) [2]. In molecular inorganic chemistry these two electronic processes have been traditionally studied independently. Thus, the electron dynamics has been extensively investigated in mixedvalence dimers [3] as exemplified by the Creutz-Taube complex [(NH3)5RuII(pyrazine)RuIII(NH3)5]. In this kind of molecular complexes one extra electron is delocalized over two diamagnetic metal sites. Therefore, they constitute model systems for the study of the ele…

Localisation vs. delocalisation in the dimeric mixed-valence clusters in the generalised vibronic model. Magnetic manifestations

Abstract The problem of localisation–delocalisation in the dimeric mixed-valence clusters is considered in the framework of the generalised vibronic model. The model takes into account both the local vibrations on the metal sites (Piepho–Krausz–Schatz model) and the multicenter (molecular) vibrations changing the intermetallic distances (as suggested by Piepho). In the framework of the semiclassical adiabatic approach the potential surfaces are analysed and different kinds of localised and delocalised states are found. On the basis of the calculated degrees of the localisation the conventional Robin and Day classification of mixed-valence compounds is reconsidered in view of the generalised…

Spin Switching in Molecular Quantum Cellular Automata Based on Mixed-Valence Tetrameric Units

In this article we focus on the study of spin effects in a single square-planar mixed-valence cell comprising two electrons and in coupled molecular cells for quantum cellular automata. Using the vibronic model we demonstrate that the polarizabilities of the cell are different in spin-singlet and spin-triplet states of the electronic pair. Based on this inference the concept of spin switching in molecular quantum cellular automata is proposed, and the conditions under which this effect is feasible are derived. In order to reveal these conditions we have performed a series of quantum-mechanical calculations of the vibronic energy levels of the isolated cell and of the cell subjected to the e…

High-Nuclearity Magnetic Clusters: Generalized Spin Hamiltonian and Its Use for the Calculation of the Energy Levels, Bulk Magnetic Properties, and Inelastic Neutron Scattering Spectra

A general solution of the exchange problem in the high-nuclearity spin clusters (HNSC) containing arbitrary number of exchange-coupled centers and topology is developed. All constituent magnetic centers are supposed to possess well-isolated orbitally non-degenerate ground states so that the isotropic Heisenberg-Dirac-Van Vleck (HDVV) term is the leading part of the exchange spin Hamiltonian. Along with the HDVV term, we consider higher-order isotropic exchange terms (biquadratic exchange), as well as the anisotropic terms (anisotropic and antisymmetric exchange interactions and local single-ion anisotropies). All these terms are expressed as irreducible tensor operators (ITO). This allows u…

Coherent Spin Dependent Landau-Zener Tunneling in Mixed Valence Dimers

In this contribution we introduce the concept of single molecule ferroelectric based on the vibronic pseudo Jahn-Teller model of mixed valence dimeric clusters belonging to the Robin and Day class II compounds. We elucidate the main factors controlling the nonadiabatic Landau-Zener tunneling between the low lying vibronic levels induced by a pulse of the electric field. The transition probabilities are shown to be dependent on the both time of the pulse and the total spin of the cluster. A possibility to control the spin-dependent Landau-Zener tunneling by applying a static magnetic field is discussed.

Modelling the properties of magnetic clusters with complex structures: how symmetry can help us

The purpose of this article is to answer the question of how symmetry helps us to investigate and understand the properties of nanoscopic magnetic clusters with complex structures. The systems of choice will be the three types of polyoxometalates (POMs): (1) POMs containing localised spins; (2) reduced mixed-valence (MV) POMs; (3) partially delocalised POMs in which localised and delocalised subunits coexist and interact. The theoretical tools based on various kinds of symmetry are the following: (1) irreducible tensor operator (ITO) approach based on the so-called 'spin-symmetry' and MAGPACK program; (2) group-theoretical assignment of the exchange multiplets based on spin- and point symme…

Magnetic Exchange between Orbitally Degenerate Ions:  A New Development for the Effective Hamiltonian

A new approach to the problem of the kinetic exchange for orbitally degenerate ions is developed. The constituent multielectron metal ions are assumed to be octahedrally coordinated, and strong crystal field scheme is employed, making it possible to take full advantage from the symmetry properties of the fermionic operators and collective electronic states. In the framework of the microscopic approach, the highly anisotropic effective Hamiltonian of the kinetic exchange is constructed in terms of spin operators and standard orbital operators (matrices of the unit cubic irreducible tensors). As distinguished from previous considerations, the effective Hamiltonian is derived for a most genera…

High nuclearity mixed-valence magnetic clusters: theoretical study of the spin coupling in the C602− fulleride ion

Abstract The problem of delocalization of a pair of electrons over the fullerene C 60 is considered, with the aim of elucidating the nature of the ground spin state, as well as the structure of the low-lying energy levels in this mixed-valence molecule C 60 2− . A model that considers the Coulomb interactions between the two extra electrons, as well as the two single-electron transfer processes involved in the electron delocalization, is developed. The influence of these electronic parameters on the spectrum of the low-lying energy levels is discussed. We find that the ground state is always a spin singlet, whatever the relative values of these parameters are.

Electric Field Control of Spin States in Trigonal Two-Electron Quantum Dot Arrays and Mixed-Valence Molecules: II. Vibronic Problem

In this article, the vibronic model for an electric field switchable mixed-valence trimer containing two delocalized electrons or holes is proposed and examined. The role of the vibronic coupling on the electric field effects is analyzed by means of the semiclassical adiabatic approach and, alternatively, with the aid of the numerical analysis of the Schrodinger equation with due allowance for the kinetic energy of the ions (dynamic problem). The adiabatic potential landscapes have been calculated by taking into account the influence of the electric field. As the adiabatic approximation has a limited frame of validity, the study of the electric field effects has also been performed within m…

Localization–Delocalization in Bridged Mixed-Valence Metal Clusters: Vibronic PKS Model Revisited

Here we describe a new vibronic model of mixed valence (MV) dimer inspired by the conventional Piepho, Krausz, and Schatz (PKS) approach. We attempted to partially lift the main restriction of the PKS model dealing with the vibronically independent moieties of a MV molecule. The refined version of the PKS model in which the bridging ligands are included deals with the three main interactions: electron transfer (integral t0) related to the high-symmetric ligand configuration, on-site vibronic coupling (parameter υ) arising from the modulation of the crystal field on the metal sites by the breathing displacements of their nearest ligand surroundings, and intercenter vibronic coupling (paramet…

Manipulation of the spin in single molecule magnets via Landau-Zener transitions

We theoretically investigate the effects of a magnetic pulse on a single-molecule magnet (SMM) initially magnetized by a dc field along the easy axis of magnetization. In the Landau\char21{}Zener (LZ) scheme, it is shown that the final spin state is a function of the shape and duration of the pulse, conditioned by the decoherence time of the SMM. In the case of coherent tunneling, the asymmetric pulses are shown to reverse the direction of the magnetization, while the symmetric pulses can only decrease the value of the initial magnetization. It is also demonstrated that the application of an external variable dc field in the hard plane of magnetization provides the possibility to tune the r…

Electric field control of the spin state in mixed-valence magnetic molecules.

Multiferroic molecules for spintronics: In a many-electron mixed-valence dimer with dominant double exchange, as compared with antiferromagnetic superexchange, the electric field is shown to induce a spin crossover from the ferromagnetic spin state to the antiferromagnetic one. This leads to a sharp decrease in the magnetic moment of the molecule and a simultaneous stepwise increase in the electric dipole (see figure).

Mixed-Valence Magnetic Molecular Cell for Quantum Cellular Automata: Prospects of Designing Multifunctional Devices through Exploration of Double Exchange

In this article, we propose to use multielectron square-planar mixed-valence (MV) molecules as molecular cells for quantum cellular automata (QCA) devices. As distinguished from previous proposals ...

Semiclassical approximation in the magnetic problem of exchange-coupled mixed valence clusters

Abstract The frameworks of the applicability of the semiclassical adiabatic approach suggested by Borras-Almenar, Coronado and Tsukerblat to the magnetic problem of mixed valence clusters are considered in a model taking into account magnetic exchange, double exchange and vibronic interaction. The results for the quantum-mechanical and semicalssical calculation of the temperature-variable magnetic moments are compared with those within the scope of the semiclassical approximation for the dimeric d 1 —d 2 clusters and trimeric d 1 —d 1 —d 2 systems with partial delocalization over a pair of ions. The semiclassical approach describes with high accuracy the temperature dependencies of the magn…

Exchange Interactions I: Mechanisms

A most important phenomenon in molecular magnetism is the exchange interaction between magnetic centers. Its relevance as well as the terms and concepts required to its rationalization were stated long ago by physicists working in the quantum-mechanical theory of magnetism (Heisenberg, Dirac, van Vleck, Anderson, Zener, and many others). Depending on the extent of delocalization of the magnetic moments and on the metallic/non-metallic properties of the solid four kinds of exchange coupling were usually distinguished in the physical literature namely direct exchange, superexchange, indirect exchange and itinerant exchange [1]. The relations of these types of couplings are depicted in Figure …

Electrically switchable magnetic exchange in the vibronic model of linear mixed valence triferrocenium complex

In this article, we report our development of a vibronic model for the electric-field control of antiferromagnetic superexchange in the mixed-valence (MV) triferrocenium complex FeIII-FeII-FeIII proposed as a possible candidate for the molecular implementation of a quantum logic gate. Along with the electronic interactions, such as electron transfer between the iron ions in different oxidation degrees and Coulomb repulsion of the extra holes, the proposed model of the triferrocenium complex also takes into account the vibronic coupling as an inherent ingredient of the problem of mixed valency. The latter is described by the conventional Piepho-Krauzs-Shatz (PKS) model adapted to the linear …

Electric field controllable magnetic coupling of localized spins mediated by itinerant electrons: a toy model

In this paper, we propose a toy model to describe the magnetic coupling between the localized spins mediated by the itinerant electron in partially delocalized mixed-valence (MV) systems. This minimal model takes into account the key interactions that are common for all such systems, namely, electron transfer in the valence-delocalized moiety and magnetic exchange between the localized spins and the delocalized electrons. The proposed descriptive model is exactly solvable which allows us to qualitatively and quantitatively discuss the main features of the whole class of partially delocalized MV systems. In the case of relatively strong exchange coupling, the combined action of these two int…

Mixed-valence polyoxometalate clusters. III. Vibronic problem for the 2-electron reduced heteropoly blue with the Keggin structure

Abstract A general approach to the vibronic problem of delocalized electronic pairs in mixed-valence compounds is developed and applied to understand the ways of electron delocalization in dodecanuclear polyoxometalate clusters containing two moving electrons. The interplay between electronic and vibronic interactions is examined. The electronic spectrum is shown to consist of two spin triplets 3 T 1 and 3 T 2 and three spin singlets 1 A 1 , 1 E and 1 T 2 levels determined by the double-transfer processes (parameter P ). Jahn-Teller and pseudo-Jahn-Teller problems ( 3 T 1 + 3 T 2 ) ⊗ ( e + t 2 ) and ( 1 A 1 + 1 E + 1 T 2 ) ⊗ ( e + t 2 ) have been considered in the framework of the Piepho-Kr…

Vibronic Model for Intercommunication of Localized Spins via Itinerant Electron

In this article, we propose a vibronic pseudo Jahn–Teller model for partially delocalized mixed-valence molecules aimed to describe the magnetic coupling between the localized spins mediated by the delocalized electron. The simplest partially delocalized system that retains the main studied features is assumed to consist of a one-electron mixed-valence dimer, which is connected to the two terminal magnetic ions. The model involves the following key interactions: electron transfer in the spin-delocalized subsystem of a mixed-valence molecule, which is mimicked by a dimeric unit, coupling of the itinerant electrons with the molecular vibrations, and isotropic magnetic exchange between the loc…

Mixed-valence polyoxometalate clusters. II. Delocalization of electronic pairs in 18-site heteropoly blues with Wells-Dawson structure

Abstract The problem of delocalization of two electrons in the 18-site Wells-Dawson polyoxometalate is examined from a general approach that takes into account both single- and double-transfer processes, as well as the Coulomb interactions between the two delocalized electrons. The electronic energy levels of this mixed-valence cluster are calculated and the conditions giving rise to the stabilization of a singlet ground spin state for the electronic pair are elucidated. It is shown that the spin pairing results from the simultaneous effects of single- and double-electron transfer processes, which are operative even when the two delocalized electrons are fairly widely separated in the Wells…

Electric field control of the optical properties in magnetic mixed-valence molecules

We propose the use of an electric field stimulus to strongly affect the optical properties of ferromagnetic mixed-valence (MV) dimers. This proposal is based on the prediction of an anomalous Stark effect in the intervalence absorption bands of these multi-electron MV systems. As distinguished from the conventional Stark effect observed in one-electron dimers, a strong change of the intervalence bands accompanies the crossing of the different spin levels caused by the application of an electric field. This new effect can be referred to as giant spin-dependent Stark effect. In spintronics this opens up the possibility for optical detection of the spin state in these magnetic molecules.

Magnetic exchange interaction in clusters of orbitally degenerate ions. II. Application of the irreducible tensor operator technique

Abstract The irreducible tensor operator technique in R3 group is applied to the problem of kinetic exchange between transition metal ions possessing orbitally degenerate ground states in the local octahedral surrounding. Along with the effective exchange Hamiltonian, the related interactions (low-symmetry crystal field terms, Coulomb interaction between unfilled electronic shells, spin–orbit coupling and Zeeman interaction) are also taken into account within a unified computational scheme. Extension of this approach to high-nuclearity systems consisting of transition metal ions in the orbital triplet ground states is also demonstrated. As illustrative examples, the corner-shared D4h dimers…

Electronic and vibronic problems of nanosized mixed valence clusters: Advances and challenges

Here we discuss the electronic and vibronic problems of mixed valency (MV) in molecular clusters which are of current interest in areas as diverse as solid-state chemistry, biochemistry, and molecular magnetism. Modern research in these areas is focused on the nanosized clusters at the border between classical and quantum scales and for this reason they are particularly difficult to study. First, we describe a general approach to the evaluation of the energy pattern of MV systems containing arbitrary number of localized spins and itinerant electrons with due account for the double exchange and other relevant interactions, like interelectronic Coulomb repulsion in instantly localized configu…

Toward multifunctional molecular cells for quantum cellular automata: exploitation of interconnected charge and spin degrees of freedom

We discuss the possibility of using mixed-valence (MV) dimers comprising paramagnetic metal ions as molecular cells for quantum cellular automata (QCA). Thus, we propose to combine the underlying idea behind the functionality of QCA of using the charge distributions to encode binary information with the additional functional options provided by the spin degrees of freedom. The multifunctional ('smart') cell is supposed to consist of multielectron MV d(n)-d(n+1)-type (1 ≤ n ≤ 8) dimers of transition metal ions as building blocks for composing bi-dimeric square planar cells for QCA. The theoretical model of such a cell involves the double exchange (DE), Heisenberg-Dirac-Van Vleck (HDVV) excha…

A symmetry adapted approach to the dynamic Jahn-Teller problem: Application to mixed-valence polyoxometalate clusters with keggin structure

In this article, we present a symmetry-adapted approach aimed to the accurate solution of the dynamic vibronic problem in large scale Jahn-Teller (JT) systems. The algorithm for the solution of the eigen-problem takes full advantage of the point symmetry arguments. The system under consideration is supposed to consist of a set of electronic levels mixed by the active JT and pseudo JT vibrational modes. Applying the successive coupling of the bosonic creation operators, we introduce the irreducible tensors that are called multivibronic operators. Action of the irreducible multivibronic operators on the vacuum state creates the vibrational symmetry adapted basis that is subjected to the Gram-…

Mixed-valence polyoxometalate clusters. I. Delocalization of electronic pairs in dodecanuclear heteropoly blues with keggin structure

Abstract The problem of delocalization of a pair of electrons over dodecanuclear polyoxometalate clusters with the Keggin structure is considered with the aim of explaining the spin pairing in these multi-nuclear mixed-valence systems. A general approach that considers the Coulomb interactions between the two delocalized electrons, as well as the single and double electron transfer processes which can be operative in delocalization of the electronic pairs is developed. The new approach is based on the site-symmetry concept which makes possible a group theoretical classification for the delocalized states of electronic pairs. This procedure proves to be very efficient in the calculation of t…

Magnetic exchange between metal ions with unquenched orbital angular momenta: basic concepts and relevance to molecular magnetism

This review article is a first attempt to give a systematic and comprehensive description (in the framework of the unified theoretical approach) of the exchange interactions in polynuclear systems based on orbitally degenerate metal ions in the context of their relevance to the modern molecular magnetism. Interest in these systems is related to the fundamental problems of magnetism and at the same time steered by a number of impressive potential applications of molecular magnets, like high-density memory storage units, nanoscale qubits, spintronics and photoswitchable devices. In the presence of orbital degeneracy, the conventional spin Hamiltonian (Heisenberg–Dirac–van Vleck model) becomes…

Quantum Cellular Automata: a Short Overview of Molecular Problem

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Coherent Manipulation of Polarization in Mixed-Valence Compounds by Electric Pulse via Landau–Zener Transitions

In this contribution, we predict and theoretically investigate the effects of the electric field pulse in mixed valence (MV) dimers. These systems exhibit bistability with a large internal dipole moment mediated by the itinerant electron trapped by the vibronic coupling. In this sense, they are similar to single molecular magnets (SMMs) that are bistable systems possessing large long-living magnetization and exhibiting Landau−Zener (LZ) transitions. We propose a scheme for a controllable LZ tunnelling in MV systems that provides also a possibility to control the dipole moment of a dimeric MV unit. It is supposed that the static electric field initially polarizes the system, and then the uni…

Exploration of the double exchange in quantum cellular automata: proposal for a new class of cells

In this communication we propose to considerably extend the class of systems suitable as cells for quantum cellular automata by including magnetic quantum dots and molecular mixed valence dimers exhibiting double exchange. As distinguished from the previous works we propose to use not only charges as the information carriers but also spin degrees of freedom. In this context we focus on the two key points: (1) properties of the magnetic cell as reservoir for charges carrying binary information, and (2) identification of conditions under which spin degrees of freedom can be employed.

A Symmetry Adapted Approach to the Dynamic Jahn-Teller Problem

In this article we present a symmetry-adapted approach aimed to the accurate solution of the dynamic Jahn-Teller (JT) problem. The algorithm for the solution of the eigen-problem takes full advantage of the point symmetry arguments. The system under consideration is supposed to consist of a set of electronic levels \({\Gamma }_{1},{\Gamma }_{2}\ldots {\Gamma }_{n}\) labeled by the irreducible representations (irreps) of the actual point group, mixed by the active JT and pseudo JT vibrational modes \({\Gamma }_{1},{\Gamma }_{2}\ldots {\Gamma }_{f}\) (vibrational irreps). The bosonic creation operators b +(Γγ) are transformed as components γ of the vibrational irrep Γ. The first excited vibra…

Exchange-transfer in mixed-valence clusters with one migrating hole

Abstract A new mechanism for exchange-transfer specific to hole-type mixed-valence clusters is proposed. The intermediate state in the second-order exchange-transfer process is achieved by the jump of the electron from the spin-core of the dn+1 ion into the empty orbital of the dn ion. As distinguished from the mixed-valence clusters with one delocalized electron this intermediate state is the high-spin one giving rise to a ferromagnetic contribution to the ground manifold. On the basis of angular momentum theory a general solution of the exchange-transfer problem is given for arbitrary nuclearity mixed-valence hole-type clusters with many-electron paramagnetic spin-cores. The interplay bet…

Molecular analog of multiferroics: Electric and magnetic field effects in many-electron mixed-valence dimers

We show here that mixed-valence (MV) magnetic molecules with a significant electron delocalization are extremely sensitive to an external electric field. In particular, we focus on the symmetric many-electron MV binuclear complexes that are on the borderline between Robin and Day classes II and III. In these molecules, the double-exchange, which has been shown to lead to the ferromagnetic ground spin state, competes with the electric field, which tends to localize the spin, thus creating an electric dipole and stabilizing the spin states with lower multiplicities. This provides an efficient and easy way to control the ground spin state of the molecule through the double-exchange mechanism. …

Magnetic exchange interaction in clusters of orbitally degenerate ions. I. Effective Hamiltonian

Abstract A new effective Hamiltonian is reported for the kinetic exchange between two arbitrary terms 2S A +1 Λ A and 2S B +1 Λ B that can be ground or excited in octahedrally coordinated transition metal ions. This Hamiltonian is applicable to both homo- and heterometallic clusters. For the homonuclear cluster the resonance part of the effective Hamiltonian is also presented for the case when one of the ions is excited. The operator part of the exchange Hamiltonian contains symmetry adapted products of the cubic irreducible tensors acting in orbital spaces ΛA and ΛB and scalar product of site spin operators. The parameters of the Hamiltonian are defined by the relevant intercenter transfer…

Exchange Interactions II: Spin Hamiltonians

In Part I the physical mechanism of exchange interactions have been discussed. In this part we introduce the general concept of spin-hamiltonian. Isotropic exchange hamiltonian for many-electron polynuclear clusters (Heisenberg-Dirac-van Vleck-HDVV model [1-6]) will be derived. Spin-hamiltonian approach allows to separate the full exchange problem into two independent ones: 1) evaluation of the energy levels of the exchange system considering Jij as a set of semiempirical parameters, and 2) quantum mechanical calculation of exchange parameters with the aim of elucidation of the main physical mechanisms of the exchange coupling. In this part we shall focus on the problem of calculation of sp…

Electric Field Generation and Control of Bipartite Quantum Entanglement between Electronic Spins in Mixed Valence Polyoxovanadate [GeV14O40]8–

As part of the search for systems in which control of quantum entanglement can be achieved, here we consider the paramagnetic mixed valence polyoxometalate K2Na6[GeV14O40]·10H2O in which two electrons are delocalized over the 14 vanadium ions. Applying a homogeneous electric field can induce an antiferromagnetic coupling between the two delocalized electronic spins that behave independently in the absence of the field. On the basis of the proposed theoretical model, we show that the external field can be used to generate controllable quantum entanglement between the two electronic spins traveling over a vanadium network of mixed valence polyoxoanion [GeV14O40]8–. Within a simplified two-lev…

Orbitally dependent kinetic exchange in cobalt(II) pairs: origin of the magnetic anisotropy

Abstract A comprehensive theoretical study of the magnetic exchange between Co 2+ ions is reported. Using the microscopic background we deduce the general Hamiltonian for a corner-shared bioctahedral system involving kinetic exchange, spin–orbit coupling and low-symmetry local crystal field. This Hamiltonian acting within orbitally degenerate ground manifold 4 ( T 1g ) A ⊗ 4 ( T 1g ) B of the cobalt pair is expressed in terms of orbital and spin operators. We elucidate the major electronic factors controlling the exchange anisotropy in the Co(II) pairs. The degree of the magnetic anisotropy is shown to depend on the strength of the cubic crystal field and on the relative efficiency of two k…

Vibronic recovering of functionality of quantum cellular automata based on bi-dimeric square cells with violated condition of strong Coulomb repulsion.

Strong Coulomb repulsion between the two charges in a square planar mixed-valence cell in quantum cellular automata (QCA) allows us to encode the binary information in the two energetically beneficial diagonal distributions of the electronic density. In this article, we pose a question: to what extent is this condition obligatory for the design of the molecular cell? To answer this question, we examine the ability to use a square-planar cell composed of one-electron mixed valence dimers to function in QCA in a general case when the intracell Coulomb interaction U is not supposed to be extremely strong, which means that it is comparable with the characteristic electron transfer energy (viol…