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 Exchange between Orbitally Degenerate Metal Ions: The Problem of Magnetic Anisotropy

Abstract In this paper we show that a strong magnetic anisotropy appears in exchange mixed–valence clusters containing orbitally degenerate metal ions. Combining an effective Hamiltonian approach with the technique of the irreducible tensor operators (ITO) and pseudoangular momentum representation we have solved the problem of magnetic exchange in localized and delocalized (mixed–valence) systems with different overall symmetries ( D 2 h , D 3 h , D 4 h ). The energy pattern as well as the character of the magnetic anisotropy is closely related to the ground term of the ions, electron transfer pathways, and overall symmetry of the system being affected also by the local crystal fields, spin…

Can the Double Exchange Cause Antiferromagnetic Spin Alignment?

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

Double Exchange in Orbitally Degenerate Mixed Valence Clusters: Magnetic Anisotropy, Vibronic Effects

In this paper we consider the vibronic problem of the double exchange in mixed-valence dimers containing transition metal ions in orbitally degenerate ground states. The vibronic model includes interaction with the breathing local modes (Piepho-Krausz-Schatz-PKS) as well as the modulation of metal-metal distances as suggested by Piepho. The double exchange in orbitally degenerate systems is shown to produce strong magnetic anisotropy of orbital nature. PKS interaction is expected to suppress the magnetic anisotropy of the system, while the intercenter vibrations tend to enhance it. The roles of spin-orbit coupling and temperature are revealed for the systems with different geometries.

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…

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.

SIMPRE: A software package to calculate crystal field parameters, energy levels, and magnetic properties on mononuclear lanthanoid complexes based on charge distributions

This work presents a fortran77 code based on an effective electrostatic model of point charges around a rare earth ion. The program calculates the full set of crystal field parameters, energy levels spectrum, and wave functions, as well as the magnetic properties such as the magnetization, the temperature dependence of the magnetic susceptibility, and the Schottky contribution to the specific heat. It is designed for real systems that need not bear ideal symmetry and it is able to determine the easy axis of magnetization. Its systematic application to different coordination environments allows magneto-structural studies. The package has already been successfully applied to several mononucle…

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.

Magnetic exchange interaction in a pair of orbitally degenerate ions: Magnetic anisotropy of [Ti2Cl9]−3

The theory of the kinetic exchange in a pair of orbitally degenerate ions developed by the authors [J. Phys. Chem. A 102, 200 (1998)] is applied to the case of face-shared bioctahedral dimer (overall D3h-symmetry). The effective kinetic exchange Hamiltonian is found for a 2T2–2T2 system taking into account all relevant transfer pathways and charge-transfer crystal field states. The influence of different transfer integrals involved in the kinetic exchange on the energy pattern and magnetic properties of the system is examined. The role of other related interactions (trigonal crystal field, spin–orbit coupling) is also discussed in detail. Using the pseudoangular momentum representation and …

Rational Design of Single-Ion Magnets and Spin Qubits Based on Mononuclear Lanthanoid Complexes

Here we develop a general approach to calculating the energy spectrum and the wave functions of the low-lying magnetic levels of a lanthanoid ion submitted to the crystal field created by the surrounding ligands. This model allows us to propose general criteria for the rational design of new mononuclear lanthanoid complexes behaving as single-molecule magnets (SMMs) or acting as robust spin qubits. Three typical environments exhibited by these metal complexes are considered, namely, (a) square antiprism, (b) triangular dodecahedron, and (c) trigonal prism. The developed model is used to explain the properties of some representative examples showing these geometries. Key questions in this ar…

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…

Modeling the magnetic properties and Mössbauer spectra of multifunctional magnetic materials obtained by insertion of a spin-crossover Fe(III) complex into bimetallic oxalate-based ferromagnets.

In this article, we present a theoretical microscopic approach to describe the magnetic and spectroscopic behavior of multifunctional hybrid materials which demonstrate spin crossover and ferromagnetic ordering. The low-spin to high-spin transition is considered as a cooperative phenomenon that is driven by the interaction of the electronic shells of the Fe ions with the full symmetric deformation of the local surrounding that is extended over the crystal lattice via the acoustic phonon field. The proposed model is applied to the analysis of the series [Fe(III)(sal2-trien)] [Mn(II)Cr(III)(ox)3]·solv, in short 1·solv, where solv = CH2Cl2, CH2Br2, and CHBr3.

Purely Spectroscopic Determination of the Spin Hamiltonian Parameters in High-Spin Six-Coordinated Cobalt(II) Complexes with Large Zero-Field Splitting.

Accurate determination of the spin Hamiltonian parameters in transition-metal complexes with large zero-field splitting (ZFS) is an actual challenge in studying magnetic and spectroscopic properties of high-spin transition metal complexes. Recent critical papers have convincingly shown that previous determinations of these parameters, based only on the magnetic data, have low accuracy and reliability. A combination of X-band electron paramagnetic resonance (EPR) spectroscopy and SQUID magnetometry seems to be a more convincing and accurate approach. However, even in this case, the accuracy of the determination of the spin Hamiltonian parameters is strongly limited. In this work, we propose …

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…

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 ...

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…

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…

Magnetic Properties of Mixed-Valence Clusters: Theoretical Approaches and Applications

Vibronic Localization of the Electronic Pair in Polynuclear Mixed-Valence Polyoxometalates*

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.

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-…

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.

Kinetic exchange Hamiltonian for orbitally degenerate ions

Abstract A new approach to the problem of the kinetic exchange for orbitally degenerate ions is developed. The highly anisotropic effective Hamiltonian is expressed in terms of unit irreducible tensor operators and spin operators. All parameters of the exchange Hamiltonian are expressed through relevant transfer integrals, crystal field and Racah parameters for the metal ions. As an example the edge-shared ( D 2 h ) bioctahedral cluster is discussed and some comments on the considerations of Anderson, Goodenough and Kanamori and McConnell are given.

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…

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. …

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…

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…