Theoretical insight into clocking in a molecular mixed-valence cell of quantum cellular automata through the vibronic approach.

In this article, we develop a vibronic theory of clocking in molecular quantum cellular automata (QCA). The clocking mechanism is considered for a trigonal trimeric mixed-valence (MV) system with one mobile electron, which is shown to act as the dimeric unit encoding binary information (Boolean states 0 or 1) coupled to a third redox center (Null state). The model includes the electron transfer between the three centers; vibronic coupling of the mobile charge with the "breathing" modes, forming a double degenerate Jahn-Teller vibration of the molecular triangle; and two electric fields, one collinear to the dimeric unit, which controls the binary states, and the other perpendicular to this unit, performing clocking. In the framework of the adiabatic approximation, the potential surface of the trimeric system has been studied and the condition determining switching and clocking has been analyzed in terms of the two controlling fields and the vibronic and transfer parameters. A thorough understanding of the site populations is achieved through the quantum-mechanical solution of the vibronic problem, maintaining the adiabatic condition for the controlling fields. It is shown that a MV trimer can act as a molecular clocked QCA cell, with favorable conditions being a positive electron transfer parameter and sufficiently strong vibronic coupling.

Dimeric vs bidimeric cells for molecular quantum cellular automata composed of oxidized norbornadiene and its polycyclic derivatives.

Quantum Dot Cellular Automata (QCA) is an emerging trend in the field of nanoelectronics, and computing can be regarded as an alternative to the traditional complementary metal-oxide-semiconductor technology. The paper is devoted to the study of the key functional properties of the cells for molecular QCA based on mixed valence molecules. The theoretical results for the heat dissipation under the conditions of the fast nonadiabatic switching event and cell-cell response function are obtained in the framework of the quantum-mechanical vibronic approach. These results are parameterized using the previous reliable ab initio calculations performed for oxidized norbornadiene and its polycyclic derivatives with variable lengths of the bridge. The comparative analysis of the dimeric and bidimeric molecular cells composed of these compounds is given. It is underlined that the conditions of a strong non-linear response and a low heat release are contradictory. However, despite this problem, a parametric regime is proposed, which provides a low heat release in combination with a strong nonlinear response of the working cell to the electric field induced by the polarized driver cell.

In the quest for an optimal parametric regime of nonadiabatic switching ensuring low heat release in conjunction with high polarizability of mixed-valence molecular dimers.

The effects of electronic and vibronic interactions on the specific heat release occurring in the course of nonadiabatic switching of the electric field polarizing a one-electron mixed-valence dimer is analyzed within the framework of the Piepho-Krausz-Schatz vibronic model. The search for an optimal parametric regime from the point of view of minimizing heat release is carried out taking into account the requirement to maintain a strong nonlinear response of the dimer to the applied electric field. Calculations of the specific heat release and the response performed in the framework of the quantum mechanical vibronic approach show that although the heat release is minimal under a weak electric field acting on the dimer in combination with weak vibronic coupling and/or strong electron transfer, such a combination of the parameters is incompatible with the requirement of a strong nonlinear response. Unlike this, for molecules exhibiting strong vibronic interactions and/or weak transfer, a rather strong nonlinear response can be obtained even with a very weak electric field, which, in turn, ensures low heat release. Thus, we can conclude that an efficient strategy to improve characteristics of molecular quantum cellular automata devices or other molecular switchable devices based on mixed-valence dimers consists in usage of molecules subjected to the action of a weak polarizing field, which are characterized by strong vibronic coupling and/or weak transfer.

Polaronic Mechanism of Vibronic Localization in Mixed-Valence Cation Radicals with a Non-Conjugated Chromophore on the Bridge.

In quest of a controllable intramolecular electron transfer (ET) across a bridge, we study the cation-radical form of the parent 1,4-diallyl-butane (I) and its derivatives (II)-(VI). In these mixed-valence (MV) compounds, the bridge of variable length connecting allyl redox sites can be either saturated (-CH2 CH2-) (I, III, and V) or unsaturated, modified by the π-spacer (-HC═CH-) (II, IV, and VI). Ab initio calculations for the charge delocalized transition structure and for fully optimized localized form of 1,ω-diallyl cation radicals I-VI allowed us to estimate the potential barriers for ET between the terminal allyl groups, vibronic coupling, and ET parameters. The ET barrier in all compounds with the π-fragment on the bridge is shown to be higher with respect to that in the systems with a saturated bridge. We propose a model based on the concept of a specific polaronic effect of the spacer. Charge localization at an allyl group creates an electric field polarizing the π-fragment and the bridge as a whole. The induced dipole moment interacts with the localized charge giving rise to the additional vibronic stabilization in a self-consistent manner without an appreciable change of localized charge. Utilization of this spacer-driven polaronic effect is expected to provide a route to a controllable ET in bridged MV compounds.

Mixed-Valence Bridged Norbornylogous Compounds as Switchable Cells for Molecular Quantum Cellular Automata: A Compromise between High Polarizability and Low Power Dissipation.

In this article, we analyze power dissipation in the nonadiabatic switching event in mixed-valence (MV) molecular cells of quantum cellular automata (QCA) in combination with a key functional property of cells such as polarizability in the applied electric field. We demonstrate that although the requirements for a strong nonlinear response of the cell to the applied electric field and low heat release are competing from the point of view of molecular parameters, this by no means can be regarded as an insurmountable obstacle for achieving functional advantages and possibility of practical application of QCA. The general theoretical consideration is applied to the series of MV compounds exemplifying electric field-switchable MV molecules, which include oxidized norbornadiene [C7H8]+ (I) and its polycyclic derivatives [C12H12]+ (II), [C17H16]+, (III), [C27H24]+ (IV), and [C32H28]+ (V). Based on the results of high-level ab initio calculations performed for the series of compounds with variable length of the bridge connecting redox groups, we show that strongly localized cation radicals with long bridges can be easily polarized even by a fairly weak electric field. This ensures quite low power dissipation, which is shown to coexist with a rather strong nonlinear cell-cell response. We thus conclude that consideration of the series of MV dimers with controllable electron transfer provides a reasonable way to design molecule-based QCA cells with the required properties.

Spin polarization effects in trigonal mixed-valence complexes exhibiting double exchange supported by external spin-cores.

The theory of the magnetic coupling between the localized spins, mediated by the mobile excess electron, is generalized to the case of a trigonal, six-center, four-electron molecule with partial valence delocalization. The combination of the electron transfer occurring within the valence-delocalized subsystem and the interatomic exchange producing coupling of the spin of the mobile electron of valence-delocalized fragment with the three localized spins forming the valence-localized subsystem leads to the appearance of a special kind of double exchange (DE), termed the "external core double exchange" (ECDE), in order to distinguish such DE from the conventional "internal core double exchange" for which the mobile electron is coupled with the spin-cores on the same center via the intra-atomic exchange. The effect of the ECDE on the ground spin state of the considered trigonal molecule is compared with earlier reported effect produced by DE in the four-electron, mixed-valence (MV) trimer. A high diversity of the ground spin states is revealed, depending on the relative magnitudes and signs of the electron transfer and interatomic exchange parameters, with part of these states not appearing to be the ground states in a trigonal trimer exhibiting DE. We briefly discuss some examples of trigonal MV systems from the point of view of the possibility to have different combinations of signs of the transfer and exchange parameters and, accordingly, different ground spin states. The tentative role of the considered systems in molecular electronics and spintronics is also noticed.

Controllable Electron Transfer in Mixed-Valence Bridged Norbornylogous Compounds: Ab Initio Calculation Combined with a Parametric Model and Through-Bond and Through-Space Interpretation.

In the context of a computationally guided approach to the controllable electron transfer in mixed-valence (MV) systems, in this article, we study the electron transfer (ET) in the series of oxidized norbornadiene C7H8 (I) and its polycyclic derivatives, C12H12 (II), C17H16, (III), C27H24 (IV), and C32H28 (V), with variable lengths of the bridge connecting redox sites. The work combines an ab initio CASSCF evaluation of the electronic structure of systems I-V with the parametric description in the framework of the biorbital two-mode vibronic model. The model involves coupling with the "breathing" mode and intercenter vibration modulating the distances between the redox fragments. The ab initio calculations were performed for two types of optimized structures of I-V: (a) charge-localized global minimum (Cs) and (b) symmetric configuration (C2v) with the delocalized charge. This allows one to estimate the potential barrier separating charge-localized configurations as well as vibronic coupling parameters and the electron transfer integral. Along with the adiabatic approach, the quantum-mechanical analysis of the vibronic levels has been applied to precisely estimate the quantum effect of tunneling splitting. We estimate the "through-space" and "through-bond" contributions to the parameters interrelated with the charge transfer (CT). The through-space effect proves to be a major factor of ET at a short distance between the redox centers, whereas the through-bond contribution is dominant at a long distance. Vibronic coupling under the condition of through-space ET leads to the localization of the positive charge on the π-chromophore, while the through-bond component of ET results in compensating σ-shifts and subsequent charge delocalization over the bridge. The limitations of the parametric approach were discussed in the context of the two components contributing to the ET. Particularly, the bridge polarization in the course of through-bond ET proves to be beyond the basis of the employed parametric model.

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 (violated strong U limit). Using the two-mode vibronic model treated within the semiclassical (adiabatic) and quantum-mechanical approaches, we demonstrate that strong vibronic coupling is able to create a considerable barrier between the two diagonal-type charge configurations, thus ensuring bistability and polarizability of the cells even if the Coulomb barrier is not sufficient. The cases of weak and moderate Coulomb repulsion and strong vibronic coupling are exemplified by consideration of the cation radicals of the two polycyclic derivatives of norbornadiene [C12H12]+ and [C17H16]+ with the terminal C=C chromophores playing the role of redox sites. By using the detailed ab initio data, we reveal the main characteristics of the bi-dimeric cells composed of these molecules and illustrate the pronounced effect of the vibronic recovery clearly manifesting itself in the shape of the cell-cell response function. Revealing such "vibronic recovery" of strong localization when the strong U limit is violated suggests a way to a significant expansion of the class of molecular systems suitable as QCA cells.

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 electrons with the molecular B1g -vibration composed of four full-symmetric local vibrations. The latter interaction is shown to significant amplify the ability of the electric field produced by the driver-cell to polarize the excess electrons in the working cell, which can be termed "the effect of the vibronic enhancement of the cell-cell interaction". This effect leads to a redetermination of the conditions for switching between different spin-states, as well as to a significant change in the shapes of the cell-cell response functions. The obtained results demonstrate the importance of the vibronic coupling in all aspects (such as description of a free cell and cell-cell response) of the theory of molecular QCA based on MV clusters.

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 dn-dn+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) exchange, Coulomb repulsion between the two excess electrons belonging to different dimeric half-cells and also the vibronic coupling. Consideration is focused on the topical case in which the difference in Coulomb energies of the two excess electrons occupying nearest neighboring and distant positions significantly exceeds both the electron transfer integral and the vibronic energy. In this case the ground spin-state of the isolated square cell is shown to be the result of competition of the second-order DE producing a ferromagnetic effect and the HDVV exchange that is assumed to be antiferromagnetic. In order to reveal the functionality of the magnetic cells, the cell-cell response function is studied within the developed model. The interaction of the working cell with the polarized driver-cell is shown to produce an antiferromagnetic effect tending to suppress the ferromagnetic second-order DE. As a result, under some conditions the electric field of the driver cell is shown to force the working cell to exhibit spin-switching from the state with maximum dimeric spin values to that having minimal spin values.

A parametric two-mode vibronic model of a dimeric mixed-valence cell for molecular quantum cellular automata and computational ab initio verification.

In this article we propose a two-mode vibronic model of a molecular cell for quantum cellular automata. The molecular cell is represented by a mixed-valence dimeric cluster in which the mobile electron is coupled to two kinds of molecular vibrations. The first type of vibration is represented by the so-called "breathing" modes localized on the redox sites, which are traditionally considered within the Piepho, Krausz and Schatz vibronic model as a source of the trapping effect. The second type includes the "intercenter" vibration, which changes the distance between the redox centers enhancing thus the degree of delocalization in the bonding orbital of the cell. The cell-cell response function as a key characteristic of the cell is evaluated in the framework of the dynamic (quantum-mechanical) solution of the two-mode vibronic problem. To elucidate the physical sense of precise quantum-mechanical results, a more imaginative semiclassical (adiabatic) picture is used. Competitive effects of the two kinds of active vibrations on the cell-cell response function are analyzed and the conditions are established under which a mixed-valence dimer can work as a functioning molecular cell in a quantum cellular automation device. One of the aims of this article was to combine the parametric approach that gives a very common description (that allows the qualitative comparison of properties in a series of compounds) with the ab initio evaluations providing numerical estimations of the parameters involved in the semiempirical approach for a real molecule. Along with the parametric approach the quantum-chemical modelling is used for investigating the cation-radical of the tetramethyleneethane molecule which was shown to belong to the class of strongly delocalized systems. It was demonstrated that an efficient control over the electronic and vibronic parameters can be achieved through the design of its derivatives through a spacer interposed between the two allyl fragments. The strongly conjugated C[double bond, length as m-dash]C spacer was shown to partially block the channel mediating electronic communication so that the molecule becomes strongly localized. The interconnection between the parametric and ab initio approaches is established.

Pair-delocalization in trigonal mixed-valence clusters: new insight into the vibronic origin of broken-symmetry ground states.

A new vibronic mechanism for the stabilization of pair-delocalized electronic states in trigonal trimeric mixed valence complexes (such as iron-sulfur [Fe3S4]0 proteins) is proposed. Unlike the previously reported mechanism based on the Piepho-Krausz-Schatz model dealing with the local "breathing" vibrations, the present mechanism involves the multicenter vibrations of the triangular complex, which change the metal-metal distances. The former mechanism of the vibronic coupling in combination with the double exchange and Heisenberg type exchange (superexchange) interactions accounts for the existence of the pair-delocalized states of many-electron mixed valence clusters in the intermediate ground spin states. In contrast to the previous model, within which the conditions for the occurrence of pair delocalized states are spin-dependent, the pair delocalization phenomenon in the proposed model is exclusively based on a clear physical mechanism of the interplay between the inter-center vibronic coupling and electron transfer. Therefore, the proposed mechanism demonstrates that the pair delocalization is a more common feature of mixed valence complexes and can appear not only in multi-electron trimers as a result of the interplay between several parameters, but even in one-electron mixed valence trimers in which neither double exchange nor superexchange is operative. The conditions for the pair delocalization in the proposed model are shown to be dependent on the value and sign of the electron transfer parameter as well as on the ratio of the frequencies of the fully symmetric (a1) and doubly degenerate (e) vibrations of a triatomic molecule.

Semiclassical versus quantum-mechanical vibronic approach in the analysis of the functional characteristics of molecular quantum cellular automata.

In the context of the decisive role that vibronic interactions play in the functioning of molecular quantum cellular automata, in this article we give a comparative analysis of the two alternative vibronic approaches to the evaluation of the key functional characteristics of molecular cells. Semiclassical Born-Oppenheimer approximation and quantum mechanical evaluations of the vibronic energy pattern, electronic density distributions and cell-cell response function are performed for two-electron square-planar mixed valence molecular cells subjected to the action of a molecular driver. Special emphasis is put on the description of the cell-cell response function, which describes strong non-linearity as a prerequisite for the effective action of quantum cellular automata. Comparison of results obtained within the semiclassical and quantum-mechanical approaches has revealed a drastic difference between the shapes of the cell-cell response functions evaluated within these two approaches in the case of moderate vibronic coupling when the energy levels of the square cell interacting with a weakly polarized driver undergo large tunneling splitting in shallow adiabatic potential minima. In contrast, in the limits of strong vibronic coupling (a double-well adiabatic potential with deep minima) and weak vibronic coupling (a single well adiabatic potential) the adiabatic approximation is shown to describe the cell-cell response function with rather good accuracy.

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.

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-level picture of the energy pattern of the electronic pair based on the previous ab initio analysis, we evaluate the temperature and field dependencies of concurrence and thus indicate that the entanglement can be controlled via the temperature, magnitude, and orientation of the electric field with respect to molecular axes of [GeV14O40]8-.

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 interactions is shown to give rise to a specific kind of double exchange coupling termed here as "external core" double exchange. In the opposite case of relatively strong electron transfer, the general Hamiltonian is shown to be reduced to the effective Hamiltonian of indirect exchange of the localized spins. We argue a possibility to efficiently control the magnetic coupling of the localized spins using an external electric field acting on the delocalized part of the system. Finally, we discuss the perspectives of the present model for molecular spintronics and spin qubits.

Theoretical Modeling of the Magnetic Behavior of Thiacalix[4]arene Tetranuclear Mn(II)2Gd(III)2 and Co(II)2Eu(III)2 Complexes.

In view of a wide perspective of 3d-4f complexes in single-molecule magnetism, here we propose an explanation of the magnetic behavior of the two thiacalix[4]arene tetranuclear heterometallic complexes Mn(II)2Gd(III)2 and Co(II)2Eu(III)2. The energy pattern of the Mn(II)2Gd(III)2 complex evaluated in the framework of the isotropic exchange model exhibits a rotational band of the low-lying spin excitations within which the Landé intervals are affected by the biquadratic spin-spin interactions. The nonmonotonic temperature dependence of the χT product observed for the Mn(II)2Gd(III)2 complex is attributed to the competitive influence of the ferromagnetic Mn-Gd and antiferromagnetic Mn-Mn exchange interactions, the latter being stronger (J(Mn, Mn) = -1.6 cm(-1), Js(Mn, Gd) = 0.8 cm(-1), g = 1.97). The model for the Co(II)2Eu(III)2 complex includes uniaxial anisotropy of the seven-coordinate Co(II) ions and an isotropic exchange interaction in the Co(II)2 pair, while the Eu(III) ions are diamagnetic in their ground states. Best-fit analysis of χT versus T showed that the anisotropic contribution (arising from a large zero-field splitting in Co(II) ions) dominates (weak-exchange limit) in the Co(II)2Eu(III)2 complex (D = 20.5 cm(-1), J = -0.4 cm(-1), gCo = 2.22). This complex is concluded to exhibit an easy plane of magnetization (arising from the Co(II) pair). It is shown that the low-lying part of the spectrum can be described by a highly anisotropic effective spin-(1)/2 Hamiltonian that is deduced for the Co(II)2 pair in the weak-exchange limit.

Single-Ion Magnet Et4N[CoII(hfac)3] with Nonuniaxial Anisotropy: Synthesis, Experimental Characterization, and Theoretical Modeling.

In this article we report the synthesis and structure of the new Co(II) complex Et4N[CoII(hfac)3] (I) (hfac = hexafluoroacetylacetonate) exhibiting single-ion magnet (SIM) behavior. The performed analysis of the magnetic characteristics based on the complementary experimental techniques such as static and dynamic magnetic measurements, electron paramagnetic resonance spectroscopy in conjunction with the theoretical modeling (parametric Hamiltonian and ab initio calculations) demonstrates that the SIM properties of I arise from the nonuniaxial magnetic anisotropy with strong positive axial and significant rhombic contributions.

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 account the two relevant electron transfer processes (through the side and through the diagonal of the square) as well as the difference in Coulomb energies for different instant positions of localization of the hole pair. The combined Jahn-Teller (JT) and pseudo JT vibronic coupling is treated within the conventional Piepho-Krauzs-Schatz model adapted to a bi-electronic MV species with the square-planar topology. The adiabatic potentials are evaluated for the low lying Coulomb levels in which the antipodal sites are occupied, the case just actual for utilization in mQCA. The conditions for the vibronic self-trapping in spin-singlet and spin-triplet states are revealed in terms of the two actual transfer pathways parameters and the strength of the vibronic coupling. Spin related effects in degrees of the localization which are found for spin-singlet and spin-triplet states are discussed. The polarization of the cell is evaluated and we demonstrate how the partial delocalization caused by the joint action of the vibronic coupling and electron transfer processes influences polarization of a four-dot cell. The results obtained within the adiabatic approach are compared with those based on the numerical solution of the dynamic vibronic problem. Finally, the Coulomb interaction between the cells is considered and the influence of the vibronic coupling on the shape on the non-linear cell-cell response function is revealed.

Microscopic theory of cooperative spin crossover: Interaction of molecular modes with phonons.

In this article, we present a new microscopic theoretical approach to the description of spin crossover in molecular crystals. The spin crossover crystals under consideration are composed of molecular fragments formed by the spin-crossover metal ion and its nearest ligand surrounding and exhibiting well defined localized (molecular) vibrations. As distinguished from the previous models of this phenomenon, the developed approach takes into account the interaction of spin-crossover ions not only with the phonons but also a strong coupling of the electronic shells with molecular modes. This leads to an effective coupling of the local modes with phonons which is shown to be responsible for the cooperative spin transition accompanied by the structural reorganization. The transition is characterized by the two order parameters representing the mean values of the products of electronic diagonal matrices and the coordinates of the local modes for the high- and low-spin states of the spin crossover complex. Finally, we demonstrate that the approach provides a reasonable explanation of the observed spin transition in the [Fe(ptz)6](BF4)2 crystal. The theory well reproduces the observed abrupt low-spin → high-spin transition and the temperature dependence of the high-spin fraction in a wide temperature range as well as the pronounced hysteresis loop. At the same time within the limiting approximations adopted in the developed model, the evaluated high-spin fraction vs. T shows that the cooperative spin-lattice transition proves to be incomplete in the sense that the high-spin fraction does not reach its maximum value at high temperature.