Understanding the Electronic Structure of Magnetic Trinuclear Complexes Based on the Tris-Dioxolene Triphenylene Non-Innocent Bridging Ligand, a Theoretical Study.

A complete theoretical analysis using first the simple Hückel model followed by more sophisticated multi-reference calculations on a trinuclear Ni(II) complex (Tp#Ni3 HHTP), bearing the non-innocent bridging ligand HHTP3- , is carried out. The three semiquinone moieties of HHTP3- couple antiferromagnetically and lead to a single unpaired electron localized on one of the moieties. The calculated exchange coupling integrals together with the zero-field parameters allow, when varied within a certain range, reproducing the experimental data. These results are generalized for two similar other trinuclear complexes containing Ni(II) and Cu(II). The electronic structure of HHTP3- turns out to be independent of both the chemical nature and the geometry of the metal ions. We also establish a direct correlation between the geometrical and the electronic structures of the non-innocent ligand that is consistent with the results of calculations. It allows experimentalists to get insight into the magnetic behavior of this type of complexes by an analysis of their X-ray structure.

Antisymmetric Exchange in a Real Copper Triangular Complex.

The antisymmetric exchange, also known as the Dzyaloshinskii-Moriya interaction (DMI), is an effective interaction that may be at play in isolated complexes (with transition metals or lanthanides, for instance), nanoparticles, and highly correlated materials with adequate symmetry properties. While many theoretical works have been devoted to the analysis of single-ion zero-field splitting and to a lesser extent to symmetric exchange, only a few ab initio studies deal with the DMI. Actually, it originates from a subtle interplay between weak electronic interactions and spin-orbit couplings. This article aims to highlight the origin of this interaction from theoretical grounds in a real tri-copper(II) complex, capitalizing on previous methodological studies on bi-copper(II) model complexes. By tackling this three-magnetic-center system, we will first show that the multispin model Hamiltonian is appropriate for trinuclear (and likely for higher nuclearity) complexes, then that the correct application of the permutation relationship is necessary to explain the outcomes of the ab initio calculations, and finally, that the model parameters extracted from a binuclear model transfer well to the trinuclear complex. For a more theory-oriented purpose, we will show that the use of a simplified structural model allows one to perform more demanding electronic structure calculations. On this simpler system, we will first check that the previous transferability is still valid, prior to performing more advanced calculations on the derived two-magnetic-center model system. To this end, we will explain in detail the physics of the DMI in the copper triangle of interest, before advocating further theory/experiment efforts.

Impact of the electric field on isotropic and anisotropic spin Hamiltonian parameters.

One may obviously think that the best way to control magnetic properties relies on using a magnetic field. However, it is not convenient to focus a magnetic field on a small object, whereas it is much easier to do so with an electric field. Magnetoelectric coupling allows one to control the magnetization with the electric field and the polarization with the magnetic field and could therefore provide a solution to this problem. This paper aims at quantifying the impact of the electric field on both the isotropic magnetic exchange and the Dzyaloshinskii-Moriya interaction in the case of a binuclear system of S = 1/2 spins. This study follows previous studies that showed that very high Dzyaloshinskii-Moriya interaction, i.e., the antisymmetric exchange, can be generated when close to first order spin orbit coupling. We will, therefore, explore this regime in a model Cu(II) complex that exhibits a quasi-degeneracy of the dx2-y2 and dxy orbitals. This situation is indeed the one that allows us to obtain the largest spin orbit couplings in transition metal complexes. We will show that both the magnetic exchange and the Dzyaloshinskii-Moriya interaction are very sensitive to the electric field and that it would therefore be possible to modulate and control magnetic properties by the electric field. Finally, rationalizations of the obtained results will be proposed.

Trinuclear Cyanido-Bridged [Cr2 Fe] Complexes: To Be or not to Be a Single-Molecule Magnet, a Matter of Straightness.

Trinuclear systems of formula [{Cr(LN3O2Ph )(CN)2 }2 M(H2 LN3O2R )] (M=MnII and FeII , LN3O2R stands for pentadentate ligands) were prepared in order to assess the influence of the bending of the apical M-N≡C linkages on the magnetic anisotropy of the FeII derivatives and in turn on their Single-Molecule Magnet (SMM) behaviors. The cyanido-bridged [Cr2 M] derivatives were obtained by assembling trans-dicyanido CrIII complex [Cr(LN3O2Ph )(CN)2 ]- and divalent pentagonal bipyramid complexes [MII (H2 LN3O2R )]2+ with various R substituents (R=NH2 , cyclohexyl, S,S-mandelic) imparting different steric demand to the central moiety of the complexes. A comparative examination of the structural and magnetic properties showed an obvious effect of the deviation from straightness of the M-N≡C alignment on the slow relaxation of the magnetization exhibited by the [Cr2 Fe] complexes. Theoretical calculations have highlighted important effects of the bending of the apical C-N-Fe linkages on both the magnetic anisotropy of the FeII center and the exchange interactions with the CrIII units.

Extraction of giant Dzyaloshinskii-Moriya interaction from ab initio calculations: First-order spin-orbit coupling model and methodological study.

The Dzyaloshinskii-Moriya interaction is expected to be at the origin of interesting magnetic properties, such as multiferroicity, skyrmionic states, and exotic spin orders. Despite this, its theoretical determination is far from being established, neither from the point of view of ab initio methodologies nor from that of the extraction technique to be used afterward. Recently, a very efficient way to increase its amplitude has been demonstrated near the first-order spin-orbit coupling regime. Within the first-order regime, the anisotropic spin Hamiltonian involving the Dzyaloshinskii-Moriya operator becomes inappropriate. Nevertheless, in order to approach this regime and identify the spin Hamiltonian limitations, it is necessary to characterize the underlying physics. To this end, we have developed a simple electronic and spin-orbit model describing the first-order regime and used ab initio calculations to conduct a thorough methodological study.

How to create giant Dzyaloshinskii-Moriya interactions? Analytical derivation and ab initio calculations on model dicopper(II) complexes.

This paper is a theoretical "proof of concept" on how the on-site first-order spin-orbit coupling (SOC) can generate giant Dzyaloshinskii-Moriya interactions in binuclear transition metal complexes. This effective interaction plays a key role in strongly correlated materials, skyrmions, multiferroics, and molecular magnets of promising use in quantum information science and computing. Despite this, its determination from both theory and experiment is still in its infancy and existing systems usually exhibit very tiny magnitudes. We derive analytical formulas that perfectly reproduce both the nature and the magnitude of the Dzyaloshinskii-Moriya interaction calculated using state-of-the-art ab initio calculations performed on model bicopper(II) complexes. We also study which geometrical structures/ligand-field forces would enable one to control the magnitude and the orientation of the Dzyaloshinskii-Moriya vector in order to guide future synthesis of molecules or materials. This article provides an understanding of its microscopic origin and proposes recipes to increase its magnitude. We show that (i) the on-site mixings of 3d orbitals rule the orientation and magnitude of this interaction, (ii) increased values can be obtained by choosing more covalent complexes, and (iii) huge values (∼1000 cm-1) and controlled orientations could be reached by approaching structures exhibiting on-site first-order SOC, i.e., displaying an "unquenched orbital momentum."

Cyano-Bridged Fe(II)-Cr(III) Single-Chain Magnet Based on Pentagonal Bipyramid Units: On the Added Value of Aligned Axial Anisotropy.

A cyano-bridged Fe(II)-Cr(III) single-chain magnet designed to ensure a parallel orientation of the axial anisotropy of the building units is reported. This ferromagnetic chain compound consists of a pentagonal bipyramid Fe(II) complex with Ising-type anisotropy and a dicyanide Cr(III) complex interlinked through their apical positions. It is characterized by an energy gap for the magnetization reversal of Δeff/ kB = 113 K and exhibits magnetic hysteresis with a coercive field of 1400 Oe at 2 K which positions this compound among the very few examples of SCMs with spin reversal barriers above 100 K. The quite remarkable performances of this single-strand SCM are attributed to the alignment of the local anisotropy axes, which is supported by ab initio modeling. A discrete Cr2Fe complex based on the same building units and behaving as a SMM in zero field is also reported.

Magnetic Anisotropy in Pentacoordinate NiII and CoII Complexes: Unraveling Electronic and Geometrical Contributions.

The magnetic properties of the pentacoordinate [MII (Me4 cyclam)N3 ]+ (Me4 cyclam=tetramethylcyclam; N3 =azido; M=Ni, Co) complexes were investigated. Magnetization and EPR studies indicate that they have an easy plane of magnetization with axial anisotropy parameters D close to 22 and greater than 30 cm-1 for the Ni and Co complexes, respectively. Ab initio calculations reproduced the experimental values of the zero-field splitting parameters and allowed the orientation of the anisotropy tensor axes with respect to the molecular frame to be determined. For M=Ni, the principal anisotropy axis lies along the Ni-Nazido direction perpendicular to the Ni(Me4 cyclam) mean plane, whereas for M=Co it lies in the Co(Me4 cyclam) mean plane and thus perpendicular to the Co-Nazido direction. These orientations match one of the possible solutions experimentally provided by single-crystal cantilever torque magnetometry. To rationalize the geometry and its impact on the orientation of the anisotropy tensor axis, calculations were carried out on model complexes [NiII (NCH)5 ]2+ and [CoII (NCH)5 ]2+ by varying the geometry between square pyramidal and trigonal bipyramidal. The geometry of the complexes was found to be the result of a compromise between the electronic configuration of the metal ion and the structure-orienting effect of the Me4 cyclam macrocycle. Moreover, the orientation of the anisotropy axes is mainly dependent on the geometry of the complexes.

Pentagonal Bipyramid FeII Complexes: Robust Ising-Spin Units towards Heteropolynuclear Nanomagnets.

Pentagonal bipyramid FeII complexes have been investigated to evaluate their potential as Ising-spin building units for the preparation of heteropolynuclear complexes that are likely to behave as single-molecule magnets (SMMs). The considered monometallic complexes were prepared from the association of a divalent metal ion with pentadentate ligands that have a 2,6-diacetylpyridine bis(hydrazone) core (H2 LN3O2R ). Their magnetic anisotropy was established by magnetometry to reveal their zero-field splitting (ZFS) parameter D, which ranged between -4 and -13 cm-1 and was found to be modulated by the apical ligands (ROH versus Cl). The alteration of the D value by N-bound axial CN ligands, upon association with cyanometallates, was also assessed for heptacoordinated FeII as well as for related NiII and CoII derivatives. In all cases, N-coordinated cyanide ligands led to large magnetic anisotropy (i.e., -8 to -18 cm-1 for Fe and Ni, +33 cm-1 for Co). Ab initio calculations were performed on three FeII complexes, which enabled one to rationalize the role of the ligand on the nature and magnitude of the magnetic anisotropy. Starting from the pre-existing heptacoordinated complexes, a series of pentanuclear compounds were obtained by reactions with paramagnetic [W(CN)8 ]3- . Magnetic studies revealed the occurrence of ferromagnetic interactions between the spin carriers in all the heterometallic systems. Field-induced slow magnetic relaxation was observed for mononuclear FeII complexes (Ueff /kB up to 53 K (37 cm-1 ), τ0 =5×10-9  s), and SMM behavior was evidenced for a heteronuclear [Fe3 W2 ] derivative (Ueff /kB =35 K and τ0 =4.6 10-10  s), which confirmed that the parent complexes were robust Ising-type building units. High-field EPR spectroscopic investigation of the ZFS parameters for a Ni derivative is also reported.

Structural Dependence of the Ising-type Magnetic Anisotropy and of the Relaxation Time in Mononuclear Trigonal Bipyramidal Co(II) Single Molecule Magnets.

This paper describes the correlation between Ising-type magnetic anisotropy and structure in trigonal bipyramidal Co(II) complexes. Three sulfur-containing trigonal bipyramidal Co(II) complexes were synthesized and characterized. It was shown that we can engineer the magnitude of the Ising anisotropy using ligand field theory arguments in conjunction with structural parameters. To prepare this series of compounds, we used, on the one hand, a tetradentate ligand containing three sulfur atoms and one amine (NS3tBu) and on the other hand three different axial ligands, namely, Cl-, Br-, and NCS-. The organic ligand imposes a trigonal bipyramidal arrangement with the three sulfur atoms lying in the trigonal plane with long Co-S bond distances. The magnetic properties of the compounds were measured, and ab initio calculations were used to analyze the anisotropy parameters and perform magneto-structural correlations. We demonstrate that a smaller axial zero-field splitting parameter leads to slower relaxation time when the symmetry is strictly axial, while the presence of very weak rhombicity decreases the energy barrier and speeds the relaxation of the magnetization.

Design of a Binuclear Ni(II) Complex with Large Ising-type Anisotropy and Weak Anti-Ferromagnetic Coupling.

The preparation of a binuclear Ni(II) complex with a pentacoordinate environment using a cryptand organic ligand and the imidazolate bridge is reported. The coordination sphere is close to trigonal bipyramidal (tbp) for one Ni(II) and to square pyramidal (spy) for the other. The use of the imidazolate bridge that undergoes π-π stacking with two benzene rings of the chelating ligand induces steric hindrance that stabilizes the pentacoordinate environment. Magnetic measurements together with theoretical studies of the spin states energy levels allow fitting the data and reveal a large Ising-type anisotropy and a weak anti-ferromagnetic exchange coupling between the metal ions. The magnitude and the nature of the magnetic anisotropy and the difference in anisotropy between the two metal ions are rationalized using wave-function-based calculations. We show that a slight distortion of the coordination sphere of Ni(II) from spy to tbp leads to an Ising-type anisotropy. Broken-symmetry density functional calculations rationalize the weak anti-ferromagnetic exchange coupling through the imidazolate bridge.

From Positive to Negative Zero-Field Splitting in a Series of Strongly Magnetically Anisotropic Mononuclear Metal Complexes.

A series of mononuclear [M(hfa)2(pic)2] (Hhfa = 1,1,1,5,5,5-hexafluoro-2,4-pentanedione; pic = 4-methylpyridine; M = FeII, CoII, NiII, ZnII) compounds were obtained and characterized. The structures of the complexes have been resolved by single-crystal X-ray diffraction, indicating that, apart from the zinc derivative, the complexes are in a trans configuration. Moreover, a dramatic lenghthening of the Fe-N distances was observed, whereas the nickel(II) complex is almost perfectly octahedral. The magnetic anisotropy of these complexes was thoroughly studied by direct-current (dc) magnetic measurements, high-field electron paramagnetic resonance, and infrared (IR) magnetospectroscopy: the iron(II) derivative exhibits an out-of-plane anisotropy (DFe = -7.28 cm-1) with a high rhombicity, whereas the cobalt(II) and nickel(II) complexes show in-plane anisotropy (DCo ∼ 92-95 cm-1; DNi = 4.920 cm-1). Ab initio calculations were performed to rationalize the evolution of the structure and identify the excited states governing the magnetic anisotropy along the series. For the iron(II) complex, an out-of-phase alternating-current (ac) magnetic susceptibility signal was observed using a 0.1 T dc field. For the cobalt(II) derivative, the ac magnetic susceptibility shows the presence of two field-dependent relaxation phenomena: at low field (500 Oe), the relaxation process is beyond single-ion behavior, whereas at high field (2000 Oe), the relaxation of magnetization implies several mechanisms including an Orbach process with Ueff = 25 K and quantum tunneling of magnetization. The observation by µ-SQUID magnetization measurements of hysteresis loops of up to 1 K confirmed the single-ion-magnet behavior of the cobalt(II) derivative.

Design and Magnetic Properties of a Mononuclear Co(II) Single Molecule Magnet and Its Antiferromagnetically Coupled Binuclear Derivative.

The preparations of related mononuclear and binuclear Co(II) complexes with a quasi-identical local C3v symmetry using a cryptand organic ligand are reported. The mononuclear complex behaves as a single molecule magnet (SMM). A relatively weak antiferromagnetic exchange coupling (J) of the same order of magnitude as the local magnetic anisotropy (D) is determined experimentally and theoretically for the binuclear complex. The weak magnitude of the antiferromagnetic exchange coupling, analyzed using a combination of broken-symmetry density functional theory and wave function based calculations, is ascribed to the weak overlap between the singly occupied orbitals because of the local C3v symmetry of the Co(II) ions; the organic ligand was found to contribute to the exchange coupling as the azido bridge that directly links the Co(II) ions. Calculation of the energy and wave functions of the spin states for the binuclear complex, in the general case, allows analysis of the effect of the |J/D| ratio on the magnetic behavior of the binuclear complex and prediction of the optimum range of values for the complex to behave as two weakly interacting SMMs.

Unraveling σ and π Effects on Magnetic Anisotropy in cis-NiA4 B2 Complexes: Magnetization, HF-HFEPR Studies, First-Principles Calculations, and Orbital Modeling.

By using complementary experimental techniques and first-principles theoretical calculations, magnetic anisotropy in a series of five hexacoordinated nickel(II) complexes possessing a symmetry close to C2v , has been investigated. Four complexes have the general formula [Ni(bpy)X2 ]n+ (bpy=2,2'-bipyridine; X2 =bpy (1), (NCS- )2 (2), C2 O42- (3), NO3- (4)). In the fifth complex, [Ni(HIM2 -py)2 (NO3 )]+ (5; HIM2 -py=2-(2-pyridyl)-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazolyl-1-hydroxy), which was reported previously, the two bpy bidentate ligands were replaced by HIM2 -py. Analysis of the high-field, high-frequency electronic paramagnetic resonance (HF-HFEPR) spectra and magnetization data leads to the determination of the spin Hamiltonian parameters. The D parameter, corresponding to the axial magnetic anisotropy, was negative (Ising type) for the five compounds and ranged from -1 to -10 cm-1 . First-principles SO-CASPT2 calculations have been performed to estimate these parameters and rationalize the experimental values. From calculations, the easy axis of magnetization is in two different directions for complexes 2 and 3, on one hand, and 4 and 5, on the other hand. A new method is proposed to calculate the g tensor for systems with S=1. The spin Hamiltonian parameters (D (axial), E (rhombic), and gi ) are rationalized in terms of ordering of the 3 d orbitals. According to this orbital model, it can be shown that 1) the large magnetic anisotropy of 4 and 5 arises from splitting of the eg -like orbitals and is due to the difference in the σ-donor strength of NO3- and bpy or HIM2 -py, whereas the difference in anisotropy between the two compounds is due to splitting of the t2g -like orbitals; and 2) the anisotropy of complexes 1-3 arises from the small splitting of the t2g -like orbitals. The direction of the anisotropy axis can be rationalized by the proposed orbital model.

Ising-type Magnetic Anisotropy and Slow Relaxation of the Magnetization in Four-Coordinate Amido-Pyridine FeII Complexes.

A family of four-coordinate FeII complexes formed with N,N'-chelating amido-pyridine ligands was synthesized, and their magnetic properties were investigated. These distorted tetrahedral complexes exhibit significant magnetic anisotropy with zero-field splitting parameter D ranging between -17 and -12 cm-1. Ab initio calculations enabled identification of the structural factors that control the nature of the magnetic anisotropy and the rationalization of the variation of D in these complexes. It is shown that a reduced N-Fe-N angle involving the chelating nitrogen atoms of the ligands is at the origin of the negative D value and that the torsion between the two N-Fe-N planes imposed by steric hindrances further increases the |D| value. Field-induced slow relaxation of magnetization was observed for the three compounds, and a single-molecule magnet behavior with an energy barrier for magnetization flipping (Ueff) of 27 cm-1 could be evidenced for one of them.

Electrically switchable magnetic molecules: inducing a magnetic coupling by means of an external electric field in a mixed-valence polyoxovanadate cluster.

Herein we evaluate the influence of an electric field on the coupling of two delocalized electrons in the mixed-valence polyoxometalate (POM) [GeV14 O40 ](8-) (in short V14 ) by using both a t-J model Hamiltonian and DFT calculations. In absence of an electric field the compound is paramagnetic, because the two electrons are localized on different parts of the POM. When an electric field is applied, an abrupt change of the magnetic coupling between the two delocalized electrons can be induced. Indeed, the field forces the two electrons to localize on nearest-neighbors metal centers, leading to a very strong antiferromagnetic coupling. Both theoretical approaches have led to similar results, emphasizing that the sharp spin transition induced by the electric field in the V14 system is a robust phenomenon, intramolecular in nature, and barely influenced by small changes on the external structure.

Spin decontamination of broken-symmetry density functional theory calculations: deeper insight and new formulations.

This work re-examines the problem of the broken-symmetry Density-Functional Theory (DFT) solutions in diradical systems, in particular for the calculation of magnetic couplings. The Ms = 0 solution is not an eigenfunction of the S(2) spin operator and the evaluation of the singlet state energy requires a spin-decontamination. A popular approximation is provided by the so-called Yamaguchi formula, which operates using the expectation values of S(2) relative to both Ms = 1 and Ms =0 solutions. Referring to a previous decomposition of the magnetic coupling in terms of direct exchange, kinetic exchange and core polarization, it is shown that this expression will lead to unreliable values of the singlet-triplet energy gap when the spin polarization of the core orbitals becomes large. The here-proposed method of spin-decontamination is based on the Effective Hamiltonian Theory and uses the overlap between the two degenerate Ms = 0 solutions. An approximate and convenient formula, which uses the expectation values of S(2) of the Ms = 0 solutions before and after core polarization is proposed, which is free from the Yamaguchi's formula artefact, as illustrated on an organic diradical presenting a very high value of 〈S(2)〉 for the Ms = 0 solution, the antiferromagnetic coupling being due to the spin polarization mechanism.

Interplay between local anisotropies in binuclear complexes.

A systematic study has been undertaken to determine how local distortions affect the overall (molecular) magnetic anisotropies in binuclear complexes. For this purpose we have applied a series of distortions to two binuclear Ni(II) model complexes and extracted the magnetic anisotropy parameters of multispin and giant-spin model Hamiltonians. Furthermore, local and molecular magnetic axes frames have been determined. It is shown that certain combinations of local distortions can lead to constructive interference of the local anisotropies and that the largest contribution to the anisotropic exchange does not arise from the second-rank tensor normally included in the multispin Hamiltonian, but rather from a fourth-rank tensor. From the comparison of the extracted parameters, simple rules are obtained to maximize the molecular anisotropy by controlling the local magnetic anisotropy, which opens the way to tune the anisotropy in binuclear or polynuclear complexes.

Singly occupied MOs in mono- and diradical conjugated hydrocarbons: comparison between variational single-reference, π-fully correlated and Hückel descriptions.

This work compares three descriptions of the unpaired electrons distribution in conjugated monoradical and diradical hydrocarbons involving one or two methylene groups attached to an aromatic skeleton. The first one is the simple Hückel topological Hamiltonian, the singly occupied molecular orbitals (SOMO) of which may be analytically obtained. The second one is the restricted open-shell self-consistent field (ROHF-SCF) method. The so-obtained distribution of the unpaired electrons on the skeleton appears deeply different from that predicted by the Hückel Hamiltonian, being more strongly localized on the external methylene groups. More elaborate methods treat all π electrons in the π valence molecular orbitals (MOs) through a full valence π complete active space self-consistent field (CASSCF) treatment. The distributions of the unpaired electrons (given by the natural MOs of occupation number close to 1) are surprisingly similar to those predicted by the Hückel model. The spin density distributions, including spin polarization effects, can be improved by further configuration interactions involving one hole-one particle excitations and compared with the experimental hyperfine coupling constant ratios. This comparison confirms the lack of delocalization of the magnetic orbitals defined from the self-consistent single-reference treatment. We show that, provided correct SOMO are used, a single excitation CI performed on top of a single reference gives accurate spin densities. Finally, a rationalization of the role of the dynamic correlation in correcting the excessive localization of the unpaired electron(s) at the ROHF level on the exocyclic methylene group(s) is given, attributing it to the dynamic charge polarization of the charge transfer configurations between methylene and the aromatic frame.

Giant Ising-type magnetic anisotropy in trigonal bipyramidal Ni(II) complexes: experiment and theory.

This paper reports the experimental and theoretical investigations of two trigonal bipyramidal Ni(II) complexes, [Ni(Me(6)tren)Cl](ClO(4)) (1) and [Ni(Me(6)tren)Br](Br) (2). High-field, high-frequency electron paramagnetic resonance spectroscopy performed on a single crystal of 1 shows a giant uniaxial magnetic anisotropy with an experimental D(expt) value (energy difference between the M(s) = ± 1 and M(s) = 0 components of the ground spin state S = 1) estimated to be between -120 and -180 cm(-1). The theoretical study shows that, for an ideally trigonal Ni(II) complex, the orbital degeneracy leads to a first-order spin-orbit coupling that results in a splitting of the M(s) = ± 1 and M(s) = 0 components of approximately -600 cm(-1). Despite the Jahn-Teller distortion that removes the ground term degeneracy and reduces the effects of the first-order spin-orbit interaction, the D value remains very large. A good agreement between theoretical and experimental results (theoretical D(theor) between -100 and -200 cm(-1)) is obtained.