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.

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.

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.

Difficulty of the evaluation of the barrier height of an open-shell transition state between closed shell minima: The case of small C4n rings.

C4n cyclacenes exhibit strong bond-alternation in their equilibrium geometry. In the two equivalent geometries, the system keeps an essentially closed-shell character. The two energy minima are separated by a transition state suppressing the bond-alternation, where the wave function is strongly diradical. This paper discusses the physical factors involved in this energy difference and possible evaluations of the barrier height. The barrier given as the energy difference between the restricted density functional theory (DFT)/B3LYP for the equilibrium and the broken symmetry DFT/B3LYP of the transition state is either negative or small, in contradiction with the most reliable Wave Function Theory calculations. The minimal (two electrons in two molecular orbitals) Complete Active Space self-consistent field (CASSCF) overestimates the barrier, and the subsequent second-order perturbation cancels it. Due to the collective character of the spin-polarization effect, it is necessary to perform a full π CASSCF + second-order perturbation to reach a reasonable value of the barrier, but this type of treatment cannot be applied to large molecules. DFT procedures treating on an equal foot the closed-shell and open-shell geometries have been explored, such as Mixed-Reference Spin-Flip Time-dependent-DFT and a new spin-decontamination proposal, namely, DFT-dressed configuration interaction, but the results still depend on the density functional. M06-2X without or with spin-decontamination gives the best agreement with the accurate wave function results.

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.

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.

Chemical tuning of spin clock transitions in molecular monomers based on nuclear spin-free Ni(ii).

We report the existence of a sizeable quantum tunnelling splitting between the two lowest electronic spin levels of mononuclear Ni complexes. The level anti-crossing, or magnetic "clock transition", associated with this gap has been directly monitored by heat capacity experiments. The comparison of these results with those obtained for a Co derivative, for which tunnelling is forbidden by symmetry, shows that the clock transition leads to an effective suppression of intermolecular spin-spin interactions. In addition, we show that the quantum tunnelling splitting admits a chemical tuning via the modification of the ligand shell that determines the crystal field and the magnetic anisotropy. These properties are crucial to realize model spin qubits that combine the necessary resilience against decoherence, a proper interfacing with other qubits and with the control circuitry and the ability to initialize them by cooling.

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."

Distributed Gaussian orbitals for the description of electrons in an external potential.

In this work, we demonstrate the viability of using distributed Gaussian orbitals as a basis set for the calculation of the properties of electrons subjected to an external potential. We validate our method by studying one-electron systems for which we can compare to exact analytical results. We highlight numerical aspects that require particular care when using a distributedGaussian basis set. In particular, we discuss the optimal choice for the distance between two neighboring Gaussian orbitals. Finally, we show how our approach can be applied to many-electron problems.

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.

Bicapped Keggin polyoxomolybdates: discrete species and experimental and theoretical investigations on the electronic delocalization in a chain compound.

Three monomeric polyoxometalates [M(C10H8N2)3][α-PMoMoO40Zn2(C10H8N2)2]·2H2O (M-PMo12Zn2, M = Fe, Co, Ru) with {Zn(bpy)2}2+ units capped on reduced α-Keggin polyanions and [M(bpy)3]2+ counter-ions were synthesized under hydrothermal conditions. The 1D polymer [N(C4H9)4][Ru(C10H8N2)3][α-PMoMoO43] (Ru-PMo14) was prepared by a similar strategy, in the absence of 2,2'-bpy ligands. In this chain capped reduced Keggin anions are linked via Mo-O-Mo bridges and are surrounded by both tetrabutylammonium cations and [Ru(bpy)3]2+ counter-ions. The compounds were characterized in the solid state by single crystal and powder X-ray diffraction and IR spectroscopy and in solution by 31P NMR spectroscopy. 31P diffusion ordered NMR spectroscopy (DOSY) indicates that the diffusion coefficient of the dissolved species of Ru-PMo14 corresponds to a dimeric structure. Magnetic susceptibility measurements performed on Ru-PMo14 show the existence of antiferromagnetic interactions between the d1 electrons of the six MoV centers, with a singlet spin ground state. However, attempts to fit the data in the 2-300 K temperature range with Heisenberg Hamiltonians adapted for 0 or 1D systems suggest that these electrons are delocalized. Density Functional Theory (DFT) and Wave Function Theory (WFT) calculations indicate a migration of the electrons of the capping MoV centers into the PMo12 units at high temperature, allowing the rationalization of the experimental observations.

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.

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.

Engineering the magnetic coupling and anisotropy at the molecule-magnetic surface interface in molecular spintronic devices.

A challenge in molecular spintronics is to control the magnetic coupling between magnetic molecules and magnetic electrodes to build efficient devices. Here we show that the nature of the magnetic ion of anchored metal complexes highly impacts the exchange coupling of the molecules with magnetic substrates. Surface anchoring alters the magnetic anisotropy of the cobalt(II)-containing complex (Co(Pyipa)2), and results in blocking of its magnetization due to the presence of a magnetic hysteresis loop. In contrast, no hysteresis loop is observed in the isostructural nickel(II)-containing complex (Ni(Pyipa)2). Through XMCD experiments and theoretical calculations we find that Co(Pyipa)2 is strongly ferromagnetically coupled to the surface, while Ni(Pyipa)2 is either not coupled or weakly antiferromagnetically coupled to the substrate. These results highlight the importance of the synergistic effect that the electronic structure of a metal ion and the organic ligands has on the exchange interaction and anisotropy occurring at the molecule-electrode interface.

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.

An extended DFTB-CI model for charge-transfer excited states in cationic molecular clusters: model studies versus ab initio calculations in small PAH clusters.

We present an extension of the constrained density functional tight binding scheme combined with configuration interaction (DFTB-CI) to efficiently compute excited states of molecular cluster cations and their oscillator strengths from the ground state. The present extension consists of generalizing the initial model, relying on configurations with holes in the monomer HOMOs only, to configurations involving sub-HOMO holes, allowing for the description of higher excited states. The extended scheme is benchmarked on selected energy pathways with respect to available ab initio and new CASPT2 reference calculations on the benzene, naphthalene and pyrene dimer cations. The ability of the model to describe the potential energy surfaces and the transition dipole moments is discussed. The vertical electronic absorption spectra of the three dimer cations are calculated and compared with the theoretical litterature and available experimental data. Finally, the electronic absorption spectra of low energy isomers of the trimer and tetramer pyrene cluster cations are also predicted.

Accuracy of embedded fragment calculation for evaluating electron interactions in mixed valence magnetic systems: study of 2e-reduced lindqvist polyoxometalates.

Accurate quantum chemical calculations on real-world magnetic systems are challenging, the inclusion of electron correlation being the bottleneck of such task. One method proposed to overcome this difficulty is the embedded fragment approach. It tackles a chemical problem by dividing it into small fragments, which are treated in a highly accurate way, surrounded by an embedding included at an approximate level. For the vast family of medium-to-large sized polyoxometalates, two-electron-reduced systems are habitual and their magnetic properties are interesting. In this paper, we aim at assessing the quality of embedded fragment calculations by checking their ability to reproduce the electronic spectra of a complete system, here the mixed-metal series [MoxW6-xO19](4-) (x = 0-6). The microscopic parameters extracted from fragment calculations (electron hopping, intersite electrostatic repulsion, local orbital energy, etc.) have been used to reproduce the spectra through model Hamiltonian calculations. These energies are compared to the results of the highly accurate ab initio difference dedicated configuration interaction (DDCI) method on the complete system. In general, the model Hamiltonian calculations using parameters extracted from embedded fragments nearly exactly reproduce the DDCI spectra. This is quite an important result since it can be generalized to any inorganic magnetic system. Finally, the occurrence of singlet or triplet ground states in the series of molecules studied is rationalized upon the interplay of the parameters extracted.

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.

In search of a rational dressing of intermediate effective Hamiltonians.

The intermediate effective Hamiltonians are designed to provide M exact energies and the components of the corresponding eigenvectors in the N-dimensional model space, with N > M. The effective Hamiltonian is not entirely defined by these N × M conditions, and several dressings of the Hamiltonian matrix in the model space are possible. Some of them lead to unreliable N - M roots associated with the intermediate model space. This defect appears dramatically when one refers to the weak separability property, namely, the fact that in a noninteracting A···B problem where the model space only involves excitations on A, the consideration of the excitations on B should not affect the spectrum of A. We suggest variants that should maintain the physical meaning of the intermediate roots. Numerical comparisons illustrate the relevance of this proposal.

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.