Detailed ab initio first-principles study of the magnetic anisotropy in a family of trigonal pyramidal iron(II) pyrrolide complexes

Comprehensive Exploration of Optics and Magnetism in a Hydrothermally Synthesized Nickel(II) Complex

The hydrothermal reaction of 2-MeIm (2-MeIm: 2-methylimidazole) with nickel sulfate hexahydrate in methanol afforded a mononuclear complex formulated as [Ni(SO4)(2-MeIm)2(H2O)3]·CH3OH (1). The title compound was described by X-ray single-crystal diffraction, thermal assessment, IR, and UV-vis spectroscopy. The crystal structure of 1 is composed of segregated [Ni(SO4)(2-MeIm)2(H2O)3] neutral entities and a solvent methanol molecule. Two (2-MeIm) ligands, a sulfate group, and a water molecule reside in the equatorial positions of the vertices in this 6-fold coordination. Two aqua ligands lay in the apical positions, resulting in a subtly distorted octahedral framework, as was supported by spectroscopic analysis. The complex's self-assembly is firmly governed by robust O-H···O/N-H···O interactions. Further details on these bonds have been furnished via Hirshfeld surface scrutiny and 2D fingerprint plots. As proven by TGA/DSC analysis, raising the temperature of 1 above 60 °C instigates progressive decomposition stages, which culminates in the production of metal oxide as the ultimate product at 700 °C. The optical analysis suggests the dielectric nature of the material with large direct and indirect gap energies of 5.25 and 4.96 eV, respectively. The results of magnetic studies suggest that 1 undergoes a transition to a magnetically ordered state below 6 K.

Field-Induced Slow Magnetization Relaxation of a Tetrahedral S=2 FeIIS4-Containing Complex

In the work described herein, the spin relaxation properties of the mononuclear tetrahedral S=2 [Fe{(SPiPr2)2N}2] complex (1) were studied by employing static and dynamic magnetic measurements at liquid helium temperatures. In the absence of an external direct current (DC) magnetic field, 1 exhibits fast magnetization relaxation. However, in the presence of external magnetic fields of a few kOe, slow relaxation is induced as monitored by alternating current (AC) magnetic susceptibility measurements up to 10 kHz, in the temperature range 2-5 K. Analysis of the temperature dependence of the corresponding relaxation time reveals contributions by Quantum Tunnelling of Magnetization, and the Direct and Orbach processes in the magnetization relaxation mechanism of 1. The energy barrier, Ueff, of the Orbach process, as determined by this analysis, is compared with that related to the zero-field splitting parameters of 1 which were previously determined by high- frequency and -field electron paramagnetic resonance and Mössbauer spectroscopies.

Magneto-Structural Correlation of Five-Coordinate Trigonal Bipyramidal High Spin Cobalt(II) Complexes

Here, we combined magnetometry, multi-frequency electronic paramagnetic resonance, and wave function based ab initio calculations to investigate magnetic properties of two high spin Co(II) complexes Co(BDPRP) (BDPRP=2,6-bis((2-(S)-di(4-R)phenylhydroxylmethyl-1-pyrrolidi-nyl)methyl)pyridine, R=H for 8; R=tBu for 9). Complexes 8 and 9 featuring effective D3h symmetry were found to possess D=24.0 and 32.0 cm-1, respectively, in their S=3/2 ground states of1 e ' ' d x z / y z 4 1 e ' d x y / x 2 - y 2 2 1 a 1 ' d z 2 1 ${{\left(1{{\rm e}}^{{\rm { {^\prime}}}{\rm { {^\prime}}}}\right({d}_{xz/yz}\left)\right)}^{4}{\left(1{{\rm e}}^{{\rm { {^\prime}}}}\right({d}_{{xy/{x}^{2}-y}^{2}}\left)\right)}^{2}{\left(1{{\rm a}}_{1}^{{\rm { {^\prime}}}}\right({d}_{{z}^{2}}\left)\right)}^{1}}$ . Ligand field analyses revealed that the low-lying d-d excited states make either positive or vanishing contributions to D. Hence, total positive D values were measured for 8 and 9, as well as related D3h high spin Co(II) complexes. In contrast, negative D values are usually observed for C3v congeners. In-depth analyses suggested that lowering symmetry from D3h to C3v induces orbital mixing between1 e d x z / y z ${1{\rm e}\left({d}_{xz/yz}\right)}$ and2 e d x y / x 2 - y 2 ${2{\rm e}\left({d}_{{xy/{x}^{2}-y}^{2}}\right)}$ and admixes excited state4 A 2 1 e → 2 e ${{}^{4}{{\rm A}}_{2}\left(1e\to 2e\right)}$ into the ground state. Both factors turn the total D value progressively negative with the increasing distance (δ) of the Co(II) center out of the equatorial plane. Therefore, δ determines the sign and magnitude of final D values of five-coordinate trigonal bipyramidal S=3/2 Co(II) complexes as measured for a series of such species with varying δ.

Influence of the phonon-bottleneck effect and low-energy vibrational modes on the slow spin-phonon relaxation in Kramers-ions-based Cu(II) and Co(II) complexes with 4-amino-3,5-bis-(pyridin-2-yl)-1,2,4-triazole and dicyanamide

Two new complexes, bis-[4-amino-3,5-bis-(pyridin-2-yl)-1,2,4-triazole-κ2N2,N6]bis-(dicyanamide-κN8)copper(II), [Cu(abpt)2(dca)2] (1) and bis-[4-amino-3,5-bis-(pyridin-2-yl)-1,2,4-triazole-κ2N2,N6]bis-(dicyanamide-κN8)cobalt(II), [Co(abpt)2(dca)2] (2), have been prepared and magneto-structurally characterised. Single crystal studies of both complexes have shown that their crystal structures are molecular, in which the central atoms are six-coordinated in the form of a distorted octahedron by two bidentate abpt and two monodentate dca ligands. Even if both complexes have the same composition and crystallize in the same P1̄ space group, they are not isostructural. Both structures contain strong intermolecular N-H⋯N hydrogen bonds and π-π stacking interactions. IR spectra are consistent with the solved structures of both complexes and confirmed the terminal character of the dca ligands and the bidentate coordination of the abpt ligands. The analysis of the magnetic properties showed that both complexes exhibit field-induced slow spin-phonon relaxation. In both complexes, the slow spin-phonon relaxation is influenced by a severe phonon-bottleneck effect that affects the direct process, a dominant relaxation mechanism at low temperatures in both complexes. The phonon-bottleneck effect in 1 was suppressed by simply reducing the crystallite size, and further analysis of the field dependence of the relaxation time yielded the characteristic energy of vibrational modes of 11 cm-1 participating in the Raman process at low magnetic fields. The analysis of magnetic properties and ab initio calculations confirmed that 2 represents a system with a moderate uniaxial anisotropy yielding an average energy barrier of 82 cm-1 (from all four nonequivalent Co(II) sites in the structure of 2).

Correlating Valence and 2p3d RIXS Spectroscopies: A Ligand-Field Study of Spin-Crossover Iron(II)

The molecular spin-crossover phenomenon between high-spin (HS) and low-spin (LS) states is a promising route to next-generation information storage, sensing applications, and molecular spintronics. Spin-crossover complexes also provide a unique opportunity to study the ligand field (LF) properties of a system in both HS and LS states while maintaining the same ligand environment. Presently, we employ complementing valence and core-level spectroscopic methods to probe the electronic excited-state manifolds of the spin-crossover complex [FeII(H2B(pz)2)2phen]0. Light-induced excited spin-state trapping (LIESST) at liquid He temperatures is exploited to characterize magnetic and spectroscopic properties of the photoinduced HS state using SQUID magnetometry and magnetic circular dichroism spectroscopy. In parallel, Fe 2p3d RIXS spectroscopy is employed to examine the ΔS = 0, 1 excited LF states. These experimental studies are combined with state-of-the-art CASSCF/NEVPT2 and CASCI/NEVPT2 calculations characterizing the ground and LF excited states. Analysis of the acquired LF information further supports the notion that the spin-crossover of [FeII(H2B(pz)2)2phen]0 is asymmetric, evidenced by a decrease in eπ in the LS state. The results demonstrate the power of cross-correlating spectroscopic techniques with high and low LF information content to make accurate excited-state assignments, as well as the current capabilities of ab initio theory in interpreting these electronic properties.

The resolution of the weak-exchange limit made rigorous, simple and general in binuclear complexes

The correct interpretation of magnetic properties in the weak-exchange regime has remained a challenging task for several decades. In this regime, the effective exchange interaction between local spins is quite weak, of the same order of magnitude or smaller than the various anisotropic terms, which generates a complex set of levels characterized by spin mixing. Although the model multispin Hamiltonian in the absence of local orbital momentum, , is considered good enough to map the experimental energies at zero field and in the strong-exchange limit, theoretical works pointed out limitations of this simple model. This work revives the use of ĤMS from a new theoretical perspective, detailing point-by-point a strategy to correctly map the computational energies and wave functions onto ĤMS, thus validating it regardless of the exchange limit. We will distinguish two cases, based on experimentally characterized dicobalt(II) complexes from the literature. If centrosymmetry imposes alignment of the various rank-2 tensors constitutive of ĤMS in the first case, the absence of any symmetry element prevents such alignment in the second case. In such a context, the strategy provided herein becomes a powerful tool to rationalize the experimental magnetic data, since it is capable of fully and rigorously extracting the multispin model without any assumption on the orientation of its constitutive tensors. Furthermore, the strategy allows to question the use of the spin Hamiltonian approach by explicitly controlling the projection norms on the model space, which is showcased in the second complex where local orbital momentum could have occurred (distorted octahedra). Finally, previous theoretical data related to a known dinickel(II) complex is reinterpreted, clarifying initial wanderings regarding the weak exchange limit.

Alkyl Chains Modulated Magnetization Dynamics of Mononuclear Trigonal Prismatic CoII Complexes

Four benzeneboron-capped mononuclear CoII complexes with different alkyl substitutions on the fourth position of phenylboronic acid were obtained. The CoII ions are all wrapped by the pocket-like ligands and located in trigonal prismatic coordination geometries. Alternating-current magnetic susceptibility measurements reveal that they show different magnetization dynamics, such as distinct relaxation rates at the same temperature, the faster QTM rates for the ethyl and propyl substituted complexes, as well as different relaxation processes. Magneto-structural correlation study reveals that the various deviations of coordination geometry of CoII ion, diverse crystal packings and possible different vibration modes of substituents caused by modifying alkyl chains are the key factors affecting the magnetization dynamics. This work demonstrates that the alkyl chains even locating far away from the metal center can have a large impact on the magnetic behavior of the CoII complex with a very rigid coordination geometry, offering a new perspective towards transition metal based single-molecule magnets.

State-Interaction Approach for Evaluating g-Tensors within EOM-CC and RAS-CI Frameworks: Theory and Benchmarks

Among various techniques designed for studying open-shell species, electron paramagnetic resonance (EPR) spectroscopy plays an important role. The key quantity measured by EPR is the g-tensor, describing the coupling between an external magnetic field and molecular electronic spin. One theoretical framework for quantum chemistry calculations of g-tensors is based on response theory, which involves substantial developments that are specific to the underlying electronic structure models. A simplified and easier-to-implement approach is based on the state-interaction scheme, in which perturbation is included by considering a small number of states. We describe and benchmark the state-interaction approach using equation-of-motion coupled-cluster and restricted-active-space configuration interaction wave functions. The analysis confirms that this approach can deliver accurate results and highlights caveats of applying it, such as a choice of the reference state, convergence with respect to the number of states used in calculations, etc. The analysis also contributes toward a better understanding of challenges in calculations of higher-order properties using approximate wave functions.

Eu3+ ions as a crystal-field probe for low-symmetry sites in doped phosphors - a case study: Eu3+ at triclinic sites in Li6RE(BO3)3 (RE = Y, Gd), YBO3 and ZnO and at trigonal sites in YAl3(BO3)4

We present crystal-field (CF) calculations of energy levels (Ei) of Eu3+ ions doped in various hosts aimed at exploring the low-symmetry properties of CF parameters (CFPs) and reliability of CFP modelling with decreasing site symmetry. The hosts studied are: Li6Y(BO3)3, Li6Gd(BO3)3, YBO3, and ZnO with Eu3+ at triclinic sites; YAl3(BO3)4 with Eu3+ ions at trigonal D3 symmetry. Two independent CFP modelling approaches utilizing the hosts' structural data are employed: the exchange charge model (ECM) and the superposition model (SPM). We adopt the Eu3+ actual site symmetry and not the approximated one. The Ei values calculated using CFPs modelled by the ECM and SPM mutually agree with the observed ones. For triclinic symmetry, the ECM/CFPs and SPM/CFPs were numerically distinct, yet turned out to be physically equivalent yielding identical rotational invariants, Sk (k = 2, 4, 6) and Ei. For trigonal symmetry, both CFP sets agree numerically, thus Sk and Ei are identical. This disparity poses a dilemma, since the modified crystallographic axis system was used in both approaches. The standardization of the triclinic CFPs using the 3DD package was performed to solve this dilemma. It has enabled discussing standardization aspects in experimental and computed CFP sets and elucidating intricate low-symmetry aspects inherent in CFP sets. Understanding of low-symmetry aspects in CF studies may bring about a better interpretation of the spectroscopic and magnetic properties of rare-earth ion doped host crystals. Thus, our study could provide more deep insights into the importance of clear definitions of axis systems and adequate treatment of actual site symmetry in the modelling of CFPs for low-symmetry cases which is essential for technological applications and engineering of rare-earth activated phosphor materials.

Spectroscopic and Magnetic Studies of Co(II) Scorpionate Complexes: Is There a Halide Effect on Magnetic Anisotropy?

The observation of single-molecule magnetism in transition-metal complexes relies on the phenomenon of zero-field splitting (ZFS), which arises from the interplay of spin-orbit coupling (SOC) with ligand-field-induced symmetry lowering. Previous studies have demonstrated that the magnitude of ZFS in complexes with 3d metal ions is sometimes enhanced through coordination with heavy halide ligands (Br and I) that possess large free-atom SOC constants. In this study, we systematically probe this "heavy-atom effect" in high-spin cobalt(II)-halide complexes supported by substituted hydrotris(pyrazol-1-yl)borate ligands (Tp^tBu,Me and Tp^Ph,Me). Two series of complexes were prepared: [Co^IIX(Tp^tBu,Me)] (1-X; X = F, Cl, Br, and I) and [Co^IIX(Tp^Ph,Me)(Hpz^Ph,Me)] (2-X; X = Cl, Br, and I), where Hpz^Ph,Me is a monodentate pyrazole ligand. Examination with dc magnetometry, high-frequency and -field electron paramagnetic resonance, and far-infrared magnetic spectroscopy yielded axial (D) and rhombic (E) ZFS parameters for each complex. With the exception of 1-F, complexes in the four-coordinate 1-X series exhibit positive D-values between 10 and 13 cm^-1, with no dependence on halide size. The five-coordinate 2-X series exhibit large and negative D-values between -60 and -90 cm^-1. Interpretation of the magnetic parameters with the aid of ligand-field theory and ab initio calculations elucidated the roles of molecular geometry, ligand-field effects, and metal-ligand covalency in controlling the magnitude of ZFS in cobalt-halide complexes.

Effects of distortions in ion-host systems on optical spectra, crystal-field and spin-Hamiltonian parameters of Cr3+ ions doped pyrochlores Y2Ti2O7 and Y2Sn2O7: exchange charge model and superposition model calculations

Comparative modelling of the crystal-field parameters (CFPs), CF energy levels, and effective spin-Hamiltonian parameters (SHPs), i.e., the g-factors and zero-field splitting parameter (ZFSP), D, of the ground state ⁴A_2g of the Cr³⁺ dopant ions in Y₂Ti₂O₇ and Y₂Sn₂O₇ is carried out. The CFPs are calculated using XRD structural data by employing two semi-empirical models: the exchange charge model (ECM) and superposition model (SPM). This two-fold approach ensures increased reliability of CFP modelling and thus of the final results. The modelled CFPs serve as the input to the crystal-field analysis/microscopic spin-Hamiltonian (CFA/MSH) program to predict CF energy levels and wave functions, and to extract SHPs. Since the site symmetry of Cr³⁺ ions in these crystals is trigonal D_3d, a symmetry adapted axis system (SAAS) conforming to Watanabe convention is adopted for CFP modelling. The calculated CF energies and SHPs for Y₂Ti₂O₇:Cr³⁺ are in good agreement with the experimental results. Variations of the Racah parameter B, as well as ECM and SPM parameters for Y₂Sn_2-xCr_xO₇ are correlated with the chromium concentration (x), which affects distortions of CrO₆ structures. We find that the SHPs originate predominantly from the spin-orbit coupling, though contributions from spin-spin and spin-other-orbit couplings are also appreciable and thus important for analysis of lattice distortions and structural disorder. The uniqueness of the SAAS used for CFP modelling is also discussed. The present study enables exploring the influence of the radial and angular distortions of host clusters (Ti-O₆/Sn-O₆) introduced by Cr³⁺ ions on the structural and optical properties as well as the SHPs of Cr³⁺ ions doped in Y₂Ti₂O₇ and Y₂Sn₂O₇.

Efficient Multiconfigurational Quantum Chemistry Approach to Single-Ion Magnets Based on Density Matrix Embedding Theory

Density matrix embedding theory (DMET) provides a systematic framework to combine low-level (e.g., Hartree-Fock approximation) and high-level correlated quantum chemistry methods to treat strongly correlated systems. In this work, we propose an efficient quantum embedding approach that combines DMET with the complete active space self-consistent field and subsequent state interaction treatment of spin-orbit coupling (CASSI-SO) and apply it to a theoretical description of single-ion magnets (SIMs). We have developed a novel regularized direct inversion of iterative subspace (R-DIIS) technique that ensures restricted open-shell Hartree-Fock converging to a physically correct ground state, which is found to be crucial for the efficacy of subsequent CASSI-SO calculation. The DMET+CASSI-SO approach can produce reliable zero-field splitting parameters in typical 3d-SIMs with dramatically reduced computational cost compared to its all-electron counterpart. This work therefore demonstrates the great potential of DMET-based multiconfigurational approaches for efficient ab initio study of magneto-structural correlations in complex molecular magnetic systems.

Computational design of magnetic molecules and their environment using quantum chemistry, machine learning and multiscale simulations

Having served as a playground for fundamental studies on the physics of d and f electrons for almost a century, magnetic molecules are now becoming increasingly important for technological applications, such as magnetic resonance, data storage, spintronics and quantum information. All of these applications require the preservation and control of spins in time, an ability hampered by the interaction with the environment, namely with other spins, conduction electrons, molecular vibrations and electromagnetic fields. Thus, the design of a novel magnetic molecule with tailored properties is a formidable task, which does not only concern its electronic structures but also calls for a deep understanding of the interaction among all the degrees of freedom at play. This Review describes how state-of-the-art ab initio computational methods, combined with data-driven approaches to materials modelling, can be integrated into a fully multiscale strategy capable of defining design rules for magnetic molecules.

Iron Insertion at the Assembly Site of the ISCU Scaffold Protein Is a Conserved Process Initiating Fe-S Cluster Biosynthesis

Iron-sulfur (Fe-S) clusters are prosthetic groups of proteins biosynthesized on scaffold proteins by highly conserved multi-protein machineries. Biosynthesis of Fe-S clusters into the ISCU scaffold protein is initiated by ferrous iron insertion, followed by sulfur acquisition, via a still elusive mechanism. Notably, whether iron initially binds to the ISCU cysteine-rich assembly site or to a cysteine-less auxiliary site via N/O ligands remains unclear. We show here by SEC, circular dichroism (CD), and Mössbauer spectroscopies that iron binds to the assembly site of the monomeric form of prokaryotic and eukaryotic ISCU proteins via either one or two cysteines, referred to the 1-Cys and 2-Cys forms, respectively. The latter predominated at pH 8.0 and correlated with the Fe-S cluster assembly activity, whereas the former increased at a more acidic pH, together with free iron, suggesting that it constitutes an intermediate of the iron insertion process. Iron not binding to the assembly site was non-specifically bound to the aggregated ISCU, ruling out the existence of a structurally defined auxiliary site in ISCU. Characterization of the 2-Cys form by site-directed mutagenesis, CD, NMR, X-ray absorption, Mössbauer, and electron paramagnetic resonance spectroscopies showed that the iron center is coordinated by four strictly conserved amino acids of the assembly site, Cys35, Asp37, Cys61, and His103, in a tetrahedral geometry. The sulfur receptor Cys104 was at a very close distance and apparently bound to the iron center when His103 was missing, which may enable iron-dependent sulfur acquisition. Altogether, these data provide the structural basis to elucidate the Fe-S cluster assembly process and establish that the initiation of Fe-S cluster biosynthesis by insertion of a ferrous iron in the assembly site of ISCU is a conserved mechanism.

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.

Giant Rotational Magnetocaloric Effect in Ni(en)(H2O)4·2H2O: Experiment and Theory

An experimental study of the rotational magnetocaloric effect in Ni(en)(H2O)4SO4∙2H2O (en = ethylenediamine) single crystal is presented. The study was carried out at temperatures above 2 K and was associated with adiabatic crystal rotation between the easy plane and hard axis in magnetic fields up to 7 T. The magnetocaloric properties of the studied system were investigated by isothermal magnetization measurement. The experimental observations were completed with ab initio calculations of the anisotropy parameters. A large rotational magnetic entropy change ≈12 Jkg−1K−1 and ≈16.9 Jkg−1K−1 was achieved in 5 T and 7 T, respectively. The present study suggests a possible application of this material in low-temperature refrigeration since the adiabatic rotation of the single crystal in 7 T led to a cooldown of the sample from the initial temperature of 4.2 K down to 0.34 K. Finally, theoretical calculations show that S = 1 Ni(II)-based systems with easy-plane anisotropy can have better rotational magnetocaloric properties than costly materials containing rare-earth elements in their chemical structures.

Hexacoordinate high-spin Fe(III) complexes composed of pentadentate amino-type ligand and pseudohalido coligands

A new series of Fe(III) mononuclear complexes of [Fe(Lam)(X)] type {where X = Cl (1), NCSe (2), NCS (3), N3 (4), NCO (5)} have been prepared and characterized in detail....

An exchange interaction of the antiferromagnetic nature in benzoate bridged Mn(ii) chains

Two novel 1D chains based on heptacoordinated Mn(ii) ions bridged by variously derived benzoate ligands were prepared.

Unusual Slow Magnetic Relaxation in a Mononuclear Copper(II) Complex

A hexacoordinate Cu(II) complex with the {CuO4O’N} donor set shows an intermolecular π-πstacking owing to which a 1D-chain structure is formed. The DC magnetic data at low temperature is consistent...

16OSTM10: A new open-shell transition metal conformational energies database to challenge contemporary semiempirical and force field methods

transition metal (OSTM) complexes has been developed. Contemporary composite density functional theory (DFT) (PBEh-3c, B97-3c), semiempirical (PM6, PM7) and the methods of GFNn-xTB/FF family were examined against conventional DFT (PBE-D3(BJ),...

Thermally Averaged Magnetic Anisotropy Tensors via Machine Learning Based on Gaussian Moments

We propose a machine learning method to model molecular tensorial quantities, namely, the magnetic anisotropy tensor, based on the Gaussian moment neural network approach. We demonstrate that the proposed methodology can achieve an accuracy of 0.3-0.4 cm^-1 and has excellent generalization capability for out-of-sample configurations. Moreover, in combination with machine-learned interatomic potential energies based on Gaussian moments, our approach can be applied to study the dynamic behavior of magnetic anisotropy tensors and provide a unique insight into spin-phonon relaxation.

Equation-of-Motion Coupled-Cluster Protocol for Calculating Magnetic Properties: Theory and Applications to Single-Molecule Magnets

We present a new computational protocol for computing macroscopic magnetic properties of transition-metal complexes using the equation-of-motion coupled-cluster (EOM-CC) framework. The approach follows a two-step state-interaction scheme: we first compute zero-order states using nonrelativistic EOM-CC and then use these states to evaluate matrix elements of the spin-orbit and Zeeman operators. Diagonalization of the resulting Hamiltonian yields spin-orbit- and field-perturbed eigenstates. Temperature- and field-dependent magnetization and susceptibility are computed by numerical differentiation of the partition function. To compare with powder-sample experiments, these quantities are numerically averaged over field orientations. We applied this protocol to several single-molecule magnets (SMMs) with Fe(II) and Fe(III) in trigonal pyramidal, linear, and trigonal bipyramidal coordination environments. We described the underlying electronic structure by the electron-attachment (EOM-EA) and spin-flip (EOM-SF) variants of EOM-CC. The computed energy barriers for spin inversion, and macroscopic magnetization and susceptibility agree well with experimental data. Trends in magnetic anisotropy and spin-reversal energy barriers are explained in terms of a molecular orbital picture rigorously distilled from spinless transition density matrices between many-body states. The results illustrate excellent performances of EOM-CC in describing magnetic behavior of mononuclear transition-metal SMMs.

Tetrairon(II) extended metal atom chains as single-molecule magnets

Iron-based extended metal atom chains (EMACs) are potentially high-spin molecules with axial magnetic anisotropy and thus candidate single-molecule magnets (SMMs). We herein compare the tetrairon(ii), halide-capped complexes [Fe4(tpda)3Cl2] (1Cl) and [Fe4(tpda)3Br2] (1Br), obtained by reacting iron(ii) dihalides with [Fe2(Mes)4] and N2,N6-di(pyridin-2-yl)pyridine-2,6-diamine (H2tpda) in toluene, under strictly anhydrous and anaerobic conditions (HMes = mesitylene). Detailed structural, electrochemical and Mössbauer data are presented along with direct-current (DC) and alternating-current (AC) magnetic characterizations. DC measurements revealed similar static magnetic properties for the two derivatives, with χMT at room temperature above that for independent spin carriers, but much lower at low temperature. The electronic structure of the iron(ii) ions in each derivative was explored by ab initio (CASSCF-NEVPT2-SO) calculations, which showed that the main magnetic axis of all metals is directed close to the axis of the chain. The outer metals, Fe1 and Fe4, have an easy-axis magnetic anisotropy (D = -11 to -19 cm-1, |E/D| = 0.05-0.18), while the internal metals, Fe2 and Fe3, possess weaker hard-axis anisotropy (D = 8-10 cm-1, |E/D| = 0.06-0.21). These single-ion parameters were held constant in the fitting of DC magnetic data, which revealed ferromagnetic Fe1-Fe2 and Fe3-Fe4 interactions and antiferromagnetic Fe2-Fe3 coupling. The competition between super-exchange interactions and the large, noncollinear anisotropies at metal sites results in a weakly magnetic non-Kramers doublet ground state. This explains the SMM behavior displayed by both derivatives in the AC susceptibility data, with slow magnetic relaxation in 1Br being observable even in zero static field.

Magnetic Anisotropy in a Cubane-like Ni4 Complex: An Ab Initio Perspective

Magnetic anisotropy, in the absence of an external magnetic field, relates to the degeneracy lift of energy levels. In the standard case of transition metal complexes, this property is usually modeled by an anisotropic spin Hamiltonian and one speaks of "zero-field splitting" (ZFS) of spin states. While the case of mononuclear complexes has been extensively described by means of ab initio quantum mechanical calculations, the literature on polynuclear complexes studied with these methodologies is rather scarce. In this work, advanced multiconfigurational wave function theory methods are applied to compute the ZFS of the ground S = 4 state of an actual tetranickel(II) complex, displaying a magnet behavior below 0.5 K. First, the isotropic couplings are computed in the absence of the spin-orbit coupling operator, in the full complex and also in clusters with only two active nickel(II) centers, confirming the occurrence of weak ferromagnetic couplings in this system. Second, the single-site magnetic anisotropies are computed on a cluster bearing only one active nickel(II) site, showing that the single-site anisotropy axes are not oriented in an optimal fashion for generating a large uniaxial molecular anisotropy. Furthermore, the possibility for involving only a few local orbital excited states in the calculation is assessed, actually opening the way for a consistent and manageable treatment of the ZFS of the ground S = 4 state. Third, multiconfigurational calculations are performed on the full complex, confirming the weak uniaxial anisotropy occurring for this state and also, interestingly, revealing a significant contribution of the lowest-lying orbitally excited S = 3 states. Overall, by comparison with the experiment, the reported results question the common habit of using only one structure, in particular derived from a crystallography experiment, to compute magnetic anisotropy parameters.

First-Principles Investigations of Magnetic Anisotropy and Spin-Crossover Behavior of Fe(III)-TBP Complexes

With the ongoing effort to obtain mononuclear 3d-transition-metal complexes that manifest slow relaxation of magnetization and, hence, can behave as single-molecule magnets (SMMs), we have modeled 14 Fe(III) complexes based on an experimentally synthesized (PMe₃)₂FeCl₃ complex [J. Am. Chem. Soc. 2017, 139 (46), 16474-16477], by varying the axial ligands with group XV elements (N, P, and As) and equatorial halide ligands from F, Cl, Br, and I. Out of these, nine complexes possess large zero field splitting (ZFS) parameter D in the range of -40 to -60 cm^-1. The first-principles investigation of the ground-spin state applying density functional theory (DFT) and wave function-based multiconfigurations methods, e.g., SA-CASSCF/NEVPT2, are found to be quite consistent except for few delicate cases with near-degenerate spin states. In such cases, the hybrid B3LYP functional is found to be biased toward high-spin (HS) state. Altering the percentage of exact exchange admixed in the B3LYP functional leads to intermediate-spin (IS) ground state consistent with the multireference calculations. The origin of large zero field splitting (ZFS) in the Fe(III)-based trigonal bipyramidal (TBP) complexes is investigated. Furthermore, a number of complexes are identified with very small ΔG_HS-IS^adia. values indicating the possible spin-crossover phenomenon between the bistable spin states.

A Mixed Valence CoIICoIII2 Field-Supported Single Molecule Magnet: Solvent-Dependent Structural Variation

One-pot reaction of the Schiff base N,N’-ethylene bis(salicylaldimine) (H₂L), CoCl₂.6H₂O, and [Ph₂SnCl₂] in acetone produces the mixed valence Co^IICo^III₂ compound [Co^IICo^III₂(μ-L)₂(Ph)₂(μ-Cl)₂]·(CH₃)₂CO·H₂O (1). Our recent study already revealed that the same reaction mixtures in methanol or ethanol produced a heterometallic Sn^IVCo^III (2) or monometallic Co^III complex (3), respectively. Comparison of these organometallic systems shows that the 2,1-intermetallic Ph shift occurs in any of those solvents, but their relevant structural features (mononuclear, dinuclear-heterometallic, and trinuclear mixed valence) are solvent dependent. Geometrical structural rotation is also discussed among the related organometallic Co^IICo^III₂ systems. The AC magnetic susceptibility measurements indicate that 1 is a single molecule magnet (SMM), exhibiting a field-induced slow magnetic relaxation with two modes. The relaxation time for the low-frequency channel is as slow as τ~0.6 s at T = 2.0 K and B_DC = 1.0 T.

Syntheses, structures and magnetic properties of two isostructural dicyanamide-bridged 2D polymers

Complexes [Co(biq)(μ_1,5-dca)₂]_n (1) and [Ni(biq)(μ_1,5-dca)₂]_n (2) (biq is 2,2′-biquinoline, dca is dicyanamide anion, N(CN)₂⁻) have been characterized by crystal structure analysis, and spectral and magnetic measurements.

Role of Coordination Number and Geometry in Controlling the Magnetic Anisotropy in FeII , CoII , and NiII Single-Ion Magnets

Since the last decade, the focus in the area of single-molecule magnets (SMMs) has been shifting constructively towards the development of single-ion magnets (SIMs) based on transition metals and lanthanides. Although ground-breaking results have been witnessed for Dy^III -based SIMs, significant results have also been obtained for some mononuclear transition metal SIMs. Among others, studies based on Co^II ion are very prominent as they often exhibit high magnetic anisotropy or zero-field splitting parameters and offer a large barrier height for magnetisation reversal. Although Co^II possibly holds the record for having the largest number of zero-field SIMs known for any transition metal ion, controlling the magnetic anisotropy in these systems are is still a challenge. In addition to the modern spectroscopic techniques, theoretical studies, especially ab initio CASSCF/NEVPT2 approaches, have been used to uncover the electronic structure of various Co^II SIMs. In this article, with some selected examples, the aim is to showcase how varying the coordination number from two to eight, and the geometry around the Co^II centre alters the magnetic anisotropy. This offers some design principles for the experimentalists to target new generation SIMs based on the Co^II ion. Additionally, some important Fe^II /Fe^III and Ni^II complexes exhibiting large magnetic anisotropy and SIM properties are also discussed.

Spin-phonon coupling and dynamic zero-field splitting contributions to spin conversion processes in iron(II) complexes

Magnetization dynamics of transition metal complexes manifest in properties and phenomena of fundamental and applied interest [e.g., slow magnetic relaxation in single molecule magnets, quantum coherence in quantum bits (qubits), and intersystem crossing (ISC) rates in photophysics]. While spin-phonon coupling is recognized as an important determinant of these dynamics, additional fundamental studies are required to unravel the nature of the coupling and, thus, leverage it in molecular engineering approaches. To this end, we describe here a combined ligand field theory and multireference ab initio model to define spin-phonon coupling terms in S = 2 transition metal complexes and demonstrate how couplings originate from both the static and dynamic properties of ground and excited states. By extending concepts to spin conversion processes, ligand field dynamics manifest in the evolution of the excited state origins of zero-field splitting (ZFS) along specific normal mode potential energy surfaces. Dynamic ZFSs provide a powerful means to independently evaluate contributions from spin-allowed and/or spin-forbidden excited states to spin-phonon coupling terms. Furthermore, ratios between various intramolecular coupling terms for a given mode drive spin conversion processes in transition metal complexes and can be used to analyze the mechanisms of ISC. Variations in geometric structure strongly influence the relative intramolecular linear spin-phonon coupling terms and will define the overall spin state dynamics. While the findings of this study are of general importance for understanding magnetization dynamics, they also link the phenomenon of spin-phonon coupling across fields of single molecule magnetism, quantum materials/qubits, and transition metal photophysics.

Electronic Structure and Magnetic Properties of a Titanium(II) Coordination Complex

Stable coordination complexes of Ti^II (3d²) are relatively uncommon, but are of interest as synthons for low oxidation state titanium complexes for application as potential catalysts and reagents for organic synthesis. Specifically, high-spin Ti^II ions supported by redox-inactive ligands are still quite rare due to the reducing power of this soft ion. Among such Ti^II complexes is trans-[TiCl₂(tmeda)₂], where tmeda = N,N,N',N'-tetramethylethane-1,2-diamine. This complex was first reported by Gambarotta and co-workers almost 30 years ago, but it was not spectroscopically characterized and theoretical investigation by quantum chemical theory (QCT) was not feasible at that time. As part of our interest in low oxidation state early transition metal complexes, we have revisited this complex and report a modified synthesis and a low temperature (100 K) crystal structure that differs slightly from that originally reported at ambient temperature. We have used magnetometry, high-frequency and -field EPR (HFEPR), and variable-temperature variable-field magnetic circular dichroism (VTVH-MCD) spectroscopies to characterize trans-[TiCl₂(tmeda)₂]. These techniques yield the following S = 1 spin Hamiltonian parameters for the complex: D = -5.23(1) cm^-1, E = -0.88(1) cm^-1, (E/D = 0.17), g = [1.86(1), 1.94(2), 1.77(1)]. This information, in combination with electronic transitions from MCD, was used as input for both classical ligand-field theory (LFT) and detailed QCT studies, the latter including both density functional theory (DFT) and ab initio methods. These computational methods are seldom applied to paramagnetic early transition metal complexes, particularly those with S > 1/2. Our studies provide a complete picture of the electronic structure of this complex that can be put into context with the few other high-spin and mononuclear Ti^II species characterized to date.

Effect of the distant substituent on the slow magnetic relaxation of the mononuclear Co(ii) complex with pincer-type ligands

A hexacoordinated complex [Co(pydm)2](mdnbz)2 from the family of pincer complexes was prepared and structurally characterized. The complex behaves as an S = 3/2 spin system with a considerable zero-field splitting parameter D/hc ∼ +50 cm-1. The AC susceptibility measurements show a slow magnetic relaxation with three relaxation channels: at the low-frequency (LF), intermediate-frequency (IF) and high-frequency (HF) domains. At T = 2.0 K and an external field BDC = 0.25 T, the relaxation times of the individual modes are τ(LF) = 282 ms, τ(IF) = 3.1 ms, and τ(HF) = 0.16 ms, and the mole fractions of the slowly relaxing species are x(LF) = 0.19, x(IF) = 0.45, and x(HF) = 0.37. A comparison with the analogous complex [Co(pydm)2](dnbz)2 possessing a demethylated counter anion and identical metal cation shows that even small modifications in the composition of SIMs are no longer underestimated for the slow magnetic relaxation.

Slow magnetic relaxation in hexacoordinated cobalt(ii) field-induced single-ion magnets

To gain an insight into the factors affecting the enhancement of the energy barrier in SMM/SIM, hexacoordinate pseudohalide Co(ii) complexes based on the tridentate ligand were investigated.

Multireference Ab Initio Studies of Magnetic Properties of Terbium-Based Single-Molecule Magnets

We investigate how different chemical environments influence magnetic properties of terbium(III) (Tb)-based single-molecule magnets (SMMs), using first-principles relativistic multireference methods. Recent experiments showed that Tb-based SMMs can have exceptionally large magnetic anisotropy and that they can be used for experimental realization of quantum information applications, with a judicious choice of chemical environment. Here, we perform complete active space self-consistent field calculations including relativistic spin-orbit interaction for representative Tb-based SMMs such as TbPc₂ and TbPcNc in three charge states. We calculate the low-energy electronic structure from which we compute the Tb crystal-field (CF) parameters and construct an effective pseudospin Hamiltonian. Our calculations show that the ligand type and fine points of molecular geometry do not affect the gap between the ground-state and first-excited doublets, whereas the latter varies weakly with oxidation number. On the other hand, higher-energy levels have a strong dependence on all these characteristics. For neutral TbPc₂ and TbPcNc molecules, the Tb magnetic moment and ligand spin are parallel to each other and the coupling strength between them does not depend much on the ligand type and details of the atomic structure. However, ligand distortion and molecular symmetry play a crucial role in transverse CF parameters which lead to tunnel splitting. The tunnel splitting induces quantum tunneling of magnetization by itself or by combining with other processes. Our results provide insights into the mechanisms of magnetization relaxation in the representative Tb-based SMMs.

Anionic guest-dependent slow magnetic relaxation in Co(ii) tripodal iminopyridine complexes

We report the syntheses and magnetic property characterizations of four mononuclear cobalt(ii) complex salts featuring a tripodal iminopyridine ligand with external anion receptor groups, [CoL5-ONHtBu]X2 (X = Cl (1), Br (2), I (3) and ClO4 (4)). While all four salts exhibit anion binding through pendant amide moieties, only in the case of 1 is field-induced slow relaxation of magnetisation observed, whereas in the other salts this phenomenon is absent at the limits of our instrumentation. The effect of chloride inducing a seventh Co-N interaction and concomitant structural distortion is hypothesized as the origin of the observed dynamic magnetic properties observed in 1. Ab initio computational studies carried out on a 7-coordinate Co(ii) model species survey the complex interplay of coordination number and trigonal twisting on the sign and magnitude of the axial anisotropy parameter (D), and identify structural features whose distortions can trigger large switches in the sign and magnitude of magnetic anisotropy.

1D coordination polymer (OPD)2CoIISO4 showing SMM behaviour and multiple relaxation modes

A novel one-dimensional Co^II coordination polymer (OPD)₂Co^IISO₄ was formed from alternating tetrahedral sulphate anions, Co centers and molecules of 1,2-phenylenediamine (OPD). The thermal stability of the structure was confirmed up to ∼230 °C using thermogravimetry and non-ambient powder X-ray diffraction in air. The distorted pseudo-octahedral coordination sphere of Co^II ions promotes strong magnetic anisotropy. Therefore (OPD)₂Co^IISO₄ was subjected to thorough characterization with ab initio and DFT calculations along with dc magnetic measurements both of which point to strong easy-axis anisotropy (D/k_B≈-87 K, E/k_B≈ 23 K). The analysis of ac susceptibility revealed field assisted magnetic relaxation in two field regimes: a low field one with one relaxation time and a high field one where three relaxation times were distinguished. The main role in relaxations of the fastest process (τ₁) was attributed to the direct and Raman processes.

Exceptionally slow magnetic relaxation in a mononuclear hexacoordinate Ni(ii) complex

A hexacoordinate mononuclear [Ni(pydm)₂](dnbz)₂ complex shows field-induced slow magnetic relaxation with two or three relaxation channels that are strongly supported by an external magnetic field.

Rhodium(i) complexes with carborane-substituted P,N ligands: investigations of electronic structure and dynamic behaviour

Two distorted square-planar RhI complexes (1 and 2) were obtained from [{RhCl(η4-cod)}2] and the respective P,N ligands. The metal-ligand interaction was probed with density functional theory (DFT) and ab initio (CASSCF-NEVPT2) calculations. NMR spectroscopy proved dynamic binding behaviour of the ligands in solution. The tetradenticity of the ligands also affects the electrochemical behaviour of complexes 1 and 2 significantly. Finally, preliminary catalytic studies, namely the dehydrocoupling of dimethylamine-borane, are presented.

Slow magnetic relaxation in a high-spin pentacoordinate Fe(iii) complex

A mononuclear pentacoordinate iron(iii) complex shows slow magnetic relaxation with three relaxation channels.