Crystal Field in Rare‐Earth Complexes: From Electrostatics to Bonding

Electronic Structure of a Neodymium(III) Tris(oxidiacetate) Complex from Luminescence Data and Ab Initio Calculations

Neodymium(III) is a near-infrared emissive and magnetic ion, which has found use in various high-technology applications. Yet, accurate predictions of the luminescent and magnetic properties of neodymium(III) based on the coordination environment remain to be done. Guidelines exist, but to build structure-property relationships for this element, more data are needed. Herein, we present a high-symmetry starting point. The tris(oxidiacetate) complex of neodymium(III) was prepared and crystallized, and access to the experimentally determined structure allowed us to quantify the symmetry of the compound and to perform calculations directly on the same structure that is investigated experimentally. The luminescent properties were determined and the electronic structure was computed using state-of-the-art ab initio methods. All electronic transitions in the range from 490 to 1400 nm were mapped experimentally. Using a Boltzmann population analysis, the combination of the excitation and emission spectra revealed the crystal field splitting of the 18 lowest-energy Kramers levels that experimentally could be unambiguously resolved. This assignment was supported by ab initio calculations, and the crystal field splitting was well reproduced. The electronic structure reported for the tris(oxidiacetate) complex was used to deduce the coordination structure in aqueous solution. Finally, the results are compared to empirical trends in the literature for the electronic structure of neodymium(III).

Unravelling the electronic structure, bonding, and magnetic properties of inorganic dysprosocene analogues [Dy(E4)2]- (E = N, P, As, CH)

Organometallic sandwich complexes of Dy(III) ion are ubiquitous for designing high-temperature single-ion magnets with blocking temperatures close to the liquid nitrogen boiling point. Magnetic bistability at the molecular level makes them potential candidates for nano-scale information storage materials. In the present contribution, we have thoroughly investigated the electronic structure, bonding, covalency, and magnetic anisotropy of inorganic dysprosocene complexes with a general formula of [Dy(E4)2]- (where E = N, P, As, CH) using state-of-the-art scalar relativistic density functional theory (SR-DFT), and a multiconfigurational complete active space self-consistent field (CASSCF) method with the N-electron valence perturbation theory (NEVPT2). Geometry optimization calculations predict stabilization of the [Dy(E4)2]- complexes with a linear geometry and D4h local symmetry Dy(III) ion in [Dy(N4)2]- (1) and [Dy(P4)2]- (2) complexes, while a bent geometry has been observed for the [Dy(As4)2]- (3), [Dy(P2(CH)2)2]- (4), and [Dy(As2(CH)2)2]- (5) complexes. Energy decomposition analysis (EDA) and natural bonding orbital (NBO) calculations reveal sizable 5d-ligand covalency followed by 6s/6p and weak 4f-ligand covalency in complexes 1-5. Both the natural localized molecular orbitals (NLMOs) at the DFT level and ab initio-based ligand field theory (AILFT) at the NEVPT2 level of theory predict an increase in the Dy-ligand covalency as we move from N to As. Spin-Hamiltonian parameter analysis of complexes 1-5 reveals stabilization of the mJ |±15/2〉 as the ground state with highly axial g values (gxx ∼ gyy ∼ 0 and gzz ∼ 20) and the barrier height of 2902, 1214, 1104, 1845, and 1509 K for 1-5, respectively. The Orbach effective demagnetization barrier (Ueff) for complexes 1-5 ranges between 2416-1175 K, with a record Ueff value of 2416 K observed for 1. In addition, we have explored the role of heavy element effects on the magnetic anisotropy by turning off the spin-orbit coupling of the pnictogens (N, P, and As), and our calculations clearly predict that heavy atoms in the first coordination sphere help in increasing the barrier height for magnetic relaxation. Heavy elements like P and As significantly enhance the SOC contributions, thereby providing a platform for designing and optimizing Dy(III) complexes with tailored magnetic behaviors.

Covalency versus magnetic axiality in Nd molecular magnets: Nd-photoluminescence, strong ligand-field, and unprecedented nephelauxetic effect in fullerenes NdM2N@C80 (M = Sc, Lu, Y)

Nd-based nitride clusterfullerenes NdM2N@C80 with rare-earth metals of different sizes (M = Sc, Y, Lu) were synthesized to elucidate the influence of the cluster composition, shape and internal strain on the structural and magnetic properties. Single crystal X-ray diffraction revealed a very short Nd-N bond length in NdSc2N@C80. For Lu and Y analogs, the further shortening of the Nd-N bond and pyramidalization of the NdM2N cluster are predicted by DFT calculations as a result of the increased cluster size and a strain caused by the limited size of the fullerene cage. The short distance between Nd and nitride ions leads to a very large ligand-field splitting of Nd3+ of 1100-1200 cm-1, while the variation of the NdM2N cluster composition and concomitant internal strain results in the noticeable modulation of the splitting, which could be directly assessed from the well-resolved fine structure in the Nd-based photoluminescence spectra of NdM2N@C80 clusterfullerenes. Photoluminescence measurements also revealed an unprecedentedly strong nephelauxetic effect, pointing to a high degree of covalency. The latter appears detrimental to the magnetic axiality despite the strong ligand field. As a result, the ground magnetic state has considerable transversal components of the pseudospin g-tensor, and the slow magnetic relaxation of NdSc2N@C80 could be observed by AC magnetometry only in the presence of a magnetic field. A combination of the well-resolved magneto-optical states and slow relaxation of magnetization suggests that Nd clusterfullerenes can be useful building blocks for magneto-photonic quantum technologies.

Understanding Single-Molecule Magnet properties of lanthanide complexes from 4f orbital splitting

We present an approach for connecting the magnetic anisotropy of lanthanide mononuclear complexes with their f-orbital splitting for both idealized and real coordination environments. Our proposal is straightforward to apply and provides sensible estimations of the energy spacing of the ground multiplet for axial magnetic systems. This energy splitting controls Single-Molecule Magnet properties of lanthanide complexes, determining key parameters such as the demagnetization energy barrier (Ueff). Importantly, this approach is consistent with the current paradigm of oblate and prolate preferences for the distribution of the f-electron density, but delivers a finer description for ions belonging to the same group (e.g. the oblates TbIII and DyIII). The model provides simple explanations for some general trends observed experimentally (e.g. the low barriers for ErIII complexes in comparison to DyIII or the large barriers observed for cyclopentadienyl DyIII complexes in comparison with other ligands based on organometallic rings), contributing as a valuable tool to expand our description of ligand field effects in lanthanide-based SMMs.

Strengths of covalent bonds in LnO2 determined from O K-edge XANES spectra using a Hubbard model

In LnO2 (Ln = Ce, Pr, and Tb), the amount of Ln 4f mixing with O 2p orbitals was determined by O K-edge X-ray absorption near edge (XANES) spectroscopy and was similar to the amount of mixing between the Ln 5d and O 2p orbitals. This similarity was unexpected since the 4f orbitals are generally perceived to be "core-like" and can only weakly stabilize ligand orbitals through covalent interactions. While the degree of orbital mixing seems incompatible with this view, orbital mixing alone does not determine the degree of stabilization provided by a covalent interaction. We used a Hubbard model to determine this stabilization from the energies of the O 2p to 4f, 5d(eg), and 5d(t2g) excited charge-transfer states and the amount of excited state character mixed into the ground state, which was determined using Ln L3-edge and O K-edge XANES spectroscopy. The largest amount of stabilization due to mixing between the Ln 4f and O 2p orbitals was 1.6(1) eV in CeO2. While this energy is substantial, the stabilization provided by mixing between the Ln 5d and O 2p orbitals was an order of magnitude greater consistent with the perception that covalent bonding in the lanthanides is largely driven by the 5d orbitals rather than the 4f orbitals.

Understanding electrostatics and covalency effects in highly anisotropic organometallic sandwich dysprosium complexes [Dy(CmRm)2] (where R = H, SiH3, CH3 and m = 4 to 9): a computational perspective

In this article, we have thoroughly studied the electronic structure and 4f-ligand covalency of six mononuclear dysprosium organometallic sandwich complexes [Dy(CmRm)2]n+/- (where R = H, SiH3, CH3; m = 4 to 9; n = 1, 3) using both the scalar relativistic density functional and complete active space self-consistent field (CASSCF) and N-electron valence perturbation theory (NEVPT2) method to shed light on the ligand field effects in fine-tuning the magnetic anisotropy of these complexes. Energy decomposition analysis (EDA) and ab initio-based ligand field theory AILFT calculations predict the sizable 4f-ligand covalency in all these complexes. The analysis of CASSCF/NEVPT2 computed spin-Hamiltonian (SH) parameters indicates the stabilization of mJ |±15/2〉 for [Dy(C4(SiH3)4)2]- (1), [Dy(C5(CH3)5)2]+ (2) and [Dy(C6H6)2]3+ (3) complexes with the Ucal value of 1867.5, 1621.5 and 1070.8 cm-1, respectively. On the other hand, we observed mJ |±9/2〉 as the ground state for [Dy(C7H7)2]3- (4) and [Dy(C8H8)2]- (5) complexes with significantly smaller Ucal values of 237.1 and 38.6 cm-1 respectively. For the nine-membered ring [Dy(C9H9)2]+ (6) complex, we observed the stabilization of the mJ |±1/2〉 ground state, with the first excited state being located ∼29 cm-1 higher in energy. AILFT-NEVPT2 ligand field splitting analysis indicates that the presence of π-type 4f-ligand interactions in complexes 1-3 help generate the axial-ligand field, while the δ-type interactions in complexes 4-5 generate the equatorial ligand field despite the ligands approaching from the axial direction. As the ring size increases, φ-type interactions dominate, generating a pure equatorial ligand field stabilising mJ |±1/2〉 as the ground state for 6. Calculations suggest that the nature of the ligand field mainly governs the Ucal values in the following order: 4f-Lσ > 4f-Lπ > 4f-Lδ > 4f-Lφ. Calculations were performed by replacing ligands with CHELPG charges to access the crystal field (CF) effects which suggests the stabilization of pure mJ |±15/2〉 in all the charge-embedded models (1Q-6Q). Our findings point out that the crystal field and ligand field effects complement each other and generate a giant barrier for magnetic relaxation in the small ring complexes 1-3, while a relatively weak crystal field and adverse 4f-Lδ/4f-Lφ interactions diminish the SMM behaviour in the large ring complexes 4-6.

Bonding and Magnetic Trends in the [AnIII(DPA)3]3- Series Compared to the Ln(III) and An(IV) Analogues

The crystal field parameters are determined from first-principles calculations in the [AnIII(DPA)3]3- series, completing previous work on the [LnIII(DPA)3]3- and [AnIV(DPA)3]2- series. The crystal field strength parameter follows the Ln(III) < An(III) < An(IV) trend. The parameters deduced at the orbital level decrease along the series, while J-mixing strongly impacts the many-electron parameters, especially for the Pu(III) complex. We further compile the available data for the three series. In some aspects, An(III) complexes are closer to Ln(III) than to An(IV) complexes with regard to the geometrical structure and bonding descriptors. At the beginning of the series, up to Pu(III), there is a quantitative departure from the free ion, especially for the Pa(III) complex. The magnetic properties of the actinides keep the trends of the lanthanides; in particular, the axial magnetic susceptibility follows Bleaney's theory qualitatively.

Ab initio non-covalent crystal field theory for lanthanide complexes: a multiconfigurational non-orthogonal group function approach

We present a multiconfigurational ab initio methodology based on non-orthogonal fragments for the calculation of crystal field energy levels and magnetic properties of lanthanide complexes, implementing a systematic description of non-covalent contributions to metal-ligand bonding. The approach consists of two steps. In the first step, appropriate ab initio wave functions for the various ionic fragments (lanthanide ions and coordinating ligands) are optimized separately, accounting for the influence of the surrounding environment within various approximations. In the second and final step, the scalar relativistic (DKH2) electrostatic Hamiltonian of the whole molecule is represented on the basis of the optimized metal-ligand multiconfigurational non-orthogonal group functions (MC-NOGFs), and reduced to an effective (2J + 1)-dimensional non-orthogonal configuration interaction (CI) problem via Löwdin-partitioning. Within the proposed formalism, the projected non-orthogonal CI Hamiltonian can be expanded to any desired order of perturbation theory in the fragment-localised excitations out of the degenerate space, and its eigenvalues and eigenfunctions provide systematic approximations to the crystal field energies and wave functions. We present here a preliminary implementation of the proposed MC-NOGF method developed for first-order degenerate perturbation theory within our own ab initio code CERES, and compare its performance both with the simpler non-covalent orthogonal ab initio approach, Fragment Ab Initio Model Potential (FAIMP) approximation, and the full CAHF/CASCI-SO method, accounting for metal-ligand covalency in a mean-field manner. We found that the energies and magnetic properties of 44 complexes obtained via an iteratively optimized version of our MC-NOGF first-order non-covalent method compare remarkably well with those obtained using the full CAHF/CASCI-SO method including metal-ligand covalency, thus exposing the predominantly electrostatic character of the metal-ligand interactions, and are superior to those obtained using the FAIMP approach, which in its iteratively optimised variant was believed to date to be the best ab initio description of non-covalent metal-ligand interactions.

Magnetic properties of organolanthanide(II) complexes, from the electronic structure and the crystal field effect

The magnetic properties of a series of organometallic complexes [LnCp3]- and Ln(CNT)2, where Cp = cyclopentadienyl and CNT = cyclononatetraenyl, of the lanthanide ions in the 2+ oxidation state, are theoretically studied in terms of the electronic structure obtained via multiconfigurational wave function-based methods. Calculations are performed for two groups of ion complexes selected based on their preferred electronic configuration 4fn+1 or 4fn5d1 (n is the number of f electrons in the 3+ ion). All the properties are discussed in terms of the electron density distribution of the ground state and ligand field effects. This analysis allows giving some molecular design strategies relevant to exploit the magnetic properties in applications like Single-Molecule Magnets (SMMs) for lanthanide ions in the 2+ oxidation state.

Valence electrons in lanthanide-based single-atom magnets: a paradigm shift in 4f-magnetism modeling and design

Impact of valence electrons on the magnetic properties of lanthanide-based monatomic magnetic systems on surfaces and in molecules. And FV-magnetism - as a crucial bit in the further understanding and design of a new generation of atomic magnets.

f-Orbital Mixing in the Octahedral f2 Compounds UX62- [X = F, Br, Cl, I] and PrCl63

Understanding how interactions between the f orbitals and ligand orbitals in lanthanide and actinide systems affect their physical properties is the central issue in f-element chemistry. A wide variety of approaches including both theoretical and experimental tools have been used to study these relationships. Among the most widely used tools has been crystal field theory (CFT), which bridges theory and experiment in that it is a model based largely on atomic theory that is parametrized using experimental data. Crystal field theory is quite accurate for the lanthanides, due in part to the highly contracted nature of the 4f orbitals. For actinides, crystal field theory is less accurate, potentially due to the treatment of orbital mixing. In CFT, orbital mixing is handled implicitly by allowing the electron repulsion parameters (Slater F^k parameters) and the spin-orbit coupling constant to vary. As a result, orbital mixing in CFT is isotropic in that the F^k parameters and the spin-orbit coupling constant affect all f orbitals equally. This approximation works well for the lanthanides due to the limited degree of orbital mixing in these complexes. In actinide complexes, the 5f orbitals have greater overlap with the ligand orbitals, and this approximation is less accurate than in the lanthanides. Here, we report a modification of CFT that includes the effect of orbital mixing on electron repulsion and spin-orbit coupling for each f orbital. The model is applied to the tetravalent uranium hexahalide dianions and PrCl₆^3- for which the energies of many low-lying excited states are known. The new model generally fits the data as well the traditional CFT although with fewer parameters. However, the new model does not fit the data better than the more complex CFT models of Faucher and co-workers. The results of the model show in detail how changes in overlap and orbital energies influence the energies of the bonding and antibonding orbitals.

A new series of lanthanide-based complexes with a bis(hydroxy)benzoxaborolone ligand: synthesis, crystal structure, and magnetic and optical properties

Reactions, under hydrothermal conditions, between lanthanide chlorides and the sodium salt of 2-carboxyphenylboronic acid lead to a series of lanthanide-based complexes with general chemical formula [Ln₂(C₇H₅O₂)₄(C₇O₄H₆B)₂·4H₂O] with Ln = Eu–Dy.

Crystallographic structure and crystal field parameters in the [AnIV(DPA)3]2− series, An = Th, U, Np, Pu

The [An^IV(DPA)₃]²⁻ series with An = Th, U, Np, Pu has been synthesized and characterized using SC-XRD, vibrational spectroscopy, and first principles calculations.

Derivation of Lanthanide Series Crystal Field Parameters From First Principles

Two series of lanthanide complexes have been chosen to analyze trends in the magnetic properties and crystal field parameters (CFPs) along the two series: The highly symmetric LnZn₁₆ (picHA)₁₆ series (Ln=Tb, Dy, Ho, Er, Yb; picHA=picolinohydroxamic acid) and the [Ln(dpa)₃ ](C₃ H₅ N₂ )₃ ⋅3H₂ O series (Ln=Ce-Yb; dpa=2,6-dipicolinic acid) with approximate three-fold symmetry. The first series presents a compressed coordination sphere of eight oxygen atoms whereas in the second series, the coordination sphere consists of an elongated coordination sphere formed of six oxygen atoms. The CFPs have been deduced from ab initio calculations using two methods: The AILFT (ab initio ligand field theory) method, in which the parameters are determined at the orbital level, and the ITO (irreducible tensor operator) decomposition, in which the problems are treated at the many-electron level. It has been found that the CFPs are transferable from one derivative to another, within a given series, as a first approximation. The sign of the second-order parameter B 0 2 differs in the two series, reflecting the different environments. It has been found that the use of the strength parameter S allows for an easy comparison between complexes. Furthermore, in both series, the parameters have been found to decrease in magnitude along the series, and this decrease is attributed to covalent effects.

How important is the coordinating atom in controlling magnetic anisotropy in uranium(iii) single-ion magnets? A theoretical perspective

Theoretical investigation of actinide based nanomagnets is of paramount interest in the field of molecular magnetism as they offer remarkable properties compared to their lanthanide counterparts. Unlike lanthanides, the magnetic properties of actinides can be fine-tuned by modulating the ligand field as they possess a large metal-ligand covalency. In this regard, two complexes reported earlier have gained attention: [U(BcMe)₃] (1) has been found to show Single-ion Magnet (SIM) characteristics whereas isomeric [U(BpMe)₃] (2) does not exhibit any SIM behaviour. To unravel the origin of the differences observed in magnetic anisotropy, a detailed ab initio CASSCF study has been undertaken on the X-ray structure of complexes 1 and 2. Since actinide compounds exhibit strong covalency, the desired active space needs to be benchmarked to address this issue. Here, we have enlarged the active space systematically from CAS(3,7) to CAS(3,12) where all 5f electrons in 5f orbitals are sequentially expanded to include five formally empty 6d orbitals. Our calculations reveal that the incorporation of the 6d_z² orbital is vital in reproducing many experimental observables such as temperature dependent susceptibility, g-factors, ground state m_J level, and ground-state-excited-state gap. Inclusion of this orbital in the reference space is found to describe better the UH-BH agostic interactions leading to significant variations in the computed parameters. Gaining from this understanding, we have carried out extensive bonding analysis within the DFT framework using tools such as Natural Bond Orbital (NBO) and Atoms In Molecule (AIM) to further probe these weak agostic interactions. Also, predictions to enhance the U-ligand covalency using U-sulphur bonds and the role of the U-C distance and C-U-C bite angles in the nature of anisotropy have been studied, and relevant magneto-structural correlations have been developed. Thus our results for the first time provide a comprehensive understanding of uranium based SMMs and offer ways to fine tune the anisotropy for experimental chemists.

Magnetic Coupling in the Ce(III) Dimer Ce2(COT)3

The monomer [Ce(COT)₂]^- and the dimer [Ce₂(COT)₃], with Ce(III) and COT = 1,3,5,7-cyclooctatetraenide, are studied by quantum chemistry calculations. Due to the large spin-orbit coupling, the ground state of the monomer is a strong mixing of σ and π states. The experimental isotropic coupling in the dimer was evaluated by Walter et al. to be J = -7 cm^-1 (with a Heisenberg Hamiltonian [Formula: see text]) with a small anisotropic coupling of 0.02 cm^-1. The coupling between the two Ce(III) in the dimer is calculated using CI methods. The low energy part of the spectra are modeled by spin Hamiltonians. All spin Hamiltonians parameters are deduced from ab initio calculations. g factors are calculated for both the pseudodoublet of the monomer and the pseudotriplet of the dimer and their sign have been determined. The magnetic coupling in the dimer is rationalized by a model based on crystal field theory. The kinetic and exchange contributions arising from the different configurations to the isotropic and anisotropic couplings are evaluated. It is shown that the main contribution to isotropic coupling is kinetic and originates from the f_σ-f_σ interaction due to the large transfer integral between those orbitals. However, the f_π-f_π interaction plays a non-negligible role. The anisotropic coupling originates from the difference of exchange energy of states arising from the f_σf_π configuration and is, in no matter, related to the anisotropy of the local magnetic moments as already pointed by van Vleck for a fictitious s-p system. The analysis of the natural orbitals evidences a superexchange mechanism through a σ_CH^* orbital of the bridging cycle favored by a local 4f_σ/5d_σ hybridization and that the δ type orbitals, both the HOMOs of the ligands and the virtual f_δ orbitals of the cerium atoms play an important polarization role, and to a less extend the π type orbitals, the HOMOs-1 of the ligands, and the metal f_π orbitals.

A supramolecular chain of dimeric Dy single molecule magnets decorated with azobenzene ligands

Dy^III dimers decorated with photo-isomerizable azobenzene ligands behave as single-molecule magnets and self-organize into a supramolecular chain. Ab initio calculations, magnetic and optical properties are reported.