Ab Initio Ligand-Field Theory Analysis and Covalency Trends in Actinide and Lanthanide Free Ions and Octahedral Complexes

Substituted fullerenes as a promising capping ligand towards stabilization of exohedral Dy(III) based single-ion magnets: a theoretical study

Organometallic dysprosocenium-based molecular magnets are the forefront runners in offering giant magnetic anisotropy and blocking temperatures close to the boiling point of liquid nitrogen. Attaining linearity in the organometallic dysprosocenium complexes is the key to generating giant magnetic anisotropy and blocking barriers. In the present study, we have unravelled the coordination ability of the substituted fullerene (C55X5)- (where X = CCH3, B, and N) generated by fencing around the five-membered ring of fullerene towards stabilizing a new family of exohedral dysprosium organometallic complexes showcasing giant magnetic anisotropy and blockade barriers. Eight exohedral mononuclear dysprosium organometallic complexes, namely [Dy(η5-C55X5)(η4-C4H4)] (1), [Dy(η5-C55X5)(η5-Cp)]+ (2), [Dy(η5-C55X5)(η5-Cp*)]+ (3), [Dy(η5-C55X5)(η6-C6H6)]2+ (4), [Dy(η5-C55X5)(η8-C8H8)] (5), [Dy(η5-C55X5)2]+ (6) (where X = CCH3), [Dy(η5-C55B5)2]+ (7) and [Dy(η5-C55N5)2]+ (8), were studied using scalar relativistic density functional theory (SR-DFT) and the complete active space self-consistent field (CASSCF) methodology to shed light on the structure, stability, bonding and single-ion magnetic properties. SR-DFT calculations predict complexes 1-8 to be highly stable, with a strictly linear geometry around the Dy(III) ion in complexes 6-8. Energy Decomposition Analysis (EDA) predicts the following order for interaction energy (ΔEint value): 5 > 1 > 2 ≈ 3 > 6 > 7 > 8 > 4, with sizable 4f-ligand covalency in all the complexes. CASSCF calculations on complexes 1-8 predict stabilization of mJ |±15/2〉 as the ground state for all the complexes except for 5, with the following trend in the Ucal values: 6 (1573 cm-1) ≈ 3 (1569 cm-1) > 1 (1538 cm-1) > 8 (1347 cm-1) > 2 (1305 cm-1) > 7 (1284 cm-1) > 4 (1125 cm-1) > 5 (108 cm-1). Ab initio ligand field theory (AILFT) analysis provides a rationale for Ucal ordering, where π-type 4f-ligand interactions in complexes 1-4 and 6-8 offer giant barrier height while the large (C8H8)2- rings generate δ-type interaction in 5, which diminishes the axiality in the ligand field. Our detailed finding suggests that the exohedral organometallic dysprosocenium complexes are more linear compared to bent [DyCp*2]+ cations and display a giant barrier height exceeding 1500 cm-1 with negligible quantum tunnelling of magnetization (QTM) - a new approach to design highly anisotropic dysprosium organometallic complexes.

Understanding covalency in molecular f-block compounds from the synergy of spectroscopy and quantum chemistry

One of the most intensely studied areas of f-block chemistry is the nature of the bonds between the f-element and another species, and in particular the role played by covalency. Computational quantum chemical methods have been at the forefront of this research for decades and have a particularly valuable role, given the radioactivity of the actinide series. The very strong agreement that has recently emerged between theory and the results of a range of spectroscopic techniques not only facilitates deeper insight into the experimental data, but it also provides confidence in the conclusions from the computational studies. These synergies are shining new light on the nature of the f element-other element bond.

Determination of Uranium Central-Field Covalency with 3d4f Resonant Inelastic X-ray Scattering

Understanding the nature of metal-ligand bonding is a major challenge in actinide chemistry. We present a new experimental strategy for addressing this challenge using actinide 3d4f resonant inelastic X-ray scattering (RIXS). Through a systematic study of uranium(IV) halide complexes, [UX6]2-, where X = F, Cl, or Br, we identify RIXS spectral satellites with relative energies and intensities that relate to the extent of uranium-ligand bond covalency. By analyzing the spectra in combination with ligand field density functional theory we find that the sensitivity of the satellites to the nature of metal-ligand bonding is due to the reduction of 5f interelectron repulsion and 4f-5f spin-exchange, caused by metal-ligand orbital mixing and the degree of 5f radial expansion, known as central-field covalency. Thus, this study furthers electronic structure quantification that can be obtained from 3d4f RIXS, demonstrating it as a technique for estimating actinide-ligand covalency.

Relativistic Effects in Ligand Field Theory (I): Optical Properties of d1 Atoms in Oh' Symmetry

Ligand field theory, which explains the splitting of degenerate nd atomic orbitals due to static electric fields from point-charge ligands, is rederived using Dirac orbitals instead of Schrödinger orbitals, specifically using the nd3/2 and nd5/2 spinors. This formalism is, to some extent, equivalent to incorporating the spin-orbit interaction either in the nd atomic orbitals or in the ligand field orbitals (e.g., the t2g and eg orbitals arising from Oh symmetry). The spin-orbit interaction is of fundamental importance in the description of the magnetic and optical properties of the 4d and 5d transition metal complexes. Algebraic equations for the relativistic energy levels of d1 octahedral complexes as functions of the spin-orbit coupling constant ξnd and the ligand field parameters Dq and Dp are derived. It is demonstrated that these parameters allow a direct link between the ligand field theory and ab initio relativistic calculations, consistent with the emerging ab initio ligand field theory. The spin-orbit coupling constant and ligand field parameters of ReF6 obtained from optical absorption spectra are carefuly in the light of the new theory.

Control of the geometry and anisotropy driven by the combination of steric and anion coordination effects in CoII complexes with N6-tripodal ligands: the impact of the size of the ligand on the magnetization relaxation time

Four mononuclear CoII complexes of formula [Co(L)(SCN)2(CH3OH)0.5(H2O)0.5]·1.5H2O·0.75CH3OH (1), [Co(L1)Cl2]·H2O·2CH3CN (2), [Co(L1)(SCN)2]·1.5H2O·CH3OH (3) and [Co(L1)]ClO4·2CH3OH (4) were prepared from the N6-tripodal Schiff base ligands (S)P[N(Me)NC(H)2-Q]3 (L) and (S)P[N(Me)NC(H)1-ISOQ]3 (L1), where Q and ISOQ represent quinolyl and isoquinolyl moieties, respectively. In 1, the L ligand does not coordinate to the CoII ion in a tripodal manner but using a new N,N,S tridentate mode, which is due to the fact that the N6-tripodal coordination promotes a strong steric hindrance between the quinolyl moieties. However, L1 can coordinate to the CoII ions either in a tripodal manner using CoII salts with poorly coordinating anions to give 4 or in a bisbidentate fashion using CoII salt-containing medium to strongly coordinating anions to afford 2 and 3. In the case of L1, there is no steric hindrance between ISOQ moieties after coordination to the CoII ion. The CoII ion exhibits a distorted octahedral geometry for compounds 1-3, with the anions in cis positions for the former and in trans positions for the two latter compounds. Compound 4 shows an intermediate geometry between an octahedral and trigonal prism but closer to the latter one. DC magnetic properties, HFEPR and FIRMS measurements and ab initio calculations demonstrate that distorted octahedral complexes 1-3 exhibit easy-plane magnetic anisotropy (D > 0), whereas compound 4 shows large easy-axis magnetic anisotropy (D < 0). Comparative analysis of the magneto-structural data underlines the important role that is played not only by the coordination geometry but also the electronic effects in determining the anisotropy of the CoII ions. Compounds 2-3 show a field-induced slow relaxation of magnetization. Despite its large easy-axis magnetic anisotropy, compound 4 does not show significant slow relaxation (SMR) above 2 K under zero applied magnetic fields, but its magnetic dilution with ZnII triggers SMR at zero field. Finally, it is worth remarking that compounds 2-4 show smaller relaxation times than the analogous complexes with the tripodal ligand bearing in its arms pyridine instead of isoquinoline moieties, which is most likely due to the increase of the molecular size in the former one.

Paramagnetic Properties of [AnIV(NO3)6]2- Complexes (An = U, Np, Pu) Probed by NMR Spectroscopy and Quantum Chemical Calculations

Actinide +IV complexes with six nitrates [AnIV(NO3)6]2- (An = Th, U, Np, and Pu) have been studied by 15N and 17O NMR spectroscopy in solution and first-principles calculations. Magnetic susceptibilities were evaluated experimentally using the Evans method and are in good agreement with the ab initio values. The evolution in the series of the crystal field parameters deduced from ab initio calculations is discussed. The NMR paramagnetic shifts are analyzed based on ab initio calculations. Because the cubic symmetry of the complex quenches the dipolar contribution, they are only of Fermi contact origin. They are evaluated from first-principles based on a complete active space/density functional theory (DFT) strategy, in good accordance with the experimental one. The ligand hyperfine coupling constants are deduced from paramagnetic shifts and calculated using unrestricted DFT. The latter are decomposed in terms of the contribution of molecular orbitals. It highlights two pathways for the delocalization of the spin density from the metallic open-shell 5f orbitals to the NMR active nuclei, either through the valence 5f hybridized with 6d to the valence 2p molecular orbitals of the ligands, or by spin polarization of the metallic 6p orbitals which interact with the 2s-based molecular orbitals of the ligands.

Contemporary Assessment of Energy Degeneracy in Orbital Mixing with Tetravalent f-Block Compounds

The f block is a comparatively understudied group of elements that find applications in many areas. Continued development of technologies involving the lanthanides (Ln) and actinides (An) requires a better fundamental understanding of their chemistry. Specifically, characterizing the electronic structure of the f elements presents a significant challenge due to the spatially core-like but energetically valence-like nature of the f orbitals. This duality led f-block scientists to hypothesize for decades that f-block chemistry is dominated by ionic metal-ligand interactions with little covalency because canonical covalent interactions require both spatial orbital overlap and orbital energy degeneracy. Recent studies on An compounds have suggested that An ions can engage in appreciable orbital mixing between An 5f and ligand orbitals, which was attributed to "energy-degeneracy-driven covalency". This model of bonding has since been a topic of debate because different computational methods have yielded results that support and refute the energy-degeneracy-driven covalency model. In this Viewpoint, literatures concerning the metal- and ligand-edge X-ray absorption near-edge structure (XANES) of five tetravalent f-block systems─MO2 (M = Ln, An), LnF4, MCl62-, and [Ln(NP(pip)3)4]─are compiled and discussed to explore metal-ligand bonding in f-block compounds through experimental metrics. Based on spectral assignments from a variety of theoretical models, covalency is seen to decrease from CeO2 and PrO2 to TbO2 through weaker ligand-to-metal charge-transfer (LMCT) interactions, while these LMCT interactions are not observed in the trivalent Ln sesquixodes until Yb. In comparison, while XANES characterization of AnO2 compounds is scarce, computational modeling of available X-ray absorption spectra suggests that covalency among AnO2 reaches a maximum between Am and Cm. Moreover, a decrease in covalency is observed upon changing ligands while maintaining an isostructural coordination environment from CeO2 to CeF4. These results could allude to the importance of orbital energy degeneracy in f-block bonding, but there are a variety of data gaps and conflicting results from different modeling techniques that need to be addressed before broad conclusions can be drawn.

Overdestabilization vs Overstabilization in the Theoretical Analysis of f-Orbital Covalency

The complex nature of the f-orbital electronic structures and their interaction with the chemical environment pose significant computational challenges. Advanced computational techniques that variationally include scalar relativities and spin-orbit coupling directly at the molecular orbital level have been developed to address this complexity. Among these, variational relativistic multiconfigurational multireference methods stand out for their high accuracy and systematic improvement in studies of f-block complexes. Additionally, these advanced methods offer the potential for calibrating low-scaling electronic structure methods such as density functional theory. However, studies on the Cl K-edge X-ray absorption spectra of the [Ce(III)Cl6]3- and [Ce(IV)Cl6]2- complexes show that time-dependent density functional theory with approximate exchange-correlation kernels can lead to inaccuracies, resulting in an overstabilization of 4f orbitals and incorrect assessments of covalency. In contrast, approaches utilizing small active space wave function methods may understate the stability of these orbitals. The results herein demonstrate the need for large active space, multireference, and variational relativistic methods in studying f-block complexes.

Comparison of Variational and Perturbative Spin-Orbit Coupling within Two-Component CASSCF

The modeling of spin-orbit coupling (SOC) remains a challenge in computational chemistry due to the high computational cost. With the rising popularity of spin-driven processes and f-block metals in chemistry and materials science, it is incumbent on the community to develop accurate multiconfigurational SOC methods that scale to large systems and understand the limits of different treatments of SOC. Herein, we introduce an implementation of perturbative SOC in scalar-relativistic two-component CASSCF (srX2C-CASSCF-SO). Perspectives on the limitations and accuracy of srX2C-CASSCF-SO are presented via benchmark calculations.

AOMadillo: A program for fitting angular overlap model parameters

The angular overlap model (AOM) is an established parameterization scheme within ligand field theory (LFT). In principle, its application is fairly straightforward, but can be tedious and involve a trial-and-error approach to identify and judge the best set of parameters. With the availability of quantum chemical methods to predict d-d transitions in transition metal complexes, a rich source of computational spectroscopic data with unambiguous assignments to electronic states is available. Herein, we present AOMadillo, a software package that is designed to interface the output of ab initio LFT calculations from the ORCA suite of programs and performs a least-squares fit for a chosen AOM parameterization. Many steps of the AOM parameterization are automated, so that scans of geometric parameters and evaluations of sets of similar complexes are convenient. The fitting routine is highly configurable, allowing the efficient evaluation of different parameter sets.

A DFT perspective on organometallic lanthanide chemistry

Computational studies of the coordination chemistry and bonding of lanthanides have grown in recent decades as the need for understanding the distinct physical, optical, and magnetic properties of these compounds increased. Density functional theory (DFT) methods offer a favorable balance of computational cost and accuracy in lanthanide chemistry and have helped to advance the discovery of novel oxidation states and electronic configurations. This Frontier article examines the scope and limitations of DFT in interpreting structural and spectroscopic data of low-valent lanthanide complexes, elucidating periodic trends, and predicting their properties and reactivity, presented through selected examples.

LnDOTA puppeteering: removing the water molecule and imposing tetragonal symmetry

Complexes of lanthanide(iii) ions (Ln) with tetraazacyclododecane-N,N',N'',N'''-tetraacetate (DOTA) are a benchmark in the field of magnetism due to their well-investigated and sometimes surprising features. Ab initio calculations suggest that the ninth ligand, an axial water molecule, is key in defining the magnetic properties because it breaks the potential C4 symmetry of the resulting complexes. In this paper, we experimentally isolate the role of the water molecule by excluding it from the metal coordination sphere without altering the chemical structure of the ligand. Our complexes are therefore designed to be geometrically tetragonal and strict crystallographic symmetry is achieved by exploiting a combination of solution ionic strength and solid state packing effects. A thorough multitechnique approach has been used to unravel the electronic structure and magnetic anisotropy of the complexes. Moreover, the geometry enhancement allows us to predict, using only one angle obtained from the crystal structure, the ground state composition of all the studied derivatives (Ln = Tb to Yb). Therefore, these systems also provide an excellent platform to test the validity and limitations of the ab initio methods. Our combined experimental and theoretical investigation proves that the water molecule is indeed key in defining the magnetic anisotropy and the slow relaxation of these complexes.

Periodic trends in trivalent actinide halides, phosphates, and arsenates

Due to the limited abundance of the actinide elements, computational methods, for now, remain an exclusive avenue to investigate the periodic trends across the actinide series. As every actinide element can exhibit a +3-oxidation state, we have explored model systems of gas-phase actinide trihalides, phosphates, and arsenates across the series to capture the periodic trends. By doing so, we were able to capture the periodic trends down the halogen series as well, and for the first time we are reporting a study on actinide astatides. Using scalar and spin-orbit relativistic Density Functional Theory (DFT) calculations, we have explored the variations in bond lengths, bond angles, and the charges on actinides (An). Despite the use of different sets of ligands, the trends remain similar. The properties of trivalent Pa, U, Np, and Pu are nearly identical; similar ionic radii could be the reason. The actinide elements show a tendency to exhibit a pre-Pu and a post-Cm behaviour, with Am acting as a switch. This could be due to the change in the behaviour from d-f-type to f-filling/d-type at around Pu-Cm in the actinides as already proposed in the previous literature. Bond lengths in the AnX3 increase down the halide series, and the atomic charges decrease on the actinide elements.

Influence of symmetry on the magneto-optical properties of a bifunctional macrocyclic DyIII complex

In this work, a novel complex, [Dy(LPr)(NO3)2]·(H2O)·(NO3) (1), containing a highly distorted macrocyclic ligand (LPr) and weak axial anions (NO3-), was synthesized and characterized. Even though this coordination environment is not ideal for maximizing the magnetic anisotropy of a DyIII ion, a magneto-structural analysis reveals that the high distortion of the macrocycle promotes a disposition of the hard plane and easy axis opposite to the expected one. This results in a quite symmetrical environment which allows obtaining a field induced SMM behaviour. The magnetic relaxation properties of this complex were rationalized with the aid of ab initio multireference calculations. Moreover, 1 showed the characteristic emission bands of DyIII ion, indicating that the macrocyclic ligand acts as an efficient sensitizer in the energy transfer process to the emissive state of the DyIII ion. Due to the symmetric environment of 1, the Y/B intensity ratio (0.61) results in CIE coordinates (0.278; 0.314), close to those of the white light region. To gain further insight into the mechanism leading to the luminescence properties, ab initio calculations were performed to elucidate the key factors controlling the Y/B intensity ratio in this bifunctional complex.

Probing the dynamic behaviour and magnetic identification of seven coordinated Mn(II) complexes: a combined AIMD and multi-reference approach

We present an in-depth solution phase dynamics of rare seven coordinated pentagonal bipyramidal Mn(II) complexes, together with their binding affinity anticipated using ab initio molecular dynamics (AIMD) simulations and density functional theory (DFT). Moreover, the simulations at different temperatures (25 °C and 90 °C) interpret the rigidity and stability of the ligands with Mn(II) ions. An intuitive approach for modulating the easy plane magnetic anisotropy of the mononuclear Mn(II) complex has been revealed by this work. In this regard, we have performed an extensive theoretical study based on the ab initio CASSCF/NEVPT2 method, exhibiting the presence of an easy plane magnetic anisotropy with a positive value of axial zero-field splitting (ZFS) parameter D. The complex's magnetic properties and electronic relaxation reveal that the rhombic ZFS term (E) can be modulated as the symmetry around the Mn(II) ion varies. The magnitude of the D-value increased with a more symmetrical equatorial ligand as found in the order of [Mn(pydpa)(H2O)] > [Mn(cbda)(H2O)]- > [Mn(dpaaa)(H2O)]- > [Mn(dpasam)(H2O)]-. Furthermore, we found that substituting the equatorial oxygen atom with heavier S and Se-donor atoms switches the sign of magnetic anisotropy for the Mn(II) complexes. The magnitude of the D-value increased when the energy levels of the ground state (GS) and the first excited state (ES) decreased. The observed magneto-structural correlation reveals that shortening the distance of the axial water molecule (Mn-O(w)) increases the D-value by an order of magnitude for the symmetrical [Mn(pydpa)(H2O)] complex. Overall, the combined analysis of solution phase dynamics of Mn(II) complexes and their magnetic characterization opens up new avenues in coordination chemistry, molecular magnetism, spin-crossover materials, and catalysis.

Zero-Field SMM Behavior Triggered by Magnetic Exchange Interactions and a Collinear Arrangement of Local Anisotropy Axes in a Linear Co3II Complex

A new linear trinuclear Co(II)3 complex with a formula of [{Co(μ-L)}2Co] has been prepared by self-assembly of Co(II) ions and the N3O3-tripodal Schiff base ligand H3L, which is obtained from the condensation of 1,1,1-tris(aminomethyl)ethane and salicylaldehyde. Single X-ray diffraction shows that this compound is centrosymmetric with triple-phenolate bridging groups connecting neighboring Co(II) ions, leading to a paddle-wheel-like structure with a pseudo-C3 axis lying in the Co-Co-Co direction. The Co(II) ions at both ends of the Co(II)3 molecule exhibit distorted trigonal prismatic CoN3O3 geometry, whereas the Co(II) at the middle presents an elongated trigonal antiprismatic CoO6 geometry. The combined analysis of the magnetic data and theoretical calculations reveal strong easy-axis magnetic anisotropy for both types of Co(II) ions (|D| values higher than 115 cm-1) with the local anisotropic axes lying on the pseudo-C3 axis of the molecule. The magnetic exchange interaction between the middle and ends Co(II) ions, extracted by using either a Hamiltonian accounting for the isotropic magnetic coupling and ZFS or the Lines' model, was found to be medium to strong and antiferromagnetic in nature, whereas the interaction between the external Co(II) ions is weak antiferromagnetic. Interestingly, the compound exhibits slow relaxation of magnetization and open hysteresis at zero field and therefore SMM behavior. The significant magnetic exchange coupling found for [{Co(μ-L)}2Co] is mainly responsible for the quenching of QTM, which combined with the easy-axis local anisotropy of the CoII ions and the collinearity of their local anisotropy axes with the pseudo-C3 axis favors the observation of SMM behavior at zero field.

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.

Multiconfiguration Pair-Density Functional Theory for Vertical Excitation Energies in Actinide Molecules

Modeling actinides with electronic structure theories is challenging because these systems present a strong ligand field and metal-ligand covalency. We systematically investigate the effectiveness of pair-density functional theory (PDFT) for the calculation of vertical excitation energies in An(III), [AnIIICl6]3-, and [AnVIO2]2+ (An = U, Np, Pu, and Am). We compare the performance of PDFT, hybrid PDFT, and multistate PDFT with traditional active-space methods followed by perturbation theory, like multistate CASPT2, and with experimental data. Overall, multistate PDFT gives quantitative agreement with multistate CASPT2 at a significantly reduced computational cost.

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.

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.

Fate of Oxidation States at Actinide Centers in Redox-Active Ligand Systems Governed by Energy Levels of 5 f Orbitals

We report the formation of a NpIV complex from the complexation of NpVI O2 2+ with the redox-active ligand tBu-pdiop2- =2,6-bis[N-(3,5-di-tert-butyl-2-hydroxyphenyl)iminomethyl]pyridine. To the best of our knowledge, this is the first example of the direct complexation-induced chemical reduction of NpVI O2 2+ to NpIV . In contrast, the complexation of UVI O2 2+ with tBu-pdiop2- did not induce the reduction of UVI O2 2+ , not even after the two-electron electrochemical reduction of [UVI O2 (tBu-pdiop)]. This contrast between the Np and U systems may be ascribed to the decrease of the energy of the 5 f orbitals in Np compared to those in U. The present findings indicate that the redox chemistry between UVI O2 2+ and NpVI O2 2+ should be clearly differentiated in redox-active ligand systems.

Luminescent Single-Molecule Magnets as Dual Magneto-Optical Molecular Thermometers

Luminescent thermometry allows the remote detection of the temperature and holds great potential in future technological applications in which conventional systems could not operate. Complementary approaches to measuring the temperature aiming to enhance the thermal sensitivity would however represent a decisive step forward. For the first time, we demonstrate the proof-of-concept that luminescence thermometry could be associated with a complementary temperature readout related to a different property. Namely, we propose to take advantage of the temperature dependence of both magnetic (canonical susceptibility and relaxation time) and luminescence features (emission intensity) found in Single-Molecule Magnets (SMM) to develop original dual magneto-optical molecular thermometers to conciliate high-performance SMM and Boltzmann-type luminescence thermometry. We highlight this integrative approach to concurrent luminescent and magnetic thermometry using an air-stable benchmark SMM [Dy(bbpen)Cl] (H2 bbpen=N,N'-bis(2-hydroxybenzyl)-N,N'-bis(2-methylpyridyl)ethyl-enediamine)) exhibiting Dy3+ luminescence. The synergy between multiparametric magneto-optical readouts and multiple linear regression makes possible a 10-fold improvement in the relative thermal sensitivity of the thermometer over the whole temperature range, compared with the values obtained with the single optical or magnetic devices.

The π-interactions of ammonia ligands evaluated by ab initio ligand field theory

Ammonia and amine ligands are commonly assumed to be σ-only ligands in coordination chemistry, i.e. they are not expected to interact significantly with a metal via a π path. Ligand field analyses employing the Angular Overlap Model resulted in good fits to experimental data without a π parameter for ammonia ligands, thereby supporting this assumption. In this work, we challenge this assumption and suggest that it is an oversimplification. We use complete active space calculations for electronic structure analyses of copper ammine complexes that are in good agreement with the transitions observed in experimental UV-vis spectra. These findings lead to a reinterpretation of the experimental spectra that necessitates a significant π interaction of the ammonia ligands. The strength of the ammonia π interaction is evaluated by parameterizing the ligand field splittings of a series of metal hexammine complexes ([M(NH₃)₆]ⁿ⁺ with M = Cr, Mn, Fe, Co, Ni, Ru, Os and n = 2, 3) and selected tetrammine complexes ([M(NH₃)₄]ⁿ⁺ with M = Cr, Mn, Fe, Co, Ni and n = 2 or 3) with the Angular Overlap Model. The resulting π parameters show that ammonia is a π donor of similar strength as chloride.

Theoretical study of phenylbismuth anion as a blueprint for main-group single-molecule magnets

The hypothetical [BiPh]^- anion obtained by a one-electron reduction from the respective bismuthinidene is proposed as a basis for constructing single-molecule magnets (SMMs) consisting purely of main-group elements. Based on high-level quantum-chemical calculations, the [BiPh]^- anion is predicted to be a SMM with an effective barrier of 6418 cm^-1 for the relaxation of magnetization. This barrier is much larger than any effective barrier observed so far in any experimentally characterized SMM. The reduction potential for the [BiPh]^-/BiPh couple is calculated as -1.5 V, which implies that the [BiPh]^- moiety is accessible from stable bismuthinidenes containing a BiPh moiety and sufficient steric protection for the reactive Bi atom. Thus, [BiPh]^- provides a blueprint for the realization of purely main-group SMMs which can surpass in their properties the best known dysprosium-based SMMs.

Ab Initio Investigation of the Na3[Ln(ODA)3]·2NaClO4·6H2O (Ln = Ce-Yb; ODA = Oxydiacetate) Series

In this work, the Na₃[Ln(ODA)₃]·2NaClO₄·6H₂O (Ln = Ce-Yb; ODA = oxydiacetate) series was analyzed with the ab initio ligand field theory (AILFT) module of the ORCA computational suite. The results were discussed within the framework of the angular overlap model (AOM) and compared to literature data. We find that the structural changes observed across the series exemplifies the effects of the lanthanide contraction also manifesting in the value of the AOM parameters. It is also shown that the complete active space self-consistent field (CASSCF) methodology is sufficient to describe the ligand field interactions in mononuclear lanthanide complexes, and the effects of dynamic correlation, through n-electron valence state perturbation theory (NEVPT2), are discussed. The calculated ligand field parameters of the present work are compared to the experimentally derived values from the literature.

Theoretical Investigation of Single-Molecule-Magnet Behavior in Mononuclear Dysprosium and Californium Complexes

Early-actinide-based (U, Np, and Pu) single-molecule magnets (SMMs) have yet to show magnetic properties similar to those of highly anisotropic lanthanide-based ones. However, there are not many studies exploring the late-actinides (more than half-filled f shells) as potential candidates for SMM applications. We computationally explored the electronic structure and magnetic properties of a hypothetical Cf(III) complex isostructural to the experimentally synthesized Dy(dbm)₃(bpy) complex (bpy = 2,2'-bipyridine; dbm = dibenzoylmethanoate) via multireference methods and compared them to those of the Dy(III) analogue. This study shows that the Cf(III) complex can behave as a SMM and has a greater magnetic susceptibility compared to other experimentally and computationally studied early-actinide-based (U, Np, and Pu) magnetic complexes. However, Cf spontaneously undergoes α-decay and converts to Cm. Thus, we also explored the isostructural Cm(III)-based complex. The computed magnetic susceptibility and g-tensor values show that the Cm(III) complex has poor SMM behavior in comparison to both the Dy(III) and Cf(III) complexes, suggesting that the performance of Cf(III)-based magnets may be affected by α-decay and can explain the poor performance of experimentally studied Cf(III)-based molecular magnets in the literature. Further, this study suggests that the ligand field is dominant in Cf(III), which helps to increase the magnetization blocking barrier by nearly 3 times that of its 4f congener.

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.

On the Bonding Nature in the Crystalline Tri-Thorium Cluster: Core-Shell Syngenetic σ-Aromaticity

A unique thorium-thorium bond was observed in the crystalline tri-thorium cluster [{Th(η8 -C8 H8 )(μ3 -Cl)2 }3 {K(THF)2 }2 ]∞ , though the claim of σ-aromaticity for Th3 bond has been questioned. Herein, a new type of core-shell syngenetic bonding model is proposed to describe the stability of this tri-thorium cluster. The model involves a 3c-2e bond in the Th3 core and a multicentered (ThCl2 )3 charge-shift bond with 12 electrons scattering along the outer shell. To differentiate the strengths of the 3c-2e bond and the charge-shift bond, the block-localized wavefunction (BLW) method which falls into the ab initio valence bond (VB) theory is employed to construct a strictly core/shell localized state and its contributing covalent resonance structure for the Th3 core bond. By comparing with the σ-aromatic H3 + and nonaromatic Li3 + , the computed resonance energies and extra cyclic resonance energies confirm that this Th3 core bond is truly delocalized and σ-aromatic.

Structural and Bonding Analysis in Monomeric Actinide(IV) Oxalate from Th(IV) to Pu(IV): Comparison with the An(IV) Nitrate Series

Single-crystal X-ray diffraction (SC-XRD) structures and Raman spectra of a series of new isomorphous molecular An(IV)-oxalate compounds (Th, U, Np, and Pu) are reported. These complexes are crystallized with cobalt(III) hexamine ([Co(NH₃)₆]³⁺) as the counter cations, [Co(NH₃)₆]₂[An(C₂O₄)₅]·4H₂O, revealing five bidentate nonbridging oxalate ligands in the first coordination sphere (CN = 10). The nonbridging oxalate is rather uncommon for An(IV)-oxalate systems, which are widely characterized as polymeric compounds. Density functional theory (DFT) calculations were performed to examine the bonding between An(IV) cations and oxalate ligands. For comparison, we also report results obtained for the An(IV)-hexanitrate series, [(C₂H₅)₄N]₂[An(NO₃)₆] (with An = Th, U, Np, Pu, and Ce), which consists of O-donor ligands as well but with a larger coordination number (CN = 12). The bonding analysis confirms that the actinide-oxygen bond is predominantly ionic with a minor increase in covalency from Th to U and slight variations from U to Pu. Further comparison showed that the charge transfer increases slightly when increasing the number of anions in the coordination sphere (C₂O₄^2-: CN = 10; NO₃^-: CN = 12), but covalent effects as indicated by the amount of internuclear electron density accumulation are small and similar for oxalate and nitrate.

Dipolar and Contact Paramagnetic NMR Chemical Shifts in AnIV Complexes with Dipicolinic Acid Derivatives

Actinide +IV complexes (An^IV = Th^IV, U^IV, Np^IV, and Pu^IV) with two dipicolinic acid derivatives (DPA and Et-DPA) have been studied by ¹H and ¹³C NMR spectroscopies and first-principles calculations. The Fermi contact and dipolar contributions to the actinide-induced shifts (AIS) are evaluated from a temperature dependence analysis, combined with ab initio results. It allows an experimental estimation of the axial anisotropy of the magnetic susceptibility Δχ_ax and of the hyperfine coupling constants of the NMR-active nuclei. Due to the compactness of the coordination sphere, the magnetic anisotropy of the paramagnetic center is small, and this makes the contact contribution to be the dominant one, even on the remote atoms. The sign of the hyperfine coupling constants and related spin densities is alternating on the nuclei of the ligand cycle, denoting a preponderant spin polarization mechanism. This is well reproduced by unrestricted density functional theory (DFT) calculations. Those values are furthermore slightly decreasing in the actinide series, which indicates a small decrease of the covalency from U^IV to Pu^IV.

Revisiting the Fundamental Nature of Metal-Ligand Bonding: An Impartial and Automated Fitting Procedure for Angular Overlap Model Parameters

The properties and reactivities of transition metal complexes are often discussed in terms of Ligand Field Theory (LFT), and with ab initio LFT a direct connection to quantum chemical wavefunctions was recently established. The Angular Overlap Model (AOM) is a widely used, ligand-specific parameterization scheme of the ligand field splitting that has, however, been restricted by the availability and resolution of experimental data. Using ab initio LFT, we present here a generalised, symmetry-independent and automated fitting procedure for AOM parameters that is even applicable to formally underdetermined or experimentally inaccessible systems. This method allows quantitative evaluations of assumptions commonly made in AOM applications, for example, transferability or the relative magnitudes of AOM parameters, and the response of the ligand field to structural or electronic changes. A two-dimensional spectrochemical series of tetrahedral halido metalates ([MII X4 ]2- , M=Mn-Cu) served as a case study. A previously unknown linear relationship between the halide ligands' chemical hardness and their AOM parameters was found. The impartial and automated procedure for identifying AOM parameters introduced here can be used to systematically improve our understanding of ligand-metal interactions in coordination complexes.

Extreme -Tensor Anisotropy and Its Insensitivity to Structural Distortions in a Family of Linear Two-Coordinate Ni(I) Bis-N-heterocyclic Carbene Complexes

We report a new series of homoleptic Ni(I) bis-N-heterocyclic carbene complexes with a range of torsion angles between the two ligands from 68° to 90°. Electron paramagnetic resonance measurements revealed a strongly anisotropic g-tensor in all complexes with a small variation in g_∥ ∼ 5.7-5.9 and g_⊥ ∼ 0.6. The energy of the first excited state identified by variable-field far-infrared magnetic spectroscopy and SOC-CASSCF/NEVPT2 calculations is in the range 270-650 cm^-1. Magnetic relaxation measured by alternating current susceptibility up to 10 K is dominated by Raman and direct processes. Ab initio ligand-field analysis reveals that a torsion angle of <90° causes the splitting between doubly occupied d_xz and d_yz orbitals, which has little effect on the magnetic properties, while the temperature dependence of the magnetic relaxation appears to have no correlation with the torsion angle.

Deciphering the Role of Symmetry and Ligand Field in Designing Three-Coordinate Uranium and Plutonium Single-Molecule Magnets

Actinide single-molecule magnets (SMMs) have gained paramount interest in molecular magnetism as they offer a larger barrier height of magnetization (U_eff) reversal compared to the lanthanide analogue, thanks to their greater metal-ligand covalency. However, the reported actinide SMMs to date yield a relatively smaller U_eff as there is no established design principle to enhance U_eff values. To address this issue, we have employed ab initio CASSCF/CASPT2/NEVPT2 calculations to study a series of three-coordinate U³⁺ and Pu³⁺ SMMs. To begin with, we have studied two experimentally characterized U³⁺ ion-field-induced SMMs, namely, planar [U{N(SiMe₂^tBu)₂}₃] (1) and pyramidal [U{N(SiMe₃)₂}₃] (2) complexes reported earlier. Both the complexes were found to stabilize m_J = |±1/2⟩ as the ground state with a very strong quantum tunneling of magnetization (QTM), rendering them unsuitable for SMMs. Our calculations reveal that in the pyramidal geometry (such as in 2), the energy of the 5f²6d¹ state is lowered compared to the planar geometry (as in 1), resulting in a slightly better SMM characteristic in the former. To unravel the effect of symmetry in magnetic properties, ab initio calculations were performed on two reported T-shaped complexes [U(NSiⁱPr₂)₂(I)] (3) and [U(NHAr^iPr6)₂I] (4, Ar^iPr6 = 2,6-(2,4,6-iPr₃C₆H₂)₂C₆H₃). Quite interestingly, m_J = |±9/2⟩ is found to be the ground state for both the complexes with a blocking barrier exceeding 900 cm^-1. Furthermore, to decipher the effect of the transuranic element in magnetic anisotropy, ab initio calculations were extended to the Pu analogue of 2, [Pu{N(SiMe₃)₂}₃] (5), which yields a record-breaking blocking barrier of ∼1933 cm^-1. Among the three-coordinate geometries studied, the pyramidal geometry was found to offer substantial magnetic anisotropy for Pu³⁺ ions, while a T-shaped geometry is best suited for U³⁺ ions. While the chosen theoretical protocols' overestimation of barrier height cannot be avoided, these values are still several orders of magnitude larger than the U_eff values reported for any actinide SMMs and unveil a design principle for superior three-coordinate actinide-based SMMs.

Theoretically investigating the ability of phenanthroline derivatives to separate transuranic elements and their bonding properties

The bonding and separation properties of actinide Np3+, Pu3+, Am3+, and Cm3+ complexes formed with phenanthroline derivatives were studied using the DFT method.

First-Principles Study of Optical Absorption Energies, Ligand Field and Spin-Hamiltonian Parameters of Cr3+ Ions in Emeralds

Herein, we study the electronic structure, energies, and vibronic structure of optical d-d transitions of Cr³⁺ ions doped in beryl (Be₃Si₆Al₂O₁₈:Cr³⁺, emerald). A computational protocol is developed that combines periodic density functional theory (for modeling of the bulk crystalline lattice of emerald) and the multireference configuration interaction complete active space self-consistent field method supplemented with n-electron valence second-order perturbation theory (for the calculation of the energy levels, wave functions, and spin-Hamiltonian and ligand-field parameters of the trigonal Cr³⁺ centers in the [CrO₆]^9- clusters embedded in an extended point charge field). Ligand-field parameters were extracted from mapping the effective ligand-field Hamiltonian onto the full many-particle Hamiltonian from one side and from a direct fit to energies of computed d-d transitions on the other side. These have been analyzed using ab initio ligand-field theory. The quality of the theoretical predictions is critically assessed through a detailed comparison with the available experimental data.

Creation of an unexpected plane of enhanced covalency in cerium(III) and berkelium(III) terpyridyl complexes

Controlling the properties of heavy element complexes, such as those containing berkelium, is challenging because relativistic effects, spin-orbit and ligand-field splitting, and complex metal-ligand bonding, all dictate the final electronic states of the molecules. While the first two of these are currently beyond experimental control, covalent M‒L interactions could theoretically be boosted through the employment of chelators with large polarizabilities that substantially shift the electron density in the molecules. This theory is tested by ligating BkIII with 4'-(4-nitrophenyl)-2,2':6',2"-terpyridine (terpy*), a ligand with a large dipole. The resultant complex, Bk(terpy*)(NO3)3(H2O)·THF, is benchmarked with its closest electrochemical analog, Ce(terpy*)(NO3)3(H2O)·THF. Here, we show that enhanced Bk‒N interactions with terpy* are observed as predicted. Unexpectedly, induced polarization by terpy* also creates a plane in the molecules wherein the M‒L bonds trans to terpy* are shorter than anticipated. Moreover, these molecules are highly anisotropic and rhombic EPR spectra for the CeIII complex are reported.

Covalency of Trivalent Actinide Ions with Different Donor Ligands: Do Density Functional and Multiconfigurational Wavefunction Calculations Corroborate the Observed "Breaks"?

A comprehensive ab initio study of periodic actinide-ligand bonding trends for trivalent actinides is performed. Relativistic density functional theory (DFT) and complete active-space (CAS) self-consistent field wavefunction calculations are used to dissect the chemical bonding in the [AnCl₆]^3-, [An(CN)₆]^3-, [An(NCS)₆]^3-, [An(S₂PMe₂)₃], [An(DPA)₃]^3-, and [An(HOPO)]^- series of actinide (An = U-Es) complexes. Except for some differences for the early actinide complexes with DPA, bond orders and excess 5f-shell populations from donation bonding show qualitatively similar trends in 5f ⁿ active-space CAS vs DFT calculations. The influence of spin-orbit coupling on donation bonding is small for the tested systems. Along the actinide series, chemically soft vs chemically harder ligands exhibit clear differences in bonding trends. There are pronounced changes in the 5f populations when moving from Pu to Am or Cm, which correlate with previously noted "breaks" in chemical trends. Bonding involving 5f becomes very weak beyond Cm/Bk. We propose that Cm(III) is a borderline case among the trivalent actinides that can be meaningfully considered to be involved in ground-state 5f covalent bonding.

An1.33T4Al8Si2 (An = Ce, Th, U, Np; T = Ni, Co): Actinide Intermetallics with Disordered Gd1+xFe4Si10-y Structure Type Grown from Metal Flux

An_1.33T₄Al₈Si₂ (An = Ce, Th, U, Np; T = Ni, Co) were synthesized in metal flux reactions carried out in aluminum/gallium melts. In previous work, U_1.33T₄Al₈Si₂ (T = Co, Ni) analogues were formed by arc-melting U:T:Si and reacting this mixture in Al/Ga flux. However, in the current work, all compounds were synthesized by using AnO₂ reactants, taking advantage of the ability of the aluminum in the flux to act as both solvent and reducing agent. While reactions with T = Co yielded hexagonal Gd_1.33Fe₄Si₁₀-type quaternary phases for all An, reactions with T = Ni produced these compounds only with An = U and Np. For reactions with An = Ce and Th, the reactions led instead to the formation of AnNi_3-xSi_xAl_4-yGa_y phases, with the tetragonal KCu₃S₄ structure type. Attempts to synthesize plutonium analogues Pu_1.33T₄Al₈Si₂ were also unsuccessful, producing the previously reported PuCoGa₅ and Pu₂Ni₅Si₆ instead. Magnetic data collected on the neptunium analogues Np_1.33T₄Al₈Si₂ (T = Ni, Co) show antiferromagnetic coupling at low temperatures and indicate a tetravalent state for the Np ions.

High-Frequency and -Field Electron Paramagnetic Resonance Spectroscopic Analysis of Metal-Ligand Covalency in a 4f7 Valence Series (Eu2+, Gd3+, and Tb4+)

The recent isolation of molecular tetravalent lanthanide complexes has enabled renewed exploration of the effect of oxidation state on the single-ion properties of the lanthanide ions. Despite the isotropic nature of the ⁸S ground state in a tetravalent terbium complex, [Tb(NP(1,2-bis-^tBu-diamidoethane)(NEt₂))₄], preliminary X-band electron paramagnetic resonance (EPR) measurements on tetravalent terbium complexes show rich spectra with broad resonances. The complexity of these spectra highlights the limits of conventional X-band EPR for even qualitative determination of zero-field splitting (ZFS) in these complexes. Therefore, we report the synthesis and characterization of a novel valence series of 4f⁷ molecular complexes spanning three oxidation states (Eu²⁺, Gd³⁺, and Tb⁴⁺) featuring a weak-field imidophosphorane ligand system, and employ high-frequency and -field electron paramagnetic resonance (HFEPR) to obtain quantitative values for ZFS across this valence series. The series was designed to minimize deviation in the first coordination sphere from the pseudotetrahedral geometry in order to directly interrogate the role of metal identity and charge on the complexes' electronic structures. These HFEPR studies are supported by crystallographic analysis and quantum-chemical calculations to assess the relative covalent interactions in each member of this valence series and the effect of the oxidation state on the splitting of the ground state and first excited state.

Lanthanoid Complexes as Molecular Materials: The Redox Approach

The development of molecular materials with novel functionality offers promise for technological innovation. Switchable molecules that incorporate redox-active components are enticing candidate compounds due to their potential for electronic manipulation. Lanthanoid metals are most prevalent in their trivalent state and usually redox-activity in lanthanoid complexes is restricted to the ligand. The unique electronic and physical properties of lanthanoid ions have been exploited for various applications, including in magnetic and luminescent materials as well as in catalysis. Lanthanoid complexes are also promising for applications reliant on switchability, where the physical properties can be modulated by varying the oxidation state of a coordinated ligand. Lanthanoid-based redox activity is also possible, encompassing both divalent and tetravalent metal oxidation states. Thus, utilization of redox-active lanthanoid metals offers an attractive opportunity to further expand the capabilities of molecular materials. This review surveys both ligand and lanthanoid centered redox-activity in pre-existing molecular systems, including tuning of lanthanoid magnetic and photophysical properties by modulating the redox states of coordinated ligands. Ultimately the combination of redox-activity at both ligands and metal centers in the same molecule can afford novel electronic structures and physical properties, including multiconfigurational electronic states and valence tautomerism. Further targeted exploration of these features is clearly warranted, both to enhance understanding of the underlying fundamental chemistry, and for the generation of a potentially important new class of molecular material.

How the Ancillary Ligand X Drives the Redox Properties of Biscyclopentadienyl Pentavalent Uranium Cp2U(═N-Ar)X Complexes

Relativistic zero order regular approximation (ZORA) density functional theory computations, coupled with the conductor-like screening model for solvation effects, are used to investigate the redox properties of a series of biscyclopentadienyl pentavalent uranium(V) complexes Cp₂U(═N-Ar)X (Ar = 2,6-Me₂-C₆H₃; X = OTf, C₆F₅, SPh, C═CPh, NPh₂, Ph, Me, OPh, N(TMS)₂, N═CPh₂). Regarding the U^V/U^IV and U^VI/U^V couple systems, a linear correlation (R² ∼ 0.99) is obtained at the ZORA/BP86/TZP level, between the calculated ionization energies and the measured experimental E_1/2 half-wave oxidation potentials (U^VI/U^V) and between the electron affinities and the reduction potentials E_1/2 (U^V/U^IV). The study brings to light the importance of solvation effects that are needed in order to achieve a good agreement between the theory and experiment. Introducing spin-orbit coupling corrections slightly improves this agreement. Both the singly occupied molecular orbital and the lowest unoccupied molecular orbital of the neutral U^V complexes exhibit a majority 5f orbital character. The frontier molecular orbitals show a substantial ancillary ligand X σ and/or π character that drives the redox properties. Moreover, our investigations allow estimating the redox potentials of the X = Ph, X = C₆F₅, and N(TMS)₂ U^V complexes for which no experimental electrochemical data exist.