Derivation of Lanthanide Series Crystal Field Parameters From First Principles

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.

Spin-Vibronic Dynamics in Open-Shell Systems beyond the Spin Hamiltonian Formalism

Vibronic coupling has a dramatic influence over a large number of molecular processes, ranging from photochemistry to spin relaxation and electronic transport. The simulation of vibronic coupling with multireference wave function methods has been largely applied to organic compounds, and only early efforts are available for open-shell systems such as transition metal and lanthanide complexes. In this work, we derive a numerical strategy to differentiate the molecular electronic Hamiltonian in the context of multireference ab initio methods and inclusive of spin-orbit coupling effects. We then provide a formulation of open quantum system dynamics able to predict the time evolution of the electron density matrix under the influence of a Markovian phonon bath up to fourth-order perturbation theory. We apply our method to Co(II) and Dy(III) molecular complexes exhibiting long spin relaxation times and successfully validate our strategy against the use of an effective spin Hamiltonian. Our study sheds light on the nature of vibronic coupling, the importance of electronic excited states in spin relaxation, and the need for high-level computational chemistry to quantify it.

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.

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.

Structure Determination and Refinement of Paramagnetic Materials by Solid-State NMR

Paramagnetism in solid-state materials has long been considered an additional challenge for structural investigations by using solid-state nuclear magnetic resonance spectroscopy (ssNMR). The strong interactions between unpaired electrons and the surrounding atomic nuclei, on the one hand, are complex to describe, and on the other hand can cause fast decaying signals and extremely broad resonances. However, significant progress has been made over the recent years in developing both theoretical models to understand and calculate the frequency shifts due to paramagnetism and also more sophisticated experimental protocols for obtaining high-resolution ssNMR spectra. While the field is continuously moving forward, to date, the combination of state-of-the-art numerical and experimental techniques enables us to obtain high-quality data for a variety of systems. This involves the determination of several ssNMR parameters that represent different contributions to the frequency shift in paramagnetic solids. These contributions encode structural information on the studied material on various length scales, ranging from crystal morphologies, to the mid- and long-range order, down to the local atomic bonding environment. In this perspective, the different ssNMR parameters characteristic for paramagnetic materials are discussed with a focus on their interpretation in terms of structure. This includes a summary of studies that have explored the information content of these ssNMR parameters, mostly to complement experimental data from other methods, e.g., X-ray diffraction. The presented overview aims to demonstrate how far ssNMR has hitherto been able to determine and refine the structures of materials and to discuss where it currently falls short of its full potential. We attempt to highlight how much further ssNMR can be pushed to determine and refine structure to deliver a comprehensive structural characterization of paramagnetic materials comparable to what is to date achieved by the combined effort of electron microscopy, diffraction, and spectroscopy.

Exploring Differences in Lanthanide Excited State Reactivity Using a Simple Example: The Photophysics of La and Ce Thenoyltrifluoroacetone Complexes

A series of four lanthanide thenoyltrifluoroacetone (TTA) complexes consisting of two f0 (La3+ and Ce4+) and two f1 (Ce3+) complexes was examined using steady-state and time-resolved spectroscopic techniques. The wide range of spectroscopic techniques presented herein have enabled us to discern the nature of the excited states (charge transfer, CT vs ligand localized, LL) as well as construct a Jablonski diagram for detailing the excited state reactivity within the series of molecules. The wavelength and excitation power dependence for these series of complexes are the first direct verification for the presence of simultaneous competing, noninteracting CT and LL excited states. Additionally, a computational framework is described that can be used to support spectroscopic assignments as a guide for future studies. Finally, the relationship between the obtained photophysics and possible photochemical separation mechanisms is described.

Structural Evolution of Paramagnetic Lanthanide Compounds in Solution Compared to Time- and Ensemble-Average Structures

Anisotropy in the magnetic susceptibility strongly influences the paramagnetic shifts seen in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) experiments. A previous study on a series of C3-symmetric prototype MRI contrast agents showed that their magnetic anisotropy was highly sensitive to changes in molecular geometry and concluded that changes in the average angle between the lanthanide-oxygen (Ln-O) bonds and the molecular C3 axis due to solvent interactions had a significant impact on the magnetic anisotropy and, consequently, the paramagnetic shift. However, this study, like many others, was predicated on an idealized C3-symmetric structural model, which may not be representative of the dynamic structure in solution at the single-molecule level. Here, we address this by using ab initio molecular dynamics simulations to simulate how the molecular geometry, in particular the angles between the Ln-O bonds and the pseudo-C3 axis, evolves over time in the solution, mimicking typical experimental conditions. We observe large-amplitude oscillations in the O-Ln-C̃3 angles, and complete active space self-consistent field spin-orbit calculations show that this leads to similarly large oscillations in the pseudocontact (dipolar) paramagnetic NMR shifts. The time-averaged shifts show good agreement with experimental measurements, while the large fluctuations suggest that an idealized structure provides an incomplete description of the solution dynamics. Our observations have significant implications for modeling the electronic and nuclear relaxation times in this and other systems where the magnetic susceptibility is exquisitely sensitive to the molecular structure.

Toward exact predictions of spin-phonon relaxation times: An ab initio implementation of open quantum systems theory

Spin-phonon coupling is the main driver of spin relaxation and decoherence in solid-state semiconductors at finite temperature. Controlling this interaction is a central problem for many disciplines, ranging from magnetic resonance to quantum technologies. Spin relaxation theories have been developed for almost a century but often use a phenomenological description of phonons and their coupling to spin, resulting in a nonpredictive tool and hindering our detailed understanding of spin dynamics. Here, we combine time-local master equations up to the fourth order with advanced electronic structure methods and perform predictions of spin-phonon relaxation time for a series of solid-state coordination compounds based on both transition metals and lanthanide Kramers ions. The agreement between experiments and simulations demonstrates that an accurate, universal, and fully ab initio implementation of spin relaxation theory is possible, thus paving the way to a systematic study of spin-phonon relaxation in solid-state materials.

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.

Computational and Spectroscopic Tools for the Detection of Bond Covalency in Pu(IV) Materials

Plutonium is used as a major component of new-generation nuclear fuels and of radioisotope batteries for Mars rovers, but it is also an environmental pollutant. Plutonium clearly has high technological and environmental importance, but it has an extremely complex, not well-understood electronic structure. The level of covalency of the Pu 5f valence orbitals and their role in chemical bonding are still an enigma and thus at the frontier of research in actinide science. We performed fully relativistic quantum chemical computations of the electronic structure of the Pu⁴⁺ ion and the PuO₂ compound. Using four different theoretical tools, it is shown that the 5f orbitals have very little covalent character although the 5f(_7/2) a_2u orbital with the highest orbital energy has the greatest extent of covalency in PuO₂. It is illustrated that the Pu M_4,5 edge high-energy resolution X-ray absorption near-edge structure (Pu M_4,5 HR-XANES) spectra cannot be interpreted in terms of dipole selection rules applied between individual 3d and 5f orbitals, but the selection rules must be applied between the total wavefunctions for the initial and excited states. This is because the states cannot be represented by single determinants. They are shown to involve major redistributions on the 5f electrons over the different 5f orbitals. These redistributions could be viewed as shake-up-like excitations in the 5f shell from the lowest orbital energy from J = 5f(_5/2) into higher orbital energy J = 5f(_7/2). We show that the second peak in the Pu M₄ edge and the high-energy shoulder of the Pu M₅ edge HR-XANES spectra probe the 5f(_7/2) a_2u orbital; thus, these spectral features are expected to change upon bond variations. We describe theoretical and spectroscopy tools, which can be applied for all actinide elements in materials with cubic structure.

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.

Molecular light-upconversion: we have had a problem! When excited state absorption (ESA) overcomes energy transfer upconversion (ETU) in Cr(III)/Er(III) complexes

Nine-coordinate [ErN₉] or [ErN₃O₆] chromophores found in triple helical [Er(L)₃]³⁺ complexes (L corresponds to 2,2′,6′,2′′-terpyridine (tpy), 2,6-(bisbenzimidazol-2-yl)pyridine (bzimpy), 2,6-diethylcarboxypyridine (dpa-ester) or 2,6-diethylcarboxamidopyridine (dpa-diamide) derivatives), [Er(dpa)₃]³⁻ (dpa is the 2,6-dipicolinate dianion) and [GaErGa(bpb-bzimpy)₃]⁹⁺ (bpb-bzimpy is 2,6-bis((pyridin-2-benzimidazol-5-yl)methyl-(benzimidazol-2-yl))pyridine) exhibit NIR (excitation at 801 nm) into visible (emission at 542 nm) linear light upconversion processes in acetonitrile at room temperature. The associated quantum yields 5.5(6) × 10⁻¹¹ ≤ ϕ^up_tot(ESA) ≤ 1.7(2) × 10⁻⁹ appear to be 1–3 orders of magnitude larger than those predicted by the accepted single-center excited-state absorption mechanism (ESA). Switching to the alternative energy transfer upconversion mechanism (ETU), which operates in multi-centers [CrErCr(bpb-bzimpy)₃]⁹⁺, leads to an improved quantum yield of ϕ^up_tot(ETU) = 5.8(6) × 10⁻⁸, but also to an even larger discrepancy by 4–6 orders of magnitude when compared with theoretical models. All photophysical studies point to Er(⁴I_13/2) as being the only available ‘long-lived’ (1.8 ≤ τ ≤ 6.3 μs) and emissive excited state, which works as an intermediate relay for absorbing the second photon, but with an unexpected large cross-section for an intrashell 4f → 4f electronic transition. With this in mind, the ETU mechanism, thought to optimize upconversion via intermetallic Cr → Er communication in [CrErCr(bpb-bzimpy)₃]⁹⁺, is indeed not crucial and the boosted associated upconversion quantum yield is indebted to the dominant contribution of the single-center erbium ESA process. This curious phenomenon is responsible for the successful implementation of light upconversion in molecular coordination complexes under reasonable light power intensities, which paves the way for applications in medicine and biology. Its origin could be linked with the presence of metal–ligand bonding.

Near-infrared to visible molecular upconversion exhibits quantum yields which are 2–6 orders of magnitude larger than those modeled with the accepted linear excited state absorption (ESA) or energy transfer (ETU) mechanisms: we have had a problem!

Luminescence, chiroptical, magnetic and ab initio crystal-field characterizations of an enantiopure helicoidal Yb(iii) complex

The electronic structure of a chiral Yb(iii)-based complex is fully determined by taking advantage of experimental magnetic, luminescence, and chiroptical (NIR-ECD and CPL) characterizations in combination with ab initio wavefunction calculations.

Crystal Structure and Magnetic Properties of Peacock–Weakley Type Polyoxometalates Na9[Ln(W5O18)2] (Ln = Tm, Yb): Rare Example of Tm(III) SMM

We report Peacock–Weakley complexes, Na9[Ln(W5O18)2]∙35H2O, formed with Tm(III), 1, and Yb(III), 2. Their syntheses, physico-chemical characterizations, crystal structures, and magnetic properties are described. Ab initio calculations are also reported. These polyoxometalate (POM) complexes were obtained using original synthetic conditions where acidification was performed with a stoichiometric amount of nitric acid to an acidity of Z = ν(H+)/ν(WO42–) = 8/10 = 0.80. Both the Tm(III) and Yb(III) derivatives were found to exhibit field-induced slow relaxation of their magnetization likely controlled by Raman and Orbach relaxation processes. 1 is a rare example of a Tm(III)-based single-molecule magnet (SMM) and is a consequence of the oblate tetragonal anti-prismatic symmetry of the coordination sphere.

How the Ligand Field in Lanthanide Coordination Complexes Determines Magnetic Susceptibility Anisotropy, Paramagnetic NMR Shift, and Relaxation Behavior

Complexes of lanthanide(III) ions are being actively studied because of their unique ground and excited state properties and the associated optical and magnetic behavior. In particular, they are used as emissive probes in optical spectroscopy and microscopy and as contrast agents in magnetic resonance imaging (MRI). However, the design of new complexes with specific optical and magnetic properties requires a thorough understanding of the correlation between molecular structure and electric and magnetic susceptibilities, as well as their anisotropies. The traditional Judd-Ofelt-Mason theory has failed to offer useful guidelines for systematic design of emissive lanthanide optical probes. Similarly, Bleaney's theory of magnetic anisotropy and its modifications fail to provide accurate detail that permits new paramagnetic shift reagents to be designed rather than discovered.A key determinant of optical and magnetic behavior in f-element compounds is the ligand field, often considered as an electrostatic field at the lanthanide created by the ligands. The resulting energy level splitting is a sensitive function of several factors: the nature and polarizability of the whole ligand and its donor atoms; the geometric details of the coordination polyhedron; the presence and extent of solvent interactions; specific hydrogen bonding effects on donor atoms and the degree of supramolecular order in the system. The relative importance of these factors can vary widely for different lanthanide ions and ligands. For nuclear magnetic properties, it is both the ligand field splitting and the magnetic susceptibility tensor, notably its anisotropy, that determine paramagnetic shifts and nuclear relaxation enhancement.We review the factors that control the ligand field in lanthanide complexes and link these to aspects of their utility in magnetic resonance and optical emission spectroscopy and imaging. We examine recent progress in this area particularly in the theory of paramagnetic chemical shift and relaxation enhancement, where some long-neglected effects of zero-field splitting, magnetic susceptibility anisotropy, and spatial distribution of lanthanide tags have been accommodated in an elegant way.

Analysis of charge density in nonaaquagadolinium(III) trifluoromethanesulfonate - insight into GdIII-OH2 bonding

The experimental charge-density distribution in [Gd(H₂O)₉](CF₃SO₃)₃ has been analysed and compared with the theoretical density functional theory calculations. Although the Gd-OH₂ bonds are mainly ionic, a covalent contribution is detectable when inspecting both the topological parameters of these bonds and the natural bond orbital results. This contribution originates from small electron transfer from the lone pairs of oxygen atoms to empty 5d and 6s spin orbitals of Gd³⁺.

Improvement of Ab Initio Ligand Field Theory by Means of Multistate Perturbation Theory

Over the last few years, ab initio ligand field theory (AILFT) has evolved into an important tool for the extraction of ligand field models from ab initio calculations. The inclusion of dynamic correlation on top of complete active space self-consistent field (CASSCF) reference functions, which is important for accurate results, was so far realized at the level of second-order N-electron valence state perturbation theory (NEVPT2). In this work, we introduce two alternative methods for the inclusion of dynamic correlation into AILFT calculations, the second-order dynamic correlation dressed complete active space method (DCD-CAS(2)) and the Hermitian quasi-degenerate NEVPT2 (HQD-NEVPT2). These methods belong to the class of multistate perturbation theory approaches, which allow for the mixing of CASSCF states under the effect of dynamic correlation (state-mixing). The two new versions of AILFT were tested for a diverse set of transition-metal complexes. It was found that the multistate methods have, compared to NEVPT2, an AILFT fit with smaller root mean square deviations (rmsds) between ab initio and AILFT energies. A comparison of AILFT excitation energies with the experiment shows that for some systems, the agreement gets better at the multistate level because of the smaller rmsds. However, for some systems, the agreement gets worse, which could be attributed to a cancellation of errors at the NEVPT2 level that is partly removed at the multistate level. An investigation of trends in the extracted ligand field parameters shows that at the multistate level, the ligand field splitting Δ gets larger, whereas the Racah parameters B and C get smaller and larger, respectively. An investigation of the reasons for the observed improvement for octahedral Cr^III halide complexes shows that the possibility of state-mixing relaxes constraints that are present at the NEVPT2 level and that keep Δ and B from following their individual preferences.

Electronic Structure and Photoluminescence Properties of Eu(η9-C9H9)2

The electronic structure of Eu²⁺ compounds results from a complex combination of strongly correlated electrons and relativistic effects as well as weak ligand-field interaction. There is tremendous interest in calculating the electronic structure as nowadays the Eu²⁺ ion is becoming more and more crucial, for instance, in lighting technologies. Recently, interest in semiempirical methods to qualitatively evaluate the electronic structure and to model the optical spectra has gained popularity, although the theoretical methods strongly rely upon empirical inputs, hindering their prediction capabilities. Besides, ab initio multireference models are computationally heavy and demand very elaborative theoretical background. Herein, application of the ligand-field density functional theory (LFDFT) method that is recently available in the Amsterdam Modeling Suite is shown: (i) to elucidate the electronic structure properties on the basis of the multiplet energy levels of Eu configurations 4f⁷ and 4f⁶5d¹ and (ii) to model the optical spectra quite accurately if compared to the conventional time-dependent density functional theory tool. We present a theoretical study of the molecular Eu(η⁹-C₉H₉)₂ complex and its underlying photoluminescence properties with respect to the Eu 4f-5d electron transitions. We model the excitation and emission spectra with good agreement with the experiments, opening up the possibility of modeling lanthanides in complex environment like nanomaterials by means of LFDFT at much-reduced computational resources and cost.

Relaxation dynamics in see-saw shaped Dy(iii) single-molecule magnets

Unusual see-saw shaped Dy(iii) single-molecule magnets, [K(DME)_n][L^ArDy(X)₂] (L^Ar = {C₆H₄[(2,6-ⁱPrC₆H₃)NC₆H₄]₂}²⁻), X = Cl (1) and X = I (2) were synthesized and display high effective energy barriers (U_eff = 1278–1334 K) in zero field.

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.