Ln 5d Research Articles

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.

Bond Dissociation Energies Reveal the Participation of d Electrons in f-Element Halide Bonding.

Bond dissociation energies (BDEs) reported in the literature for lanthanide monofluorides and lanthanide monochlorides LnX, where X = F or Cl, exhibit substantial irregular variations across the Ln series. It is demonstrated here that correlations of these variations with reported experimentally based atomic energies to prepare the Ln constituent for bonding reveal the nature of the bonding. Whereas some molecular characteristics are well understood in the context of highly ionic bonding, with LnX considered to be (Ln+)(X-), some significant variations in BDEs are not well rationalized simply by ionization to convert Ln to Ln+ for bonding. Focusing here on lanthanide monofluorides LnF, a consideration of alternative Ln preparation schemes shows that a particularly good rationalization of BDEs is obtained by invoking the participation of a lanthanide 5d electron in bonding. This 5d participation could be in ionic (Ln+)(F-) via π-donation from F- 2p to empty Ln+ 5d orbitals or in covalent π-bonded Ln:F via polarization from Ln 5d to F 2p, with these ionic and polar covalent perspectives ultimately being equivalent. The inference of lanthanide 5d involvement suggests that the valence 4f and 6s electrons do not effectively participate in some key aspects of the bonding, presumably due to poor spatial overlap with F 2p orbitals. An extension to actinide monofluorides, AnF, assumes analogous ionic or polar covalent bonding involving a valence 6d electron and results in predictions for BDEs that include a general decrease from left to right across the series, except for a distinctive local minimum at AmF. Determining the BDE for AmF would serve to evaluate the predictions and the underlying assumption of 6d bonding. The BDE assessments/predictions for neutral monofluorides, LnF and AnF, are also applied to cationic LnF+ and AnF+, and it is noted that the approach can be directly extended to f-element monochlorides, monobromides, and monoiodides.

Electronic structures and topological properties in nickelates Ln n+1Ni n O2n+2.

After the significant discovery of the hole-doped nickelate compound Nd0.8Sr0.2NiO2, analyses of the electronic structure, orbital components, Fermi surfaces and band topology could be helpful to understand the mechanism of its superconductivity. Based on first-principle calculations, we find that Ni n}{}3d_{x^2-y^2} states contribute the largest Fermi surface. The n}{}Ln 5d_{3z^2-r^2} states form an electron pocket at Γ, while 5dxy states form a relatively bigger electron pocket at A. These Fermi surfaces and symmetry characteristics can be reproduced by our two-band model, which consists of two elementary band representations: B1g@1a ⊕ A1g@1b. We find that there is a band inversion near A, giving rise to a pair of Dirac points along M-A below the Fermi level upon including spin-orbit coupling. Furthermore, we perform density functional theory based Gutzwiller (DFT+Gutzwiller) calculations to treat the strong correlation effect of Ni 3d orbitals. In particular, the bandwidth of n}{}3d_{x^2-y^2} has been renormalized largely. After the renormalization of the correlated bands, the Ni 3dxy states and the Dirac points become very close to the Fermi level. Thus, a hole pocket at A could be introduced by hole doping, which may be related to the observed sign change of the Hall coefficient. By introducing an additional Ni 3dxy orbital, the hole-pocket band and the band inversion can be captured in our modified model. Besides, the nontrivial band topology in the ferromagnetic two-layer compound La3Ni2O6 is discussed and the band inversion is associated with Ni n}{}3d_{x^2-y^2} and La 5dxy orbitals.

Electronic structure of Ln2O2Te (Ln=La, Sm and Gd) by X-ray absorption spectroscopy

The oxytellurides are layered structure material which shows low lattice thermal conductivity and hence making them suitable for high temperature thermoelectric applications. We report the electronic structural properties of rare-earth doped oxytellurides [Ln2O2Te (Ln = La, Sm and Gd)] prepared by solid state reaction method. This research is focused on the suitability of rare-earth oxychalcogenide as a thermoelectric material using the electronic structure investigations. The X-ray absorption spectra at O K-edge show the O 2p bonding with Ln 5d and 4f and Te 5s states and the Ln M-edges show that the valences of Ln are to be trivalent or mixed states. The Ln M-edges are also simulated with Cowan code, and electronic structures of these oxytellurides are discussed. The substitution of different rare earth metals at the Ln-site, may enhance the thermoelectric property and stability of the material.

Observation of highly stable and symmetric lanthanide octa-boron inverse sandwich complexes

While boron forms a wide range of metal borides with important industrial applications, there has been relatively little attention devoted to lanthanide boride clusters. Here we report a joint photoelectron spectroscopy and quantum chemical study on two octa-boron di-lanthanide clusters, Ln2B8- (Ln = La, Pr). We found that these clusters form highly stable inverse sandwich structures, [Ln-B8-Ln]-, with strong Ln and B8 bonding via interactions between the Ln 5d orbitals and the delocalized σ and π orbitals on the B8 ring. A (d-p)δ bond, involving the 5dδ and the antibonding π orbital of the B8 ring, is observed to be important in the Ln-B8 interactions. The highly symmetric inverse sandwich structures are overwhelmingly more stable than any other isomers. Upon electron detachment, the (d-p)δ orbitals become half-filled, giving rise to a triplet ground state for neutral La2B8 In addition to the two unpaired electrons in the (d-p)δ orbitals upon electron detachment, the neutral Pr2B8 complex also contains two unpaired 4f electrons on each Pr center. The six unpaired spins in Pr2B8 are ferromagnetically coupled to give rise to a septuplet ground state. The current work suggests that highly magnetic Ln…B8…Ln inverse sandwiches or 1D Ln…B8…Ln nanowires may be designed with novel electronic and magnetic properties.

Quantitative Evidence for Lanthanide-Oxygen Orbital Mixing in CeO2, PrO2, and TbO2.

Understanding the nature of covalent (band-like) vs ionic (atomic-like) electrons in metal oxides continues to be at the forefront of research in the physical sciences. In particular, the development of a coherent and quantitative model of bonding and electronic structure for the lanthanide dioxides, LnO2 (Ln = Ce, Pr, and Tb), has remained a considerable challenge for both experiment and theory. Herein, relative changes in mixing between the O 2p orbitals and the Ln 4f and 5d orbitals in LnO2 are evaluated quantitatively using O K-edge X-ray absorption spectroscopy (XAS) obtained with a scanning transmission X-ray microscope and density functional theory (DFT) calculations. For each LnO2, the results reveal significant amounts of Ln 5d and O 2p mixing in the orbitals of t2g (σ-bonding) and eg (π-bonding) symmetry. The remarkable agreement between experiment and theory also shows that significant mixing with the O 2p orbitals occurs in a band derived from the 4f orbitals of a2u symmetry (σ-bonding) for each compound. However, a large increase in orbital mixing is observed for PrO2 that is ascribed to a unique interaction derived from the 4f orbitals of t1u symmetry (σ- and π-bonding). O K-edge XAS and DFT results are compared with complementary L3-edge and M5,4-edge XAS measurements and configuration interaction calculations, which shows that each spectroscopic approach provides evidence for ground state O 2p and Ln 4f orbital mixing despite inducing very different core-hole potentials in the final state.

Theoretical Study on the Photoelectron Spectra of Ln(COT)2–: Lanthanide Dependence of the Metal–Ligand Interaction

We have performed a theoretical analysis of the recently reported photoelectron (PE) spectra of the series of sandwich complex anions Ln(COT)2- (Ln = La-Lu, COT = 1,3,5,7-cyclooctatetraene), focusing on the Ln dependence of the vertical detachment energies. For most Ln, the π molecular orbitals, largely localized on the COT ligands, have the energy order of e1g < e1u < e2g < e2u as in the actinide analogues, reflecting the substantial orbital interaction with the Ln 5d and 5p orbitals. Thus, it would be expected that the lanthanide contraction would increase the orbital interaction so that the overlaps between the COT π and Ln atomic orbitals tend to increase across the series. However, the PE spectra and theoretical calculations were not consistent with this expectation, and the details have been clarified in this study. Furthermore, the energy level splitting patterns of the anion and neutral complexes have been studied by multireference ab initio methods, and the X peak splittings observed in the PE spectra only for the middle-range Ln complexes were found to be due to the specific interaction between the Ln 4f and ligand π orbitals of the neutral complexes in e2u symmetry. Because the magnitude of this 4f-ligand interaction depends critically on the final state 4f electron configuration and the spin state, a significant Ln dependence in the PE spectra is explained.

Creation of 4fn-4fn-15d1 Transition Energy Diagram of Trivalent Lanthanide Ions in Fluorides Based on First-Principles Calculations

The theoretical prediction of the 4fn-4fn-15d1 transition energies of lanthanides in crystals is an important issue in the development of novel luminescent materials such as solid-state lasers or phosphors. In our previous work, the first-principles calculations of the entire multiplet structures of lanthanide (Ln) ions in LiYF4 (YLF) corresponding to 4fn and 4fn-15d1 configurations were performed using the relativistic discrete variational multi-electron (DVME) method [1]. However, the lowest 4fn-4fn-15d1transition energy was overestimated for light lanthanides while it was underestimated for heavy lanthanides. In this work, in order to improve the accuracy of the theoretical transition energy, a correction based on the molecular orbital (MO) calculation in the Slater’s transition state was introduced. The LnF8 clusters were constructed based on the crystal structures of YLF and CaF2. The fully-relativistic MO calculations were performed using the relativistic DV-Xα code. The multiplet calculations were performed using the relativistic DVME code. The Slater determinants corresponding to 4fn and 4fn-15d1 configurations were constructed from the four-component relativistic MOs and used as the basis functions to diagonalize the relativistic many-electron Hamiltonian. In order to correct the errors in the transition energy, MO calculations in the Slater’s transition state where a half electron was excited from the Ln 4f level to the Ln 5d level were also performed. A constant correction term was added to the diagonal matrix element of the many-electron Hamiltonian for 4fn-15d1 configuration so that the 4fn -4fn-15d1transition energy is consistent with the 4f-5d transition energy obtained by the MO calculation in the Slater’s transition state. The diagrams representing the lowest 4fn-4fn-15d1transition energies of trivalent lanthanide ions in YLF calculated with and without the above correction are shown in Fig. 1. The overestimation in the light lanthanides and the underestimation in the heavy lanthanides are significantly reduced by the correction and the theoretical transition energies approached to the experimental values in the literature [2-5].

Evidence for 5d-σ and 5d-π covalency in lanthanide sesquioxides from oxygen K-edge X-ray absorption spectroscopy.

The electronic structure in the complete series of stable lanthanide sesquioxides, Ln2O3 (Ln = La to Lu, except radioactive Pm), has been evaluated using oxygen K-edge X-ray absorption spectroscopy (XAS) with a scanning transmission X-ray microscope (STXM). The experimental results agree with recent synthetic, spectroscopic and theoretical investigations that provided evidence for 5d orbital involvement in lanthanide bonding, while confirming the traditional viewpoint that there is little Ln 4f and O 2p orbital mixing. However, the results also showed that changes in the energy and occupancy of the 4f orbitals can impact Ln 5d and O 2p mixing, leading to several different bonding modes for seemingly identical Ln2O3 structures. On moving from left to right in the periodic table, abrupt changes were observed for the energy and intensity of transitions associated with Ln 5d and O 2p antibonding states. These changes in peak intensity, which were directly related to the amounts of O 2p and Ln 5d mixing, were closely correlated to the well-established trends in the chemical accessibility of the 4f orbitals towards oxidation or reduction. The unique insight provided by the O K-edge XAS is discussed in the context of several recent theoretical and physical studies on trivalent lanthanide compounds.

Covalent Bonding and the Trans Influence in Lanthanide Compounds

A pair of mer-octahedral lanthanide chalcogenolate coordination complexes [(THF)(3)Ln(EC(6)F(5))(3) (Ln = Er, E = Se; Ln = Yb, E = S)] have been isolated and structurally characterized. Both compounds show geometry-dependent bond lengths, with the Ln-E bonds trans to the neutral donor tetrahydrofuran (THF) significantly shorter than the Ln-E bonds that are trans to negatively charged EC(6)F(5) ligands. Density functional theory calculations indicate that the structural trans influence evidenced by the differences in these bond lengths results from a covalent Ln-E interaction involving ligand p and Ln 5d orbitals.

Quantum chemical analysis of the bond lengths in fn and fn−1d1 states of Ce3+, Pr3+, Pa4+, and U4+ defects in chloride hosts

It is widely believed that impurity–ligand bond distances in lanthanide (Ln) and actinide (An) doped crystals, are larger in the fn−1d1 energy levels than in the fn ones. This idea, which was not justified and is probably based on the fact that Ln 5d (An 6d) orbitals have a radial extent much larger than Ln 4f (An 5f ) orbitals, has been neither confirmed nor rejected experimentally in spite of the fact that a very large number of absorption/emission spectroscopic studies on f-element doped hosts exist, because the band shapes depend on the square of the bond length offsets between initial and final electronic states. Recent quantum chemical calculations on Ln and An impurities in fluoride and chloride cubic hosts, which considered host embedding, dynamic electron correlation, and relativistic spin–free and spin–orbit coupling effects, have shown that impurity–ligand bond distances are classified in three sets according to their configuration, with the following trend: Re[fn−1d(t2g)1]&amp;lt;Re[fn]&amp;lt;Re[fn−1d(eg)1], in contradiction with the assumed expectations. In this paper we give an interpretation of this, on the basis of a constrained space orbital variation analysis of the chemical bond in states of the fn, fn−1d(t2g)1, and fn−1d(eg)1 configurations of four model systems: Cs2NaYCl6:Ce3+, Cs2NaYCl6:Pr3+, Cs2ZrCl6:Pa4+, and Cs2ZrCl6:U4+. The analysis shows that the basic difference between fn and fn−1d1 configurations regarding bond effects which are responsible for the bond distance is that, in the former, all the open-shell electrons are shielded from the ligands by the 5p (6p) filled shell and the bond length is determined by closed-shell interactions between the outermost Ln 5p6 (An 6p6) shell and the ligands, whereas in the latter one electron has crossed the 5p (6p) barrier and is much more exposed to bonding interactions with the ligands, at the same time that an internal 4f (5f ) hole has been created which induces ligand to Ln (An) charge transfer, all of it resulting in the shown trends.

Density functional study on zerovalent lanthanide bis(arene)-sandwich complexes

Several zerovalent lanthanide bis(arene)-sandwich complexes, Ln(η6-C6H6)2, Ln = La, Ce, Eu, Gd and Lu, have been studied by means of density functional theory. The calculated geometries are in good agreement with experiment. The calculated dissociation energies of the bond Ln-(η6-C6H6) may be considerably underestimated, but they correctly reveal the variation regularity. The bonding in these molecules can be described in terms of a relatively weak π-electron donation from benzene to Ln and a stronger electron back-donation from Ln 5d to the benzene π* orbitals. During bond formation, there is electron promotion from Ln 6s to 5d instead of from 4f to 5d, in opposition to the proposal of Anderson et al. The relativistic effect only slightly influences the molecular geometry, but decreases the bonding energy considerably through lowering the Ln 6s level and raising the 5d level. It enhances the trend of the bonding energy to decrease along the lanthanide series.

Effects of structure and doping on the electronic properties of La2CuO4 and Nd2CuO4

We have calculated the electronic structure of Nd 2 CuO 4 in the observed T' structure and also in hypothetical T and T ∗ structures with the linear-muffin-tin-orbital method in the atomic-sphere-approximation (LMTO-ASA). We also studied in these local density approximation (LDA) calculations the effects of Ce and Sr doping by supercell calculations. We find that the O partial density of states of the NdO 2 planes substantially shifts in energy as a function of doping and structure. By comparing our results with a similar study on La 2 CuO 4 , we note that the position of the Ln 5d states (Ln=La, Nd) through hybridization with the 2p O states in the LnO 2 planes, determines the energy shifts of these O p bands. Upon doping with Ce or Sr, the metal d-oxygen p hybridization in the Nd 1− x Ce x O 2 and Nd 1− y Sr y O 2 planes gives rise to a local energy shift of the O p bands.