Chemical Bonding of Crystalline LnB₆ (Ln = La–Lu) and Its Relationship with Ln₂B₈ Gas-Phase Complexes

Abstract

Solid-state lanthanide (Ln) borides of the simple LnB6 composition not only exhibit exciting physical behavior, in particular magnetic properties, but their electronic structure and chemical bonding are particularly intriguing as well. To shed more light on the latter, we have performed quantum-chemical (DFT+U) electronic-structure calculations and bonding analyses of the entire LnB6 series with Ln from La to Lu. Trivially, the boron framework is held together by the B 2sp orbitals, and this framework bonds to the Ln atoms via covalent–ionic interactions. The Ln 4f electrons, however, are decisive for the magnetic properties. In more detail, the effective charges of the Ln atoms as calculated by (Mulliken or Löwdin) occupation numbers of the 6s/5d/4f orbitals are compatible with experimentally assigned oxidation numbers. The shorter inter-octahedral B–B bonds, dominated by 2s–2p interactions, turn out to be stronger than the intra-octahedral B–B bonding with a more 2p–2p-like character. Interestingly, there are strong structural similarities between the LnB6 motif studied here and gas-phase Ln2B8 species showing inverse sandwich structures, and these similarities are also reflected in the electronic structure. In particular, Ln2B8 is predicted to have a large electron affinity. Hence, this work aims at providing an intrinsic link between gas-phase complexes and solid-state crystal structures in order to better understand the former species.

Perfect cubic La-doped boron clusters La6&[La@B24]+/0as the embryos of low-dimensional lanthanide boride nanomaterials

“…46,47 The Coulomb-corrected local spin-density approximation (LSDA+U) was utilized for both structural relaxation and static calculation (U ¼ 5 eV). 31,48 The cutoff energy of the plane wave basis is set to 500 eV. Atomic structures are fully relaxed using the conjugate gradient method until the maximum force on each atom was less than 0.01 eV A À1 and the energy precision was set to 10 À5 eV.…”

“…[27][28][29][30] It possesses a typical cubic CaB 6 -type lattice (Pm 3m, O h 1 ) characterized with a 3D network constituted of B 6 octahedrons, with the interstitial locations lled by trivalent La atoms. 31 Interestingly, each unit cell in LaB 6 (7) contains a B 24 cubic framework which possesses six equivalent B 8 rings on the surface sharing twelve B-B dumbbells on the edges, with each B 8 ring sandwiched between two neighboring La atoms. The strong structural similarity between the gas-phase inverse sandwich La 2 B 8 (1) complex and cubic three-dimensional (3D) LaB 6 (7) crystal has been previously noticed.…”

“…The strong structural similarity between the gas-phase inverse sandwich La 2 B 8 (1) complex and cubic three-dimensional (3D) LaB 6 (7) crystal has been previously noticed. 31 LaB 6 nanowires in cubic LaB 6 (7) lattice were also recently conrmed to be active electrochemical materials for supercapacitors. 32 However, a cubic embryo of the LaB 6 (7) lattice still remains unknown to date in a bottom-up approach starting from gas-phase clusters.…”

Cationic Pb2 Dumbbells Stabilized in the Highly Covalent Lead Nitridosilicate Pb2Si5N8

“…For quantification of the effective charge reduction by covalency in Pb 2 Si 5 N 8 , Mulliken charges Q A as defined recently were calculated . These charges arrive at +0.71, +1.73, and −1.18 for Pb, Si, and N, respectively, significantly lower than the idealized ionic charges +2, +4, and −3.…”

Computational Insights into the Interaction between Li2S/Li2S2 and Heteroatom‐Doped Graphene Materials

“…Therefore, we perform crystal orbital Hamilton population (COHP) analysis to uncover the mechanism of Li 2 S/Li 2 S 2 adsorption on B‐doped graphene. COHP and its value, ICOHP are used to measure the strength of covalent bonds . Given the circumstance that Li 2 S/Li 2 S 2 adsorb from above the graphene plane (z direction), this adsorption is more likely due to the effect of delocalized π system of graphene substrates.…”