Ionic bonding of lanthanides, as influenced by d- and f-atomic orbitals, by core-shells and by relativity

Abstract

Lanthanide trihalide molecules LnX3 (X = F, Cl, Br, I) were quantum chemically investigated, in particular detail for Ln = Lu (lutetium). We applied density functional theory (DFT) at the nonrelativistic and scalar and SO-coupled relativistic levels, and also the ab initio coupled cluster approach. The chemically active electron shells of the lanthanide atoms comprise the 5d and 6s (and 6p) valence atomic orbitals (AO) and also the filled inner 4f semivalence and outer 5p semicore shells. Four different frozen-core approximations for Lu were compared: the (1s(2) -4d(10) ) [Pd] medium core, the [Pd+5s(2) 5p(6) = Xe] and [Pd+4f(14) ] large cores, and the [Pd+4f(14) +5s(2) 5p(6) ] very large core. The errors of LuX bonding are more serious on freezing the 5p(6) shell than the 4f(14) shell, more serious upon core-freezing than on the effective-core-potential approximation. The LnX distances correlate linearly with the AO radii of the ionic outer shells, Ln(3+) -5p(6) and X(-) -np(6) , characteristic for dominantly ionic Ln(3+) -X(-) binding. The heavier halogen atoms also bind covalently with the Ln-5d shell. Scalar relativistic effects contract and destabilize the LuX bonds, spin orbit coupling hardly affects the geometries but the bond energies, owing to SO effects in the free atoms. The relativistic changes of bond energy BE, bond length Re , bond force k, and bond stretching frequency vs do not follow the simple rules of Badger and Gordy (Re ∼BE∼k∼vs ). The so-called degeneracy-driven covalence, meaning strong mixing of accidentally near-degenerate, nearly nonoverlapping AOs without BE contribution is critically discussed.

The electronic configurations of LnX (Ln=La–Eu, X=O, S, Se, Te): A FON–DFT investigation

“…Since our results agree with popular theoretical programs and approaches, we think this work is still acceptable and reliable. Similar DFT calculations on lanthanide systems have been reported in our recently works [26,59,60].…”

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

“…A purely electrostatic approach has been proposed to determine the direction of the magnetic moment, by minimizing the potential energy; the ligands are modeled by fractional charges determined by valence‐bond resonance hybrids . First‐principles calculations are regularly used to quantify the degree of covalency in metal–ligand bonding . CFPs may be deduced from first‐principles methods and the contribution of covalency to CFPs was recently confirmed to be non‐negligible …”

“…It is shownt hat am odel with three layers of charges reproduces the electrostatic field generated by the ligands and that the covalency plays aqualitative role. [15][16][17][18][19] CFPs may be deduced from first-principles methods and the contributiono fc ovalency to CFPs was recently confirmedt ob enon-negligible. This permits ar eductiono ft he many-electron problem to ad iscussion of the energy of the seven 4f orbitals.…”

“…[13] Ap urely electrostatic approach has been proposed to determinet he direction of the magnetic moment, by minimizing the potentiale nergy;t he ligandsa re modeled by fractional charges determined by valence-bond resonance hybrids. [15][16][17][18][19] CFPs may be deduced from first-principles methods and the contributiono fc ovalency to CFPs was recently confirmedt ob enon-negligible. [15][16][17][18][19] CFPs may be deduced from first-principles methods and the contributiono fc ovalency to CFPs was recently confirmedt ob enon-negligible.…”

Understanding Periodic and Non-periodic Chemistry in Periodic Tables

“…The 'comparatively simple' ε(Z) behavior of 4sp vs. 3d was sketched in Figure 5. In the first two groups, the (n−1)d and (n−2)f shells are high-energy, diffuse Rydberg levels, hardly contributing to bonding in the majority of cases (Ji et al, 2015;see however: Levy and Hargittai, 2000;Wu et al, 2018a,b), which changes from group 3 onward.…”