Periodic Trends in Lanthanide Compounds through the Eyes of Multireference ab Initio Theory

Abstract

Regularities among electronic configurations for common oxidation states in lanthanide complexes and the low involvement of f orbitals in bonding result in the appearance of several periodic trends along the lanthanide series. These trends can be observed on relatively different properties, such as bonding distances or ionization potentials. Well-known concepts like the lanthanide contraction, the double-double (tetrad) effect, and the similar chemistry along the lanthanide series stem from these regularities. Periodic trends on structural and spectroscopic properties are examined through complete active space self-consistent field (CASSCF) followed by second-order N-electron valence perturbation theory (NEVPT2) including both scalar relativistic and spin-orbit coupling effects. Energies and wave functions from electronic structure calculations are further analyzed in terms of ab initio ligand field theory (AILFT), which allows one to rigorously extract angular overlap model ligand field, Racah, and spin-orbit coupling parameters directly from high-level ab initio calculations. We investigated the elpasolite Cs2NaLn(III)Cl6 (Ln(III) = Ce-Nd, Sm-Eu, Tb-Yb) crystals because these compounds have been synthesized for most Ln(III) ions. Cs2NaLn(III)Cl6 elpasolites have been also thoroughly characterized with respect to their spectroscopic properties, providing an exceptionally vast and systematic experimental database allowing one to analyze the periodic trends across the lanthanide series. Particular attention was devoted to the apparent discrepancy in metal-ligand covalency trends between theory and spectroscopy described in the literature. Consistent with earlier studies, natural population analysis indicates an increase in covalency along the series, while a decrease in both the nephelauxetic (Racah) and relativistic nephelauxetic (spin-orbit coupling) reduction with increasing atomic number is calculated. These apparently conflicting results are discussed on the basis of AILFT parameters. The AILFT derived parameters faithfully reproduce the underlying multireference electronic structure calculations. The remaining discrepancies with respect to experimentally derived data are mostly due to underestimation of the ligand field splittings, while the dynamic correlation and nephelauxetic effects appears to be adequately covered by CASSCF/NEVPT2.

Effect of Low Spin Excited States for Magnetic Anisotropy of Transition Metal Mononuclear Single Molecule Magnets

“…In this way, experimentally derived parameters as zero-field splitting D and E, effective g-factors, and Racah and ligand field parameters can be directly compared with their calculated counterparts. In many cases, data from magnetic measurements is not enough to fit a consistent parameter set in a univocal way, which can be estimated by electronic structure methods [22][23][24].…”

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

“…The one-electron character of crystal field theory is discussed and shown to be valuable, although it is not completely quantitative. [20,21] The first-principles methodS O-CASSCF( complete active space self-consistentf ield theory with at reatment of the spinorbit (SO) coupling by state interaction) has shown its capability,i nm any cases, to reproduce the magnetic data of the complexes, and give further physical insights, especially regarding the nature of the ground and excited states, into the direction of the magnetic moment and the energetic spectrum and chemicalb onding. In the case of aromaticl igands, it is necessary to add more parameters (a displacementp arameter) to mimict he covalency.…”

“…[14] First-principles calculations are regularly used to quantify the degree of covalencyi nm etal-ligand bonding. [20,21] The first-principles methodS O-CASSCF( complete active space self-consistentf ield theory with at reatment of the spinorbit (SO) coupling by state interaction) has shown its capability,i nm any cases, to reproduce the magnetic data of the complexes, and give further physical insights, especially regarding the nature of the ground and excited states, into the direction of the magnetic moment and the energetic spectrum and chemicalb onding. [20,21] The first-principles methodS O-CASSCF( complete active space self-consistentf ield theory with at reatment of the spinorbit (SO) coupling by state interaction) has shown its capability,i nm any cases, to reproduce the magnetic data of the complexes, and give further physical insights, especially regarding the nature of the ground and excited states, into the direction of the magnetic moment and the energetic spectrum and chemicalb onding.…”

Understanding the Stability Trend Along Light Lanthanide Complexes with an Ehtylenediamine‐Type Ligand: A Quantum Chemical Study

“…Due to the rapid development of theoretical chemical technologies and computation ability, more and more theoretical studies of Ln complexes have been reported in the past 30 years. Combined with the effective core potential, Density Functional Theory has been proved to be a powerful tool for determining different Ln‐complexes’ structures, bonding nature, stability and other properties . Using DFT, Wipff and co‐workers systematically studied the structures, Ln−L interaction, and energy features of Ln complexes formed with phosphoryl ligands .…”