Selecting Quantum-Chemical Methods for Lanthanide-Containing Molecules: A Balance between Accuracy and Efficiency

A DFT perspective on organometallic lanthanide chemistry

Computational studies of the coordination chemistry and bonding of lanthanides have grown in recent decades as the need for understanding the distinct physical, optical, and magnetic properties of these compounds increased. Density functional theory (DFT) methods offer a favorable balance of computational cost and accuracy in lanthanide chemistry and have helped to advance the discovery of novel oxidation states and electronic configurations. This Frontier article examines the scope and limitations of DFT in interpreting structural and spectroscopic data of low-valent lanthanide complexes, elucidating periodic trends, and predicting their properties and reactivity, presented through selected examples.

Probing the Chemical Bond between Lanthanides and Carbon: CeC, PrC, NdC, LuC, and TmC2

Resonant two-photon ionization experiments have been conducted to probe the bond dissociation energy (BDE) of the lanthanide-carbon bond, allowing the BDEs of CeC, PrC, NdC, LuC, and Tm-C₂ to be measured to high precision. Values of D₀(CeC) = 4.893(3) eV, D₀(PrC) = 4.052(3) eV, D₀(NdC) = 3.596(3) eV, D₀(LuC) = 3.685(4) eV, and D₀(Tm-C₂) = 4.797(6) eV are obtained. Additionally, the adiabatic ionization energy of LuC was measured, giving IE(LuC) = 7.05(3) eV. The electronic structure of these species, along with the previously measured LaC, has been further investigated using quantum chemical calculations. Despite LaC, CeC, PrC, and NdC having ground electronic configurations that differ only in the number of 4f electrons present and have virtually identical bond orders, bond lengths, fundamental stretching frequencies, and metallic oxidation states, a peculiar 1.30 eV range in bond dissociation energies exists for these molecules. A natural bond orbital analysis shows that the metal atoms in these molecules have a natural charge of +1 with a 5d² 4fⁿ 6s⁰ configuration while the carbon atom has a natural charge of -1 and a 2p³ configuration. The diabatic bond dissociation energies, calculated with respect to the lowest energy level of this separated ion configuration, show a greatly reduced energy range of 0.32 eV, with the diabatic BDE decreasing as the amount of 4f character in the σ-bond increases. Thus, the wide range of measured BDEs for these molecules is a consequence of the variation in atomic promotion energies at the separated ion limit. TmC₂ has a smaller BDE than the other LnC₂ molecules, due to the tiny amount of 5d participation in the valence molecular orbitals.

Analysis of the First Ion Coordination Sphere: A Toolkit to Analyze the Coordination Sphere of Ions

Rapid and accurate approaches to characterizing the coordination structure of an ion are important for designing ligands and quantifying structure-property trends. Here, we introduce AFICS (Analysis of the First Ion Coordination Sphere), a tool written in Python 3 for analyzing the structural and geometric features of the first coordination sphere of an ion over the course of molecular dynamics simulations. The principal feature of AFICS is its ability to quantify the distortion a coordination geometry undergoes compared to uniform polyhedra. This work applies the toolkit to analyze molecular dynamics simulations of the well-defined coordination structure of aqueous Cr³⁺ along with the more ambiguous structure of aqueous Eu³⁺ chelated to ethylenediaminetetraacetic acid. The tool is targeted for analyzing ions with fluxional or irregular coordination structures (e.g., solution structures of f-block elements) but is generalized such that it may be applied to other systems.

The solution structures and relative stability constants of lanthanide-EDTA complexes predicted from computation

Ligand selectivity to specific lanthanide (Ln) ions is key to the separation of rare earth elements from each other. Ligand selectivity can be quantified with relative stability constants (measured experimentally) or relative binding energies (calculated computationally). The relative stability constants of EDTA (ethylenediaminetetraacetic acid) with La3+, Eu3+, Gd3+, and Lu3+ were predicted from relative binding energies, which were quantified using electronic structure calculations with relativistic effects and based on the molecular structures of Ln-EDTA complexes in solution from density functional theory molecular dynamics simulations. The protonation state of an EDTA amine group was varied to study pH ∼7 and ∼11 conditions. Further, simulations at 25 °C and 90 °C were performed to elucidate how structures of Ln-EDTA complexes varying with temperature are related to complex stabilities at different pH conditions. Relative stability trends are predicted from computation for varying Ln3+ ions (La, Eu, Gd, Lu) with a single ligand (EDTA at pH ∼11), as well as for a single Ln3+ ion (La) with varying ligands (EDTA at pH ∼7 and ∼11). Changing the protonation state of an EDTA amine site significantly changes the solution structure of the Ln-EDTA complex resulting in a reduction of the complex stability. Increased Ln-ligand complex stability is correlated to reduced structural variations in solution upon an increase in temperature.

Predissociation measurements of the bond dissociation energies of EuO, TmO, and YbO

The observation of a sharp predissociation threshold in the resonant two-photon ionization spectra of EuO, TmO, and YbO has been used to measure the bond dissociation energies of these species. The resulting values, D₀(EuO) = 4.922(3) eV, D₀(TmO) = 5.242(6) eV, and D₀(YbO) = 4.083(3) eV, are in good agreement with previous values but are much more precise. In addition, the ionization energy of TmO was measured by the observation of a threshold for one-color two-photon ionization of this species, resulting in IE(TmO) = 6.56(2) eV. The observation of a sharp predissociation threshold for EuO was initially surprising because the half-filled 4f⁷ subshell of Eu in its ground state generates fewer potential energy curves than in the other molecules we have studied by this method. The observation of a sharp predissociation threshold in YbO was even more surprising, given that the ground state of Yb is nondegenerate (4f¹⁴6s², ¹S_g) and the lowest excited state of Yb is over 2 eV higher in energy. It is suggested that these molecules possess a high density of electronic states at the energy of the ground separated atom limit because ion-pair states drop below the ground limit, providing a sufficient electronic state density to allow predissociation to set in at the thermochemical threshold.

Predicting lanthanide coordination structures in solution with molecular simulation

The chemical and physical properties of lanthanide coordination complexes can significantly change with small variations in their molecular structure. Further, in solution, coordination structures (e.g., lanthanide-ligand complexes) are dynamic. Resolving solution structures, computationally or experimentally, is challenging because structures in solution have limited spatial restrictions and are responsive to chemical or physical changes in their surroundings. To determine structures of lanthanide-ligand complexes in solution, a molecular simulation approach is presented in this chapter, which concurrently considers chemical reactions and molecular dynamics. Lanthanide ion, ligand, solvent, and anion molecules are explicitly included to identify, in atomic resolution, lanthanide coordination structures in solution. The computational protocol described is applicable to determining the molecular structure of lanthanide-ligand complexes, particularly with ligands known to bind lanthanides but whose structures have not been resolved, as well as with ligands not previously known to bind lanthanide ions. The approach in this chapter is also relevant to elucidating lanthanide coordination in more intricate structures, such as in the active site of enzymes.