Establishing Cost-Effective Computational Models for the Prediction of Lanthanoid Binding in [Ln(NO₃)]²⁺ (with Ln = La to Lu)

Abstract

Evaluating the efficiency of predictive methods is critical to the processes of upscaling laboratory processes to full-scale operations on an industrial scale. With regard to separation of lanthanoids, there is a considerable motivation to optimize these processes because of immediate use in nuclear fuel cycle operations, nuclear forensics applications, and rare-earth metal recovery. Efficient predictive capabilities in Gibbs free energies of reaction are essential to optimize separations and ligand design for selective binding needed for various radiochemical applications such as nuclear fuel disposition and recycling of lanthanoid fission products into useful radioisotope products. Ligand design is essential for selective binding of lanthanoids, as separating contiguous lanthanoids is challenging because of the similar behavior these elements exhibit. Modeling including electronic structure calculations of lanthanoid-containing compounds is particularly challenging because of the associated computational cost encountered with the number of electrons correlated in these systems and relativistic considerations. This study evaluates the predictive capabilities of various ab initio methods in the calculation of Gibbs free energies of reaction for [Ln(NO 3 )] 2+ compounds (with Ln = La to Lu), as nitrates are critical in traditional separation processes utilizing nitric acid. The composite methodologies evaluated predict Gibbs free energies of reaction for [Ln(NO 3 )] 2+ compounds within 5 kcal mol –1 in most cases from the target method [CCSD(T)-FSII/cc-pwCV∞Z-DK3+SO] at a fraction of the computational cost.

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

“…Because the separation of lanthanide ions in solution is often performed experimentally in nitric acid, we have chosen nitrates to fill the first coordination sphere of the lanthanides (eq ). Recent work has showcased the importance of accurately modeling lanthanide (and actinide) systems with bound nitrates. , Thus, the ligand extractant is competing with the nitrate ions, which often results in nitrates being bound to the final lanthanide–ligand complex. The computed reaction free energy differences Δ G 298 eq (Ln1,Ln2) of eq for La/Gd, Gd/Lu, and La/Lu are 2.14, 1.63, and 3.77 kcal/mol, respectively, for the TPSSh/Sapporo-TZP/DKH method and 1.60, 6.11, and 7.71 kcal/mol, respectively, for the BP86/SARC-TZVP/ZORA method.…”

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

“…To describe the RMSD calculations to ideal geometries, we focus on the solution structure of an aqua ion and an ion–ligand complex in water; however, RMSD calculations can also be done with ions in non-aqueous solvents. Ligand complexation will change the structure of the first coordination sphere, for example, in lanthanide–ligand complexes, − and RMSD calculations can be used to quantify how the structure changes. A specific example: binding with EDTA 4– will change the preferred geometry of the Lu 3+ ion from square antiprismatic in water to dodecahedral .…”

Predicting Stability Constants for Terbium(III) Complexes with Dipicolinic Acid and 4-Substituted Dipicolinic Acid Analogues using Density Functional Theory

“…Using the cleverly designed thermodynamic cycles, the systematic errors within the computational protocols may be largely canceled. 58−68 In this work, we attempted to calculate the relative stability constants for the complexation of terbium ions with a series of 4-substituted DPA analogues to preliminarily predict their efficiency in the Tb(III)-sensitized luminescence assays. In addition, population and structural analyses were carried out to elucidate the detailed electronic structures and the relative binding strengths of the complexes.…”

“…Absolute errors of |log K 1 exp – log K 1 calc | > 10 1 (with K 1 exp and K 1 calc are the experimental and calculated stability constants) have been commonplace, especially for multivalent anion ligands (due to the difficult solvation calculations of anion ligands’ diffusive electronic structures). − Nevertheless, the relative errors comparing the stability constants of ligand–ion complexes with similar structures are more constrained. Using the cleverly designed thermodynamic cycles, the systematic errors within the computational protocols may be largely canceled. − In this work, we attempted to calculate the relative stability constants for the complexation of terbium ions with a series of 4-substituted DPA analogues to preliminarily predict their efficiency in the Tb­(III)-sensitized luminescence assays. In addition, population and structural analyses were carried out to elucidate the detailed electronic structures and the relative binding strengths of the complexes.…”