Insights into rare earth element speciation: unraveling sulfate and hydrolysis complexes through DFT calculations

Rare earth elements (REE) are indispensable in numerous green technologies owing to their exceptional physical and chemical attributes. Separating REE is a pivotal process to meet the increasing demands of the high-tech industry. Understanding the hydrolysis of REE in aqueous environments marks the initial stride in comprehending their separation mechanisms. Sulfate commonly coexists in high-concentration solutions alongside REE, stemming from mineral processing. We analyzed the hydrolysis of REE and their complexes with sulfate using DFT methods. We present and discuss on the structural characteristics of hydrolysis species and sulfate complexes in alignment with existing experimental data. Estimates of Gibbs free energies for hydrolysis and sulfate complex formation were compared against literature values. REE pose challenges owing to the labile nature of aqua complexes and the pivotal role of system dynamics. We showed that hydrolysis reactions could be suitably modeled, yielding an error margin of approximately 5 kcal mol^-1 concerning experimental values, employing the M06 exchange-correlation functional with the SMD implicit solvation model. However, sulfate chemical species proved to be more challenging, exhibiting larger error margins with substantial variations across the REE series. The Raman spectrum analysis of lanthanum sulfate complexes demonstrated excellent agreement with experimental values.

We applied the M06, PBE, and PBE0 exchange-correlation functionals combined with def2-TZVP basis sets and SMD to obtain the Gibbs free energies of hydrolysis and sulfate complexation with lanthanides in aqueous solution. The calculations were performed using the ORCA program.