SLn-xTB: a new accurate extended tight-binding approach for exploring lanthanide solution chemistry

In this work, we present SLn-xTB, a new extended tight-binding (xTB) approach tailored for lanthanide solution chemistry. SLn-xTB extends the GFN1-xTB framework by introducing lanthanide-specific parameterizations and correcting for 4f orbital contributions, enabling efficient and accurate simulations of Ln-containing solutions. To optimize its parameters, we developed the GALSC (Genetic Algorithm for Lanthanide Solution Chemistry) package, which integrates an improved genetic algorithm (GA) to minimize the total energy. We validated SLn-xTB across six prototypical Ln-containing solution systems: LnF₃(H₂O)₆₄, LnCl₃(H₂O)₆₄, LnBr₃(H₂O)₆₄, Ln(H₂O)₆₄Cl₃, Ln(NO₃)₃(H₂O)₆₄, and Ln(C301)₃(H₂O)₆₄ (Ln = La-Lu). For Ln(H₂O)₆₄Cl₃, the average relative error (RE) in Ln-O bond lengths compared to experiments is only 0.97%, with individual RE values of <1.6% for all Ln. Molecular dynamics (MD) simulations using SLn-xTB (SLn-xTB-MD) further demonstrate its ability to capture the temperature-dependent dynamic behaviors of Eu(C301)₃(H₂O)₆₄ and effects of counter ions on Pm(PyDGA)₃X₃(H₂O)₆₄ (X = F^-, Cl^-, Br^-, I^-, NO₃^-, and ClO₄^-). SLn-xTB reduces computational cost compared to DFT while maintaining DFT-level accuracy. This work provides a powerful computational tool for lanthanide solution chemistry, enabling large-scale simulations that were previously infeasible with traditional methods.