New Optimized Parameters of Extended Tight-Binding Method Ln-xTB (Ln = La-Lu) to Explore Lanthanide Molecular...

In this work, we newly optimized the parameters of the extended tight-binding method Ln-xTB for the entire lanthanide (Ln) series (La to Lu) by using a genetic algorithm (GA) and incorporating a relativistic Hamiltonian, enabling accurate exploration of lanthanide molecular chemistry in complex environments. To validate the accuracy and reliability of Ln-xTB, we conducted comprehensive benchmarks on different classes of lanthanide-containing molecules (including halides, aqua complexes, and ligand-coordinated complexes) and compared results with the reported all-electron DFT calculations, effective core potential (ECP) methods, GFN0-xTB, GFN1-xTB, GFN2-xTB, RM1, Sparkle/RM1, Sparkle/AM1, Sparkle/PMn (n = 3, 6, 7), HF, MP2, CCSD(T) methods and experimental data. The results show that Ln-xTB successfully optimizes lanthanide compound structures with an average mean absolute deviation (MAD) of 0.037 Å for bond lengths relative to all-electron DFT, outperforming GFN2-xTB (MAD = 0.134 Å) and approaching the accuracy of ECP methods (MAD = 0.024 Å). Relative errors in bond lengths of Ln-xTB are predominantly within 3% (vs. all-electron DFT) and 5% (vs. experimental data). The results of benchmarks indicate the newly developed Ln-xTB method is more accurate than the previously reported GFNn-xTB (n = 0, 1, 2) methods. The structure optimization of lanthanide complexes with hundreds of atoms by using the Ln-xTB was completed in several seconds on a single CPU core. This work provides a set of accurate, efficient Ln-xTB parameters, addressing the long-standing trade-off between precision and computational cost in lanthanide molecular chemistry.