Norm-Conserving 4f-in-core Pseudopotentials and Basis Sets Optimized for Trivalent Lanthanides

We present here a set of norm-conserving 4f-in-core pseudopotentials, together with complementary valence-shell Gaussian basis sets, for the lanthanide (Ln) series (Ce - Lu). The Goedecker, Teter and Hutter (GTH) formalism is adopted with the generalized gradient approximation (GGA) for exchange-correlation functional of Perdew, Burke and Ernzerhof (PBE). The 4f-in-core pseudopotentials are built through attributing 4f-subconfiguration 4fn (n = 1 – 14) for Ln (Ln = Ce – Lu) into the atomic core region, making it possible to circumvent the difficulty of description of open 4fn valence shell. A wide variety of computational benchmarks and tests have been carried out on lanthanide systems including Ln3+-containing molecular complexes, aqueous solutions, and bulk solids, to validate the accuracy, reliability and efficiency of the optimized 4f-in-core GTH pseudopotentials and basis sets. The 4f-in-core GTH pseudopotentials successfully replicate main features of lanthanide structural chemistry and reaction energetics, particularly for non-redox reactions. The chemical bonding features of selected lanthanide systems are also discussed in details by utilizing these new 4f-in-core GTH pseudopotentials. This work bridges the idea of keeping highly localized 4f electrons in atomic core and efficient pseudopotential formalism of GTH, thus providing a highly efficient approach for studying lanthanide chemistry in multi-scale modeling of constituent-wise and structurally complicated systems, including electronic structures of condensed phase and first-principles molecular dynamics simulations.