A complete set of pseudopotentials and accompanying basis sets for all lanthanide elements are presented based on the relativistic, norm-conserving, separable, dual-space Gaussian-type pseudopotential protocol of Goedecker, Teter, and Hutter (GTH) within the generalized gradient approximation (GGA) and the exchange–correlation functional of Perdew, Burke, and Ernzerhof (PBE). The corresponding basis sets have been molecularly optimized (MOLOPT) using a contracted form with a single set of Gaussian exponents for the s, p, and d states. The f states are uncontracted explicitly with Gaussian exponents. Moreover, the Hubbard U values for each lanthanide element, for DFT+U calculations, are also tabulated, allowing for the proper treatment of the strong on-site Coulomb interactions of localized 4f electrons. The accuracy and reliability of our GTH pseudopotentials and companion basis sets optimized for lanthanides is illustrated by a series of test calculations on lanthanide-centered molecules, and solid-state systems, with the most common oxidation states. We anticipate that these pseudopotentials and basis sets will enable larger-scale density functional theory calculations and ab initio molecular dynamics simulations of lanthanide molecules in either gas or condensed phases, as well as of solid state lanthanide-containing materials, allowing further exploration of the chemical and physical properties of lanthanide systems.

9,10,11,20,21,22-Hexaphenyltetrabenzo[a,c,l,n]pentacene (1) was prepared by the reaction of 1,3-diphenylphenanthro[9,10-c]furan with the bisaryne equivalent generated from 1,2,4,5-tetrabromo-3,6-diphenylbenzene in the presence of n-butyllithium, followed by deoxygenation of the double adduct with low-valent titanium. The X-ray structure of 1 shows it to be the most highly twisted polycyclic aromatic hydrocarbon known, with an end-to-end twist of 143.6 degrees . Compound 1 was resolved by chromatography on a chiral support, and the pure enantiomers have specific rotations in excess of 7000 degrees , but the molecule racemizes slowly at 25 degrees C (t1/2 = 9.3 h, DeltaGrac = 23.8 kcal/mol).

To resolve the fleeting structures of lanthanide Ln3+ aqua ions in solution, we (i) performed the first ab initio molecular dynamics (AIMD) simulations of the entire series of Ln3+ aqua ions in explicit water solvent using pseudopotentials and basis sets recently optimized for lanthanides and (ii) measured the symmetry of the hydrating waters about Ln3+ ions (Nd3+, Dy3+, Er3+, Lu3+) for the first time with extended X-ray absorption fine structure (EXAFS). EXAFS spectra were measured experimentally and generated from AIMD trajectories to directly compare simulation, which concurrently considers the electronic structure and the atomic dynamics in solution, with experiment. We performed a comprehensive evaluation of EXAFS multiple-scattering analysis (up to 6.5 Å) to measure Ln–O distances and angular correlations (i.e., symmetry) and elucidate the molecular geometry of the first hydration shell. This evaluation, in combination with symmetry-dependent L3- and L1-edge spectral analysis, shows that the AIMD simulations remarkably reproduces the experimental EXAFS data. The error in the predicted Ln–O distances is less than 0.07 Å for the later lanthanides, while we observed excellent agreement with predicted distances within experimental uncertainty for the early lanthanides. Our analysis revealed a dynamic, symmetrically disordered first coordination shell, which does not conform to a single molecular geometry for most lanthanides. This work sheds critical light on the highly elusive coordination geometry of the Ln3+ aqua ions.