Low-lying electronic states of the lutetium dimer （Lu2） were studied based on density functional theory （DFT） using ten different density functionals together with three different relativistic effective core pseudopotentials （RECPs）. Relative state energies, equilibrium bond lengths, vibrational frequencies, and ground-state dissociation energies were evaluated. It was found that the ground state is a triplet state irrespective of the type of functional and RECP used. This result is in contrast with a previous DFT calculation which gave a singlet ground state for Lu2. By comparing with the high-level ab initio and available experimental results, it is evident that the hybrid-GGA functionals combined with the Stuttgart smallcore RECP yield the best overall agreement for the properties under study. The effects of Hartree-Fock exchange in B3LYP functional on the calculated bond length and dissociation energy of the ground state were examined, and rationalized in terms of 5d participation in Lu-Lu covalent bonding.
Density functional theory calculations were performed to study the structures and relative stability of the gadolinium complexes, Gd（H2O）n^3＋ （n=8,9）, in vacuo and in aqueous solution. The polarizable continuum model with various radii for the solute cavity was used to study the relative stability in aqueous solution. The calculated molecular geometries for n=8 and 9 obtained in vacuo are consistent with those observed in experiments. It was found that while the nona-aqua complex is favored in the gas phase, in aqueous solution the octa-aqua conformation is preferred. This result, independent of the types of cavities employed, is in agreement with the experimental observation. The reliability of the present calculation was also addressed by comparing the calculated and experimental free energy of hydration, which revealed that the UA0, UAHF, and UAKS cavities are most appropriate when only the first solvation shell is treated explicitly.
