An ab Initio Investigation of Lithium Ion Hydration

Abstract

The structures, frequencies, and interaction energies of small lithium−water clusters, Li(H2O) n +, n = 1−4, were calculated by ab initio Hartree−Fock theory with small- and medium-sized basis sets (STO-3G, 3-21G, 6-31G*, 6-31G**, 6-31+G*, 6-31+G*(5d), 6-311G*). The interaction energies were corrected for basis set superposition error (BSSE) by Mayer's CHA/CE formalism. The CHA/CE/6-31+G*//HF/6-31+G* level gives an excellent description of the binding energy. The geometry and symmetric stretch frequency for Li(H2O)4 + of 248 cm-1 (255 cm-1 expt) are well described at the HF/6-31G* level. The choice of partition of the supermolecule was demonstrated to be of minor importance (±4 kJ/mol). The binding energies were rationalized on crowding around the ion and a weakening Li−O interaction. The first ab initio calculation (STO-3G, 3-21G, 6-31G*, 6-31+G*) of a full second-solvation sphere of a metal cation is presented ([Li(H2O)4 +](H2O) n , n = 4,8). The second solvation sphere of four waters raises the frequency of the Li−O vibration by 18 cm-1 (7%).

Study of gallium(III) nitrate hydrate and aqueous solutions: Raman spectroscopy and ab initio molecular orbital calculations of gallium(III) water clusters

“…This trend persists at all levels investigated. These findings indicate only a small (0.02Å) hydration effect on the Ga-O bond length and implies also that the gas-phase geometries for the [Ga(OH 2 ) 6 3C ] cluster are almost independent of the solvent effects. Therefore, the comparison of the calculated in vacuo Ga-O distance with the experimentally observed value in aqueous solution is legitimate.…”

“…However, only the isotropic spectrum allows the undisturbed detection of the 1 mode of GaO 6 because in the polarized spectrum, 2 e ClO 4 at 464 cm 1 partially overlaps the 1 mode, leading to an incorrect position. fFurthermore, as will be shown below, the penetration of NO 3 into the first hydration sphere of [Ga(OH 2 ) 6 3C ] in concentrated solutions also leads to a slight decrease in 1 GaO 6 .g It is noteworthy that the group 13 hexaaqua ions of Al(III), Ga(III) and In(III) do not follow the simple functional relation 1 ¾ 1/(r M -O 2 as reported by Kanno,41 derived from the Born model, as visible from the 1 MO 6 wavenumber trend for the hexaaqua ions: 1 AlO 6 D 525 cm 1 , 1 GaO 6 D 526 cm 1 and 1 InO 6 D 488 cm 1 . The simple Born model is useful in many cases.…”

“…The Ga(ClO 4 ) 3 solution spectra reveal the Raman modes for the [Ga(OH 2 ) 6 3C ] species as follows. The strongly polarized band at 526 cm 1 ( D 0.005) of medium intensity and two depolarized modes at 430 cm 1 and 328 cm 1 were assigned to 1 a 1g , 2 e g and 5 f 2g of the GaO 6 unit, respectively.…”

“…The IR-active mode 3 f 1u was observed at 555 cm 1 , while the second IR-active mode could not be observed. The assignment of the GaO 6 modes together with the values of [Ga(OH 2 ) 6 3C ] in solution and in caesium alum 36 are given in Table 2. The Ga(III) ion shows the three predicted Raman-active GaO 6 modes and the Raman wavenumbers do not coincide with the IR-active mode reinforcing the centrosymmetric symmetry of the complex.…”

“…Therefore, we calculated a much bigger gallium water cluster, octadecaaquagallium(III), denoted Ga [6 C 12]. In the first sub-section below we give the results for [Ga(OH 2 ) 6 3C ], which models the complete inner sphere. In the second sub-section we describe the gallium hexaaqua ion with a complete second hydration sphere.…”