Calculation of the structural and NMR properties of the tridecameric AlO_4Al_(12)(OH)_(24)(H_2O)_(12)~(7+) polycation

摘要

The aluminum tridecameric polyoxocation, AlO_4Al_(12)(OH)_(24)(H_2O)_(12)~(7+) is a major component in partially hydrolyzed Al~(+3)(aq) solutions and has been extensively studied experimentally, mainly using NMR techniques. I have calculated the equilbrium geometry of this cation using the Hartree-Fock method and a polarized double-zeta effective core potential basis set, obtaining bond distances which agree well with X-ray crystallographic studies of selenate and sulfate salts of the polycation (Al[4]:4 * 1.85 A calc, 4 * 184 A exp: Al[6]:4 * 1.85, 2 * 2.05 A calc, 2 * 1.84, 2 * 1.88, 1.91, 2.04 A exp [where the numbers in brackets indicate the coordination numbers]). I have also calculated electric field gradients and NMR shielding constants at all the atoms using the standard 6-31G~* basis set nd Hartree-Fock and hybrid Hartree-Fock-density functional (B3LYP) techniques. Using the Hartree-Fock method, the central four-coordinate Al is calculated to be deshielded by ～56 ppm, and the six-coordinate Al atoms by ～16 ppm, vs. the Al(OH_2)_6~(+3) reference, compared to experimental shifts of 63 and 12 ppm, respectively. The central Al[4] is thus shielded by ～20 ppm with respect to the tetrahedral monomer Al(OH)_4~(-1). Al-NMR shifts obtained from the B3LYP calculations are very similar. The calculated O-NMR shifts, vs. free gas-phase H_2O, are 17 ppm for the η-OH_2 groups, 30 ppm for the μ-OH and μOH' groups, and 55 ppm for the μ_4-O group, which match well with the experimentally assigned shifts of 20, 30, and 55 ppm, respectively (vs. liquid H_2O). The B3LYP method yields O shifts, which are systematically about 40 to 50% larger. It is not clear whether the discrepancies in the calculated O shifts vs. liquid water are a result of deficiencies in the model (neglect of the aqueous environment) or in the method (lack of correlation in the Hartree-Fock method). Studies on the Al_2(OH)_2(OH_2)_8~(+4) cation with small numbers of explicit waters hydrogen-bonded to it indicate that O shifts can be perturbed strongly by the presence of solvent. The calculated ~(17)O nuclear quadrupole coupling constants, NQCC (using the 6-31G~* Hartree-Fock calibration factor of Ludwig et al., 1996 to relate electric field gradients to NQCC values) are 1.7 MHz for μ_4-O, 7.8 to 8.0 MHz for the μOH and μOH' groups and 10.7 MHz for the ηOH_2 group. The μOH values are substantially higher than experimental values of 5 to 6 MHz observed for Al_2OH groups in Al oxyhydroxides. B3LYP values are very similar. However, hydrogen bonding to water in simple model compounds like Al_2(OH)_2(OH_2)_8~(+4) reduces the -OH NQCC values to ～6 MHz.