Structure and Dynamics of Sulfate Ion in Aqueous SolutionsAn ab initio QMCF MD Simulation and Large Angle X-ray Scattering Study Viwat Vchirawongkwin, † Bernd M. Rode,* ,† and Ingmar Persson ‡ Theoretical Chemistry DiVision, Institute of General, Inorganic and Theoretical Chemistry, UniVersity of Innsbruck, Innrain 52a, A-6020 Innsbruck, Austria, and Department of Chemistry, Swedish UniVersity of Agricultural Science, P.O. Box 7015, SE-750 07 Uppsala, Sweden ReceiVed: January 11, 2007; In Final Form: February 23, 2007 The hydrated sulfate ion has been characterized in aqueous solution in structural and dynamic aspects using ab initio quantum mechanical charge field (QMCF) molecular dynamics (MD) simulation and large angle X-ray scattering (LAXS) methods. The LAXS data show an average coordination number of the sulfate ion of up to 12 water molecules bound through hydrogen bonding, while the QMCF MD simulation displays a wide range of coordination numbers between 8 and 14 with an average value of ∼11. The O s ‚‚‚O w distance cannot be distinguished from the O w ‚‚‚O w distance in the LAXS experiment; the weighted mean O‚‚‚O distance is 2.880(10) Å. In the simulation, the O s ‚‚‚O w and O w ‚‚‚O w distances are found to be very similar, namely, 2.86 and 2.84 Å, respectively. The S-O s bond and S‚‚‚O w distance have been determined by the LAXS experiment as 1.495(6) and 3.61(2) Å, respectively, indicating an average nearly tetrahedral S-O s ‚‚‚O w angle. The ∼5% deviations of simulation distances (1.47 and 3.82 Å) from the experimental ones can probably be ascribed to the neglect of correlation energy in the quantum mechanical method. The mean residence time of water ligands at O atoms, 2.57 ps, is longer than that in pure water, 1.7 ps, characterizing the sulfate ion as a weak structure maker. 1. Introduction The hydrated sulfate ion is fundamental in a range of pro- cesses in chemistry and biology. Sulfate is ubiquitous in fresh- water environments as evidence of water pollution 1,2 in atmo- spheric aerosol particles. 3,4 Despite this importance, the structure of the hydrated sulfate ion in aqueous solution is not yet well described. The characteristics of this ion in water have been studied, however, by some experimental 5-15 and theoretical 16-18 approaches. Structural data for the sulfate ion itself have been provided by X-ray diffraction investigations of several sulfate solutions, 5-15 producing sulfur-oxygen distances (S-O s ) in the range 1.45-1.50 Å and giving O s ‚‚‚O s distances in the range 2.36-2.45 Å. Intermolecular distances between the sulfate ion and water were given as the distance between the S atom and oxygen atoms of water molecules (S‚‚‚O w ; 3.67-3.89 Å) and between oxygen atoms of the sulfate ion and oxygen atoms of water molecules (O s ‚‚‚O w ; 2.88-2.95 Å). Coordination numbers in the range 6.4-8.1 have been assumed. A difference IR study showed that the sulfate ion is a weak “structure maker”, meaning that the hydrogen bonds between the sulfate ion and the surrounding water molecules should be slightly stronger than the hydrogen bonds between the water molecules in the solvent bulk. 19,20 A classical molecular dynamics (MD) simulation study by Cannon et al. 16 provided a coordination number for the first hydration shell of 13.2. Car-Parrinello molecular dynamics (CPMD) was also applied to investigate a small cluster of the hydrated sulfate ion (SO 4 (H 2 O) n 2- , n e 13), 17,18 yielding the coordination number of the first hydration shell as ∼8. In this work, both experimental and theoretical techniques are applied to investigate the structural and some dynamical properties of the sulfate ion in aqueous solution. Large angle X-ray scattering (LAXS) was chosen as the most suitable experimental tool, as long-range distances with wide distance distribution are easily detected, and the recently developed ab initio quantum mechanical charge field (QMCF) MD simulation procedure 21 was employed for the theoretical investigation. 2. Methodology 2.1. Experimental. Chemicals. Weighed amounts of lithium sulfate, Li 2 SO 4 (Fluka), were dissolved in Millipore Q filtered water, giving a 1.5294 mol‚dm -3 solution with a density of 1.1158 g‚cm -3 , a water concentration of 52.60 mol‚dm -3 , and a molar absorption coefficient of 1.746 cm -1 . Large Angle X-ray Scattering (LAXS). The scattering of Mo KR X-ray radiation (λ ) 0.7107 Å) from the free surface of an aqueous solution of lithium sulfate, with the pH adjusted to 12 with lithium hydroxide, was measured by means of a large angle Θ-Θ diffractometer. The solution was contained in a Teflon cup inside an airtight radiation shield with beryllium windows. The scattered radiation was monochromatized in a focusing LiF crystal monochromator, and the intensity was measured at 450 discrete points in the range 1° < Θ < 65°; the scattering angle is 2Θ. The number of counts accumulated was 100 000 at each pre-set angle, and the entire angular range was scanned twice, which corresponds to a statistical error of about 0.3%. The divergence of the primary X-ray beam was limited by 1, 1 / 4 , or 1 / 12 ° slits for different Θ regions, with overlapping data for scaling purposes. The experimental setup and the theory of the data treatment and modeling have been presented elsewhere. 22 All data treatment was carried out by means of the KURVLR * Corresponding author. Fax: +43(0)512/507-2714. E-mail: Bernd.M.Rode@uibk.ac.at. † University of Innsbruck. ‡ Swedish University of Agricultural Science. 4150 J. Phys. Chem. B 2007, 111, 4150-4155 10.1021/jp0702402 CCC: $37.00 © 2007 American Chemical Society Published on Web 04/03/2007