Theoretical studies on aluminate and sodium aluminate species in models for aqueous solution: Al(OH)3, Al(OH)4, and NaAl(OH)4

Ab initio quantum mechanical calculations were performed on Al(OH)3, Al(OH)4, NaAl(OH)4 and related species with varying numbers of explicit water molecules to elucidate the structural, spectral and energetic properties of the possible species. We find that Al(OH)3 reacts with H2O in the gas-phase with an exoergicity of 24.1 kcal/mol to produce Al(OH)3H2O, which has shorter Al-OH distances, larger Al-OH stretching frequencies, and a 15 ppm larger Al NMR shielding than does Al(OH)4. When the first hydration spheres of these species are included the Al NMR shieldings becomes very similar, but the O and H NMR parameters and the IR and Raman spectra still show significant differences. The hydration energy of Al(OH)3H2O is determined from a “supermolecule” calculation on Al(OH)3H2O...6H2O, whereas that for Al(OH)4 is obtained using the supermolecule calculation on Al(OH)4...6H2O plus an evaluation of the electrostatic Born hydration energy of the supermolecule. The calculated energy change for the acid dissociation reaction, Al(OH)3H2O...6H2O → Al(OH)4..6H2O + H, is +297.9 kcal/mol in the gas phase but only +2.3 kcal/mol in aqueous solution, due to the strong hydration of H and Al(OH)4..6H2O. Using quantum mechanically calculated entropies for the unhydrated species, Al(OH)3H2O and Al(OH)4, plus the experimental hydration entropy of H, the –T∆S term for this reaction is calculated as about +11.8 kcal/mol. Adding in calculated zero-point energies and room temperature enthalpy corrections gives a free energy change of +0.5 kcal/mol. Thus pKa for the acid dissociation of Al(OH)3H2O is near zero at room T, and Al(OH)4 will be dominant except under very acidic conditions. Properties are also calculated for the bare close-contact ion pair NaAl(OH)4 and for hydrated forms of both a close-contact and a solvent-separated ion pair, NaAl(OH)4...10H2O and NaAl(OH)4...11H2O. In accord with previous calculations on silicate anions and ion pairs, formation of an unhydrated close-contact ion pair increases the shielding of the Al in Al(OH)4, while reducing the Al-O symmetric stretching frequency. The calculated energy change at 298 K in aqueous solution for the ion pair formation reaction, Na...6H2O + Al(OH)4..6H2O → NaAl(OH)4...11H2O + H2O, is +17.6 kcal/mol, close to the value determined experimentally. After addition of calculated zeropoint energies, enthalpy corrections, and calculated entropy changes we obtain a ∆G value of +1.7 kcal/mol for this reaction, giving a log K around –1, consistent with significant ion pair formation. The NaAl(OH)4...11H2O species is a solvent-separated ion pair with full hydration of both its Na and Al(OH)4. Its calculated Al NMR shielding and Al-O symmetric stretching frequencies are very similar to those for Al(OH)4...6 H2O, whereas its Na NMR shielding is about 5 ppm smaller than that of Na(OH2)6, although its Na electric field gradient (and consequently its line-width) are larger. Thus it appears that Na NMR may be the best technique for characterizing this ion pair. Wesolowski and Palmer 1994), i.e., by measuring the total amount of Al in solution as a function of pH, temperature, pressure, and the concentrations of other ions, e.g., Cl. If a set of complex ion species is then assumed, their formation constants can be least squares fitted to the measured solubility data. However, there are several problems with this procedure: (1) the necessary experiments are time consuming and the metal concentrations may be both difficult to determine and strongly dependent on experimental conditions, e.g., upon the precise form of the mineral considered, (2) different sets of complexes may describe the data equally well and yet may produce widely differing values of the formation constants, and (3) the partici*E-mail: [email protected] TOSSELL: THEORY OF Na AND Al IN AQUEOUS SOLUTION 1642 pation of a chemical component in the species cannot be determined if its activity cannot be varied. For example, we cannot determine how H2O participates in species formed in dilute aqueous solution from solubility data alone and we cannot generally distinguish monomeric metal-containing species from oligomers since we cannot vary the activity of the pure mineral component. These sources of ambiquity have created substantial controversy concerning the Al-containing species present when corundum or other Al oxide and oxyhydroxide minerals dissolve in water, under various conditions. The basic equations to be considered, e.g., for the case of corundum in NaOH or NaCl aqueous solution are: Al2O3 (corundum) + 3 H2O → 2 Al(OH)3 (1) Al(OH)3 + H2O → Al(OH)4 + H (2) Al(OH)4 + Na → NaAl(OH)4. (3) Depending upon the value used for the equilibrium constant of Equation 2 the predominant species present when corundum dissolves in water near neutral pH may be either Al(OH)3 or Al(OH)4. In the same way, the increased solubility of Al2O3 in NaOH solution can be explained entirely in terms of the contribution of Al(OH)4 using certain values for this equilibrium constant, whereas lower values for the equilibrium constant of Equation 2 require contributions from the NaAl(OH)4 species of Equation 3 to match the experimental solubilities. For example, Pokrovskii and Helgeson (1995) indicated a substantial stability for species like NaAl(OH)4, whereas Anderson (1995) notes that such a species need not be invoked if the formation constant for Al(OH)4 is chosen appropriately and Walther (1997) excludes species such as NaAl(OH)4 from consideration, based partly on entropic arguments more appropriate to a gas phase reaction. Of course, the controversy involves not just ambient measurements but the characteristics of such reactions at elevated T and P in hydrothermal systems. Neutral species are expected to be favored at high T because of the decrease in the dielectric constant of water (Uematsu and Franck 1980) and because their formation from ions generally reduces the degree of order of the solvent and thus increases the overall entropy of the system (Marcus 1986). This paper is restricted to relatively low temperatures, from T = 0 K to T = 298 K. Unfortunately Equation 1 is very difficult to treat using quantum mechanical theory, because the methods used for describing the electronic structures of crystalline solids, such as corundum, are substantially different in detail from those used to describe the electronic structure of a molecule such as Al(OH)3. It is therefore difficult to avoid mathematical artifacts in comparing the total energies of corundum and Al(OH)3. Methods which treat the different phases alike, e.g., those utilizing a common force field, avoid this problem but their results are strongly dependent upon the force field parameterization and may not contribute much to a fundamental understanding of the problem. Equations 2 and 3 are much more amenable to quantum mechanical calculations. We can evaluate reaction energetics first for gas-phase forms of the species and then add corrections for hydration. However, that the methods for making such corrections are still relatively crude and that including all the physical effects (and including each only once) can be quite difficult. There is also the more fundamental question of relating quantities evaluated on a microscopic scale through quantum mechanics and quantum statistical mechanics with those determined macroscopically through experimental thermodynamics. For example, Pokrovskii and Helgeson (1995) noted that according to standard thermodynamic conventions AlO2 and Al(OH)4 are the same—i.e., differences in all the thermodynamic quantities for the reaction: AlO2 + 2 H2O → Al(OH)4 (4) are defined to be zero, whereas the change in internal energy calculated quantum mechanically for this reaction in the gas phase is –144 kcal/mol. In many cases, additional constraints can be placed upon the identity and structure of the complexes present by examining structural data, e.g., from extended X-ray absorption fine structure (EXAFS) or spectral data, e.g., infrared, Raman or NMR spectroscopies. For example, we have used these procedures to determine the speciation of As in sulfidic solutions (Helz et al. 1995). For many Al-containing minerals, the solubilities are so low (at least for most conditions of pH, T, P, etc.) that spectral data for the solution species are not presently available. It could also be the case that some types of spectra would not adequately distinguish between the different species. In determining speciation of Al-containing species in glasses EXAFS, IR, Raman, and NMR spectroscopy have all proven valuable (Stebbins et al. 1995). To help assess speciation of Al-containing complexes in solution it would therefore be useful to determine Al-O distances, IR and Raman frequencies, and Al, Na, O, and H NMR shieldings, and nuclear quadrupole coupling constants. Eremin et al. (1974) has summarized experimental data on aluminate ions in solution which has been interpreted in terms of alkalialuminate ion pairs, but in all the cases considered the small spectral changes have been attributed to ioin pair formation without any supporting calculation of what the properties of the ion-pair actually are. In addition to the calculation of properties we can directly calculate the energetics for formation of the various species in aqueous solution. This work calculates structures, spectra, and stabilities for a range of Aland Nacontaining species, both “bare” and with an approximate representation of their first hydration spheres. COMPUTATIONAL METHODS Modern quantum chemical methods are able to reproduce reaction energies to chemical accuracy (1–2 kcal/mol) for small molecules composed of light atoms in the gas phase (Hehre et al. 1986; Foresman and Frisch 1996). Evaluating the energetics of reactions in solution is much more difficult, but is a current focus of interest in quantum chemistry. The basic procedure for gas-phase reactions is to solve an approximate version of the Schrodinger equation, typically the Hartree-Fock or the Kohn-Sham equations, to reasonable accuracy (Foresman and Frisch 1996). A general problem is that mean-field procedures TOSSELL: THEORY OF Na AND Al IN AQUEOUS SOLUTION 1643 such as the Hartree-Fock, in which the instantaneous electronelectron repulsion is replaced by an averaged value, can give serious errors in energies unless the reaction is of a specific, limited “isodesmic” type. Corrections for the “correlation” error must generally be made to get accurate energies. A computationally efficient correction method is second order Moller-Plesett perturbation theory (MP2). We can treat even very heavy atoms such as Hg, for which relativistic effects are important, by using relativistic effective core potentials and an orbital basis set which treats only the valence electrons explicitly (e.g., Stevens et al. 1992; the SBK basis set). Even for third row atoms such as Al the use of effective core potentials and valence only basis sets greatly reduces the amount of computation required, with very little decrease in accuracy of result for geometries and relative stabilities. We can also calculate vibrational spectra for such gas-phase systems and evaluate zero-point vibrational energies and finite temperature translational, vibrational, and rotational contributions to the energy, enthalpy, and entropy. Our calculations of equilibrium structures, energies, vibrational frequencies, and electric field gradients were done primarily with the GAMESS quantum chemical software (Schmidt et al. 1993) whereas the calculations of NMR shieldings were done using the GIAO (gauge-including atomic orbital method; Hinton et al. 1993) incorporated in the quantum chemical software GAUSSIAN94 (Frisch et al. 1994). Both programs utilize conventional Hartree-Fock self-consistent-field molecular orbital theory, as described, e.g., in Hehre et al. (1986). Unfortunately, for some of the larger hydrated structures, such as NaAl(OH)4...11H2O, we have been unable to obtain energy convergence to the accuracy needed to reliably evaluate zeropoint energies and vibrational entropies, invariably finding some negative vibrational frequencies indicating that we are at a saddle point with respect to the orientation of some of the water molecules. We have calculated the higher vibrational frequences for these systems, corresponding to Al-O stretching vibrations, and consider them to be reliable. Analysis of zero-point energy, enthalpy, and entropy terms are therefore done using the unhydrated species, for which the vibrational calculations yield all positive frequencies. For solution reactions a serious problem is the representation of the interaction of the solute with the solvent. There are several general schemes for evaluating the solution energies, including (1) polarizable continuum models, such as the selfconsistent reaction field (SCRF) model, in which the energy change due to polarization of the bulk solvent by the charge distribution of the solute is evaluated (e.g., Wiberg et al. 1996) (2) supermolecule approachs, in which the solute and several explicit solvent molecules surrounding it are treated quantum mechanically, and (3) simulation techniques, in which many solvent molecules interact with the solute through pair or high order potentials, calculated quantum mechanically or fitted to experiment. We have previously used polarizable continuum and supermolecule approachs to study the properties of arsenic hydroxide species in solution (Tossell 1997). Here we use primarily a supermolecule approach, although we have calculated SCRF energies for some of the supermolecule ions. Born energies for the supermolecule ions are evaluated using the Rashin and Honig (1985) reformulaton of Born theory. The only quantity (aside from the dielectric constant of the solvent) needed to evaluate the Born energy is the Born radius, which unfortunately is an ambiguous quantity. In the Rashin and Honig (1985) formulation the Born radius for a species like Al(OH)4...6H2O is the (average) distance from the central Al to the O of the first hydration sphere water molecules plus the “OH” radius, chosen as 1.498 Å in Rashin and Honig (1985). The choice of hydration enthalpy for the proton is a difficult one. The best modern experimental value is probably –275 kcal/mol (Coe 1994), although this value is obtained by extrapolation of cluster experimental data. The best calculated value is about –267.3 kcal/mol (Tawa et al. 1998) and was obtained with an approach similar to that used in this work, namely quantum mechanical calculations (at a higher level than used here) upon H containing supermolecules (with 1–6 water molecules) embedded in a polarizable continuum. We therefore chose the Tawa et al. (1998) value for the proton hydration enthalpy. Although the experimental and calculated values mentioned above are quite similar, the particular choice of proton hydration enthalpy strongly influences the overall enthalpy of reaction 2, the Al(OH)3, Al(OH)4 equilibrium. Although there have been no recent quantum mechanical studies on exactly the aluminate systems considered here, a very relevant recent work is that by Moravetski et al. (1996), who considered the Si NMR shieldings of the species Si(OH)4 [isoelectronic to Al(OH)4] and its anion Si(OH)3O, interacting with H2O and with K. An important conclusion was that the Si in the Si(OH)3 anion was shielded to a moderate degree by the addition of either water or K whereas the addition of water to neutral Si(OH)4 had a much smaller effect on the Si shielding. We see similar trends for the aluminates, as will be shown below.