American Mineralogist, Volume 84, pages 877–883, 1999 Theoretical studies on the formation of mercury complexes in solution and the dissolution and reactions of cinnabar J.A. TOSSELL* Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742, U.S.A. ABSTRACT Expanding upon our previous studies of the properties of Au complexes, we present calculations for several Hg2+ species in aqueous solution and for molecular models for cinnabar. Hydration effects are treated with a combination of “supermolecule” calculations containing several explicit water molecules and polarizable continuum calculations. We focus upon the following problems: (1) calculation of the stabilities of HgL2, L = F–, Cl– , OH–, SH–, and CN– and HgCl2–n n n = 1–4; (2) development of a molecular model for cinnabar of the form Hg3S2(SH)2; and (3) dissolution or adsorption reactions using this cinnabar model. The absolute and relative formation enthalpies of the HgL2 species can be satisfactorily reproduced at the Hartree-Fock plus Moller-Plesset second order correlation correction level using relativistic effective core potential basis sets if the hydration of neutral HgL 2 is explicitly taken into account. Evaluating the energetics for the series of complexes HgCl2–n n is more difficult, because great accuracy is needed in the large hydration energies and some of the species are highly nonspherical. The Hg3S2(SH)2 species shows an equilibrium structure very much like that in cinnabar. The relative energetics for dissolution of cinnabar by H2O, H2S, SH–, and SH – + elemental S are correctly reproduced using this model molecule. Calculations on Hg3S2ClI provide a model for understanding the adsorption of I– ions on cinnabar surfaces in the presence of Cl–. INTRODUCTION The speciation of metal cations in aqueous solution strongly influences mineral dissolution and precipitation processes (Drever 1997) and the bioavailability of the metal (Mason et al. 1996). Partly because of the significance of Hg as an environmental pollutant, its speciation in natural waters is of great interest. The solubilities of Hg containing minerals in various solutions and the concentrations of Hg2+ ions in equilibrium with various ligands have been studied experimentally to deduce Hg speciation. These studies generally used methods that determine the total concentrations of Hg containing species in solution or the concentration of the Hg2+ hydrated cation. Such studies have serious limitations: (1) the speciation models are often ambiguous, with different researchers obtaining apparently different sets of species and formation constants, and (2) the participation of chemical components whose activities or concentrations cannot be varied experimentally are indeterminable, e.g., the participation of water in such species cannot be determined in aqueous solution. Spectral studies could, in principle, determine which species were present, as well as their concentrations if relative spectral intensities for the different species could be assessed. However, in many cases the species concentrations are so low that no usable spectra can be obtained. Although Hg speciation has been studied for years (Schwarzenbach and Widmer 1963; Barnes et al. 1967; Shikina et al. 1981) new results continue to emerge. For example, Paquette and Helz (1995, 1998) established that cinnabar has a higher solubility in solutions containing both elemental sul- *E-mail: tossell@chem.umd.edu 0003-004X/99/0506–0877$05.00 fur and bisulfide than in those containing bisulfide alone and identified a new Hg polysulfide species as the cause of this enhanced solubility. Recently, we have matched spectral properties calculated quantum mechanically for various As, Sb, and Au species (Tossell 1995, 1996a, 1997; Helz et al. 1995) with experimental spectral data to determine the predominant species present. We have also calculated reaction energetics for these species, but the low accuracy of our energetics prevented their use as the main criterion to determine speciation. Rather the energetic calculations were offered as further confirmation of the assignments made on spectral grounds. For example, for the As hydroxides Tossell (1997) identified a trimeric species As3O3(OH)3 existing in concentrated solutions primarily on the basis of its Raman spectrum, but noted that its high calculated thermodynamic stability provided additional, weaker evidence for its existence. Quantum mechanical methods were also used to model the structures, energetics, and spectral properties of certain “molecular” minerals, e.g., realgar, As4S4 (Tossell 1996b). For strongly covalent sulfides with small coordination numbers, such molecular approachs yielded accurate results for structures, vibrational spectra, and energetics. This paper focuses more upon the energetics of reactions in solution, to determine how well we can distinguish the stabilities of different complexes and the energetics for various dissolution reactions. Structural and spectral results are presented which may prove useful in characterizing the complexes. Two different types of reactions are considered: (1) complex formation, in which I start with isolated hydrated ions and form (hydrated) complexes, and (2) dissolution reactions, in which I start with a molecular model for the solid mineral and consider 877 878 TOSSELL: THEORY OF REACTIONS OF HGS the dissolution caused by species in solution. Each type of reaction presents its own problems for quantum mechanical calculation. In the association reactions the gas-phase reactants and products are fairly simple and can be treated at a high quantum mechanical level. The much more serious problem is the description of the hydration processes. For dissolution reactions, particularly where solids produce neutral solution species, the hydration problem is less serious, but studying a sufficiently large molecular model for the solid may not be computationally feasible. In general, small molecular models of solids represent the real solid more accurately if the solid shows small coordination numbers and substantial covalency. Such a approach is therefore feasible for HgS, cinnabar, a helical chain structure with twofold-coordinated Hg (1950) and for HgCl2, which is basically a molecular crystal with twofold-coordinated Hg (Wells 1975). As discussed by Kaupp and von Schnering (1994a) and more qualitatively by Tossell and Vaughan (1981), the small coordination numbers observed in Hg compounds are a consequence of relativistic effects. The impact of relativistic effects on the structures of heavy element compounds has also been discussed by Pyykko (1988). Other researchers have recently studied Hg complexes (Stromberg et al. 1991; Swerdtfeger et al. 1993; Kaupp and Schnering 1994), establishing the importance of relativistic effects and calculating structures and energetics at a fairly high quantum mechanical level. COMPUTATIONAL METHODS We use Hartree-Fock based techniques (Hehre et al. 1986). The basis sets used are of the relativistic effective core potential type, as implemented by Stevens, Basch, and Krauss (SBK) (Stevens et al. 1992). Polarization functions of d type only are added to each of the non-H atoms. We used the programs GAMESS (Schmidt et al. 1993) and GAUSSIAN94 (Frisch et al. 1994). In addition to the Hartree-Fock calculations we have utilized the Moller-Plesset 2nd order perturbation theory method (MP2) (Pople et al. 1976) for evaluation of the bond distances and energetics of many of the molecules studied, particularly those containing a single Hg atom. For most of the molecules considered we have also calculated the Hessian matrix to establish that we have found an equilibrium geometry and to determine the vibrational spectrum, allowing determination of the zero-point vibrational energy. The calculation of hydration effects upon chemical reactions is currently a very active area within quantum chemistry, with a number of different approachs being used by various researchers (Wiberg et al. 1996; Cramer and Truhlar 1994). To evaluate hydration enthalpies we use a multipart approach. For monatomic ions, such as Hg2+ and Cl–, and for the common small polyatomics, such as OH– or SH–, we use “experimental” hydration energies from the tables of Rashin and Honig (1985). Of course the hydration energy of a neutral compound cannot be uniquely divided into contributions from cation and anion, but by chosing the hydration energy of one particular species as a reference, most all other hydration energies can be defined with respect to it, obtaining quite consistent values. For neutral molecules, we evaluate hydration enthalpies by performing quantum mechanical supermolecule calculations with as many as 6 water molecules surrounding the solute molecule. The choice of six water molecules is somewhat arbitrary and is dictated in part by computational considerations and in part by the coordination numbers commonly observed for cations using solution X-ray diffraction or EXAFS. For a few of the species considered, e.g., Hg+2 and HgCl2, we have considered complexation with four, six, and eight water molecules, and have established that the greatest stability occurs for complexation with six water molecules. For polyatomic ions we evaluate the first hydration sphere contribution to the hydration energy by performing such a supermolecule calculation and determine the longer range contribution by performing a selfconsistent-reaction-field (SCRF) calculation (Wiberg et al. 1996) for the supermolecule immersed in a polarizable continuum with a dielectric constant equal to that in bulk H2O. The Born radius needed for the SCRF calculation is determined using the Rashin and Honig (1985) semiempirical prescription (not an essentially arbitrary electron density surface criterion as in Wiberg et al. 1996). The use of the RH effective Born radius value, rather than the radius calculated from the molecular volume by GAUSSIAN, is potentially significant because of the large magnitude of the Born term. In the GAUSSIAN94 implementation of the SCRF scheme only the dipole term is included, so that for a supermolecule with zero –2 dipole moment, e.g., Hg(OH2)+2 6 or HgCl4(OH2)6 , the Born term is the only non-zero term. Other potentially more accurate methods, such as the isodensity polarized continuum method (IPCM), are not yet implemented for the case of effective core potentials. The general procedure of combining a supermolecule calculation with a Born model or SCRF calculation is simple and intuitively appealing and has been used by a number of different researchers (e.g., Claverle et al. 1978; Freitas et al. 1992; Parchment et al. 1996) at various levels of sophistication. It basically relies upon the idea that there should be a smooth convergence of the local hydration energy for a cluster of solvent molecules to the bulk solvation energy as the number of solvent molecules is increased. Coe (1994) has demonstrated that this is approximately true, although the change in solvation energy with number of solvent molecules may not be completely continuous. It may be worthwhile to describe in detail the procedure used for the cases of Hg+2, Cl–, HgCl +1, and HgCl2. First, for Hg+2 and Cl– we use the hydration energies of -0.700 and -0.136 Hartrees (H), respectively, tabulated by Rashin and Honig (1985). An alternative would be to calculate these directly using our combined supermolecule, Born model approach. For +2 the formation of Hg(OH2)+2 and six H2O mol6 for free Hg ecules we calculate an energy change of -0.420 H, using the HF method and the polarized SBK basis and correcting for basis set superposition error (Boys and Bernardi 1970). The calculated Hg-O distance in Hg(OH 2)+2 6 is 2.428 Å (Th symmetry assumed), consistent with the experimental X-ray value of 2.40 Å obtained by Johansson (1971). Adding the Rashin and Honig value of 1.495 Å for the “O-H” bond radius to the calculated Hg-O distance we get a radius for the Born model calculation of 3.92 Å, giving a Born energy of –0.271 H, for a total hydration energy of –0.691 H, certainly in good agreement with the RH value of –0.700 H. For the case of Cl– the formation energy TOSSELL: THEORY OF REACTIONS OF HGS for Cl(OH 2)6–1, is –0.091 H (after basis set superposition correction), and the Cl-O distance has a range from 3.17 to 3.60 Å and an average value of 3.54 Å. This gives a Born energy of -0.053 H, for a total hydration energy of –0.144 H, fairly close to the the RH “exp.” value of –0.136 H. Note that in our calculations we have required the Cl– to lie at the center of the cluster, which is apparently not its lowest energy position with a small cluster (Caldwell and Kollman 1992; Coe 1994) but is appropriate for bulk solution. However, we emphasize that the reaction energies (below) are not based upon such calculated hydration energies for the monotomic and small ions, but utilize the RH experimental values. For ions such as HgCl + no tabulated hydration energies are available, so we utilize the combined supermolecule, SCRF model approach. We first calculated energies for formation of + HgCl(OH 2)+1 n , n = 4–6, from HgCl and H 2O, establishing that the most stable species had n = 5. This species is shown in Figure 1. The calculated Hg-O distances are 2.34, 2.60, 2.60, 2.64, and 2.64, while the Hg-Cl distance is 2.38 Å. Adding the RH radii of 1.94 and 1.495 Å for Cl– and OH–, respectively, we get radii along the bond directions of 3.84, 4.10, 4.10, 4.14, 4.14, and 4.32 Å, for an average of 4.11 Å. This average radius gives a Born energy of -0.0647H. The SCRF calculation as implemented in GAUSSIAN94, gives an additional polarization energy of -0.0134 from interaction of the dipole moment of HgCl(OH 2)+1 5 with the solvent polarizable continuum, for a total hydration energy of –0.251 H. For the HgCl2 case, six H2O molecules attach with an energy of –0.0475 H (four H2O molecules give a supermolecule formation energy of –0.0375 H). There is no Born energy because the species is neutral and there is no SCRF polarization energy because the dipole term is zero for HgCl2(OH2)6. The neglect of higher multipole terms probably systematically underestimates the stability of such symmetric species. However, using an average Born radius and treating lower symmetry species such as HgCl(OH 2)5+1 within a spherical approximation may also systematically underestimate their stability. 879 RESULTS Structures and vibrational spectra As is generally observed for Hg compounds (Kaupp and Schnering 1994b) calculated bond distances (Table 1) are substantially longer than experiment at the Hartree-Fock level (even when relativistic effects are included) but are considerably improved by MP2, although they are still a bit too long. The errors are similar in magnitude for the neutral species HgCl2 and Hg 3S2(SH)2 but seem somewhat larger for the HgCl4–2 anion. If we add the Born hydration energy in aqueous solution for HgCl –2 4 to the HF energy of the free anion the equilibrium distance is somewhat reduced, because shorter Hg-Cl distances give a larger Born stabilization. The calculated equilibrium distance drops from 2.63 to 2.58 Å, giving better agreement with experiment (although the experimental values is for a different condensed-phase environment). For HgS our Hg3S2(SH)2 model reproduces not only the Hg-S bond distance, but S-Hg-S and Hg-S-Hg angles, and the helical structure of HgS, cinnabar, as shown in Figure 2. Note that the calculations on the trimeric model Hg3S2(SH)2 are already extremely demanding, so that we have not considered any larger oligomers. Vibrational frequencies calculated at the HF level (Table 2) are similar to those of Kaupp and Schnering (1994b) and establish that unscaled HF values reasonably fit experiment for neutral molecules or ions with small charges. That is, for these heavy element compounds the Hartree-Fock method with conventional basis sets does not give the systematic underestimation of bond distances and overestimation of vibrational frequencies observed for light element compounds (Hehre et al. 1986). For the case of HgCl–2 4 , the calculated frequences are seriously underestimated, presumably for the same reason that the bond distance was overestimated for free HgCl–2 4 , compared to the condensed-phase experimental data. The spectrum of the molten HgCl2, KCl system is rather complicated (Janz and James 1963) and some of the spectral assignments may be in error. An extremely demanding calculation on the vibrational spectrum of HgCl4–2...6H2O yielded no significant change in the calculated frequences, indicating that explicit consideration of the Born model term would probably be a better approach. TABLE 1. Comparison of calculated and experimental Hg-X distances (in Å) Calculated HF MP2 2.33 2.30 2.33, 2.36 2.25 × 2 3.31 – HgCl 4–2 2.63 (2.58§) 2.58 +2 Hg(OH 2)6 2.43 – HgS 2.36 2.27 Hg2 S(SH) 2 2.39 2.36 Hg3 S2(SH) 2 2.39–2.41
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