A Computational Study of Mg2+ Dehydration in Aqueous Solution in the Presence of HS� and Other Monovalent Anions

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Geochimica et Cosmochimica Acta 88 (2012) 77–87 www.elsevier.com/locate/gca

A computational study of Mg2+ dehydration in aqueous solution in the presence of HS and other monovalent anions – Insights to dolomite formation

Yang Yang a,b,c, Nita Sahai a,b,d,e,⇑, Christopher S. Romanek f,g, Suvankar Chakraborty f,g

a Department of Geoscience, University of Wisconsin, Madison, 1215 West Dayton Street, Madison, WI 53706, United States b NASA Astrobiology Institute, University of Wisconsin, Madison, 1215 West Dayton Street, Madison, WI 53706, United States c Department of Chemistry and Biochemistry, Rowan University, 201 Mullica Hill Rd, Glassboro, NJ 08028-1701, United States d Department of Polymer Science, 170 University Avenue, University of Akron, Akron, OH 44325-3909, United States e NASA Astrobiology Institute, 170 University Avenue, University of Akron, Akron, OH 44325-3909, United States f Department of Earth and Environmental Sciences, University of Kentucky, Lexington, KY 40506, United States g NASA Astrobiology Institute, University of Kentucky, Lexington, KY 40506, United States

Received 4 November 2011; accepted in revised form 13 March 2012; available online 29 March 2012

Abstract

Massive sedimentary dolomite formed at near-Earth’s surface temperatures is abundant in the ancient geological rock record compared to modern deposition. Extensive experimental work to synthesize dolomite at low temperature and to reveal the formation mechanism has been attempted previously. Sulfide, the product of bacterial sulfate reduction, has been proposed in the literature to play an active role in promoting dolomite formation by facilitating desolvation of Mg2+ in the bulk solution and, thus, incorporation into the dolomite crystal structure. Chemical intuition, however, does not suggest any particular character- istic of HS that would render it an efficient promoter of Mg2+ desolvation in solution. In order to examine the previously proposed hypothesis, we conduct an ab initio reaction path ensemble (RPE) study along a dissociative mechanism to determine the energy penalty of removing a first-shell water molecule around Mg2+ compared to Mg2+ with HS located in the second coordination shell. The solvent effect and specific hydrogen-bond interactions from water beyond the first-solvation shell are addressed using large cluster models, where up to the second layer of Mg2+ hydration and the first solvation-shell of HS are included. Within the context our modeling approach, we find that HS has little, if any, effect on lowering the Mg2+ dehydration barrier in aqueous solution. Alternative mechanisms must then be invoked to explain the apparent promotional effect of HS on Mg2+ dehydration kinetics. Ó 2012 Elsevier Ltd. All rights reserved.

1. INTRODUCTION strata of all ages from the Precambrian to the Cenozoic (Krauskopf and Bird, 1995). Modern dolomite formation Massive layers of sedimentary dolomite formed at Earth’s is observed only in speciﬁc environments, such as highly surface or near-surface temperatures (<50 °C) are found in saline lakes, deep-sea sediments and supersaturated saline la- goons, and only in minor quantities. Extensive attempts to synthesize dolomite have been carried out to reveal the mech- ⇑ anism of dolomite formation (Liebermann, 1967; Katz and Corresponding author at: Department of Polymer Science, 170 Matthews, 1977; Baker and Kastner, 1981). Although dolo- University Avenue, University of Akron, Akron, OH 44325-3909, mite precipitation is obtained under some extreme condi- United States. Tel.: +1 330 972 5795; fax: +1 330 972 5290. E-mail address: [email protected] (N. Sahai). tions, e.g., high temperature (Katz and Matthews, 1977;

Baker and Kastner, 1981), increased Mg2+ and Ca2+ concen- of Mg2+ results in a very stable first hydration shell (Sup- trations (e.g., dolomite will precipitate directly from solution plementary data Electronic Annex, Section 1). As a first at a minimum salinity of 4–6 times of normal sea water at pH step, we consider a dissociative mechanism where a first- 2+ 2 is 8–9) (Liebermann, 1967), high pH condition with the pres- shell water leaves the Mg center before the CO3 can ence of supporting ions (e.g., NO3 )(Krauskopf and Bird, coordinate. We use a combination of computational meth- 1995), synthesis at Earth’s near-surface conditions have been ods ranging from classical molecular dynamics (MD) simu- unsuccessful (Land, 1998). The difficulty of low-temperature lations to ab initio quantum mechanical calculations with dolomite formation in modern times compared to the vast model clusters. Alternative solution-phase mechanisms are 2 abundance in the geological record is referred to as the “dolo- the associative mechanism where a ligand such as CO3 mite problem”. More generally, the synthesis of mixed cation binds with a hexa-coordinated metal center to form a hep- carbonates ((Fe, Ca, Mg)CO3) at Earth’s near-surface tem- ta-coordinated intermediate (Eigen and Wilkins, 1965), and peratures is difficult inorganically (Romanek et al., 2009), the concerted or interchange mechanism where water leaves 2 2+ although such phases are known geologically as fine-grained and CO3 associates simultaneously with the Mg center early diagenetic phases in sedimentary rocks (Matsumoto (e.g., Bleuzen et al., 1997). The promoting effect of HS and Iijima, 1981; Mozley and Carothers, 1992), as cements may also involve a heterogeneous mechanism at the inter- in oil reservoir rocks (Thyne and Gwinn, 1994) and in the face of a solid precursor phase. Our rationale for choosing Martain meteorite ALH84001 (Mittlefehldt, 1994; Romanek to examine the dissociative mechanism in bulk solution is et al., 1994). Microbial involvement in the formation of explained below briefly, and in detail in Supplementary mixed-cation carbonates including dolomites has been pro- data Electronic Annex, Section 2. posed previously (Liebermann, 1967; Baker and Kastner, Previous workers have used computational electronic 1981; Patterson and Kinsman, 1982; Hardie, 1987; structure and molecular simulation methods to stay the sol- Vasconcelos et al., 1995; Mortimer and Coleman, 1997; Mor- vation and water-exchange kinetics around metal ions timer et al., 1997; Vasconcelos and McKenzie, 1997; Warth- including Mg2+,Ca2+,Al3+, and Fe3+ (Rustad et al., 1995; mann et al., 2000; Moreira et al., 2004; Morse et al., 2007). Kerisit et al., 2003; Kerisit and Parker, 2004; Stack et al., Thus, the occurrence of dolomite or other mixed-cation car- 2005; Jiao et al., 2006; Piana et al., 2006; Spagnoli et al., bonates may serve as a biosignature on Earth and on other 2006; Wang et al., 2007; Criscenti et al., 2008; Evans et al., solid worlds such as Mars. 2008; Kerisit and Rosso, 2009; Hamm et al., 2010). The struc- In order to form the dolomite crystal structure, direct ture and dynamics of Mg2+ and Ca2+ hydration are signifi- 2+ 2+ 2 Mg /Ca -CO3 interactions need to be established. The cantly different (see Electronic Annex, Section 1). For dehydration of Mg2+ at temperatures <50 °C has, therefore, example, the water exchange rate around Ca2+ is five orders been deemed as critical step for dolomite formation (Lipp- of magnitude faster than for Mg2+. Due to the significantly mann, 1973), although the exact mechanism is still unknown. different hydration features of Mg2+ versus Ca2+, the forma- 2+ 2 2+ 2 Chemical promotion by organic ligands and inorganic an- tion of the Mg -CO3 versus the Ca -CO3 species pro- ions such as sulfide by bacterial sulfate reduction has been ceeds via different mechanisms. proposed (Hardie, 1987; Oomori and Kitano, 1987; Buckin An associative mechanism is found for Ca2+ involving a et al., 1994; Vasconcelos et al., 1995; Falini et al., 1996; pentagonal bipyramidal intermediate (Di Tommaso and de Vasconcelos and McKenzie, 1997; Morse et al., 2007; Hamm Leeuw, 2008), and the energy barrier is also small et al., 2010). Based on the proposed promoting role of HS in 2.0 kcalc˙mol1 (Ikeda et al., 2007; Electronic Annex, Sec- 2+ 2+ 2 Mg desolvation, high-magnesium calcite and disordered tion 2). An associative mechanism to form Mg -CO3 dolomite was successfully synthesized at room temperature interaction is not viable because the seven-fold coordina- (Zhang, 2009; Zhang et al., 2010). The procedure involved tion for Mg2+ is both thermodynamically and kinetically mixing NaHCO3 +Na2S (with or without pyrite)/sodium unfavorable, whereas the dissociative mechanism involving acetate (C2H3NaO2) solution and CaCl2 + MgCl2 solution. a five-fold intermediate is not energetically forbidden (Ike- Dolomite did not form without Na2S, and control experi- da et al., 2007; Electronic Annex, Section 2). Once the five- 2 ments apparently excluded the effect of pH increase. The fold coordination is formed, CO3 may, presumably, enter authors showed a correlation between MgCO3 content of the first-coordination shell and regenerate the six-fold coor- the high-magnesium calcite formed with the Na2S concentra- dination. Hence, we study here the dissociative mechanism tion. The authors, however, did not provide a formation combining MD simulations to generate local solvent struc- mechanism, and suggested only that the low dielectric con- tures around the solute and Density Functional Theory stant of aqueous sulfide somehow promoted Mg2+ dehydra- Reaction Path Energy calculations for the energy profiles tion in solution. (see Electronic Annex, Section 3). The effects of thermal Chemical intuition, based on considerations of charge fluctuations are accounted for by using multiple snapshots density, chemical hardness/softness, or molecular electronic from the MD simulations to prepare the large cluster mod- structures, however, does not suggest any particular charac- els, and statistical results are analyzed. teristics of HS that would render it an effective promoter. At the atomistic level, we assume that the pathway in- Yet, this idea of HS-promoted Mg2+ dehydration in solu- volves interactions between the negative charge of HS tion persists in the literature, and serves as the primary and the dissociating water that directly interacts with the motivation of our work. HS, thus lowering the energy barrier for the Mg2+ We study the mechanism for Mg2+ dehydration without dehydration process. In principle, HS may facilitate disso- and with HS in the bulk solution. The high charge-density ciation of the water molecule that does not directly interact Y. Yang et al. / Geochimica et Cosmochimica Acta 88 (2012) 77–87 79 with HS, but our small cluster models results suggest that emphasize that the 2 ns MD simulations are not intended such a pathway is not favorable (see Section 2 and Elec- to capture the entire water dissociation process which is tronic Annex, Section 4). very around Mg2+ (6.7 105 s1), corresponding to an order of magnitude of 1 exchange event per microsecond 2. METHODS (Bleuzen et al., 1997). The MD simulation is only used to generate local water structure around Mg2+. We believe Computational methods are described briefly in this sec- that the 2 ns time scale length is sufficient to sample local 2+ tion for the non-specialist. Details are provided below and Mg -water interactions in the first two hydration shells, in the Electronic Annex. Due to the dynamic solution struc- which are the relevant coordination shells for the reaction ture, ideally, the water dissociation energy from the ion cen- path explored in our study. Our simulation period is also ter should be investigated using the free-energy calculation at the uppermost limit of timescales compared to other re- (e.g., Umbrella Sampling method) with high-level quantum lated computational studies which had time-scales ranging mechanical molecular dynamics simulation techniques, from 20 ps to 1–2 ns (Obst and Bradaczek, 1996; Kone- e.g., Car–Parrinello molecular dynamics (CPMD), where shan et al., 1998; Kurnikova et al., 1998; Martinez et al., both the intrinsic dissociation energy and the solvent effect 1999; Yang and Cui, 2007; Yang and Cui, 2009; Di Tomm- are addressed. But such calculations are computationally aso and de Leeuw, 2010; Hamm et al., 2010). 2+ prohibitive (Electronic Annex, Section 3). An alternative For the Mg solution, we perform MD simulations choice to overcome this difficulty is to perform the free-en- with a quantum mechanical/molecular mechanical (QM/ ergy calculation within a quantum mechanical/molecular MM) potential (Warshel and Levitt, 1976; Gao and Truh- mechanical (QM/MM) framework, where the reacting spe- lar, 2002; Riccardi et al., 2006b), where the self-consis- cies and the immediate environment are treated with quan- tent-charge density-functional-tight-binding (SCC-DFTB) tum mechanical methods and the rest of the solution method (Elstner et al., 1998) and CHARMM force field system is described with the classical molecular mechanical (MacKerell et al., 1998) serve, respectively, as the QM force field (Warshel and Levitt, 1976; Field et al., 1990). and MM components. SCC-DFTB is a semi-empirical den- We use large cluster models in order to address the solvent ef- sity functional theory, which, coupled with CHARMM fect and specific hydrogen bond interactions from water be- force field, has been widely and successfully applied to yond the first-solvation shell of Mg2+. Up to the second layer study various condensed-phase problems, ranging from of Mg2+ hydration and the first solvation-shell of HS are in- chemical reactions in aqueous solution to catalytic pro- cluded in these large clusters. cesses in heterogeneous enzymatic environments (Cui Classical molecular dynamics simulations are employed et al., 2001; Riccardi et al., 2006a,b; Yang and Cui, 2007; to study the dynamic solution structure and to prepare snap- Phatak et al., 2008; Yang et al., 2008a). 2+ ˚ shots of the initial water structures around the solute for the The Mg ion is solvated with a water droplet of 22 A large cluster models. Statistical results are also analyzed. The radius using TIP3P water model (Fig. 1). The CHARMM MD simulations are performed using CHARMM package program, with Miscellaneous Mean Field Potential (MMFP) 2+ (Brooks et al., 1983, 2009). Density functional theory is then module is applied. We impose a harmonic restraint on Mg used to conduct reaction path ensemble (RPE) studies (Yang and Cui, 2009) with QChem 3.1 packages (Shao et al., 2006). We also use small cluster models, where only first-shell water molecules around Mg2+ are taken into account, in order to study the intrinsic promoting ability of HS and other ligands, and to gauge results of our large-cluster REP calculations. If HS bears a special promoting ability for Mg2+ dehydration, such a capacity should be observed with the small cluster model calculation, where first-shell water interactions with Mg2+ and sulfide are maximized because there is no solvent beyond the first shell. For the small cluster model, we perform ab initio minimum energy path (MEP) calculations for hexahydrated Mg2+ and for hexahydrated Mg2+ with HS or other monovalent ligands in the second coordination shell of Mg2+. Results are pre- sented in the Electronic Annex, Section 4.

2.1. Molecular dynamics simulations of Mg2+ and Mg2+ with HS in aqueous solution

2+ ˚ We carry out MD simulations for Mg2+-only and Mg2+ Fig. 1. Solvation of Mg with a large water drop (22 A) used in the molecular dynamics simulation. Mg2+ is represented as a green with HS aqueous solutions up to 2 ns in order (1) to exam- 2+ ball, water molecules are rendered in the “surface” mode with white ine dynamic solvent structures around Mg within the 2 ns and red colors. (For interpretation of the references to color in this simulation length, and (2) to generate reasonable local sol- figure legend, the reader is referred to the web version of this 2+ vent structures around Mg for large cluster models. We article.) 80 Y. Yang et al. / Geochimica et Cosmochimica Acta 88 (2012) 77–87 around the center of the droplet to keep the ion at the center for the gradient of root-mean-square (GRMS) of of the droplet. Mg2+ plus all water molecules within 5 A˚ from 0.05 kcal (mol A˚ )-1 with the adopted basis Newton–Raph- the Mg2+ center (first and second solvation shells) are treated son method (i.e., 1440–1800 CPU hours to complete a sin- quantum mechanically. A set of locally optimized Hubbard gle energy scan). derivatives (Yang et al., 2007; Yang et al., 2008b) are applied The model snapshot structures are first optimized at to Mg, O and H elements. This approach has given consistent B3LYP/6–31+G* level. Using the optimized structures, solution structures compared to those from previous CPMD minimum energy path (MEP) calculations are then per- 2+ (Car and Parrinello, 1985) simulations (Ikeda et al., 2007). formed at the same theory level. The Mg –Owater distance Using the SHAKE algorithm to constrain all bonds involv- is defined as the reaction coordinate, with a step size of ing hydrogen permits us to use an integration time step of 0.2 A˚ . For the Mg2+ with HS models, we set the first-shell 1fs (Ryckaert et al., 1977). For 300 ps simulations at water molecule that directly interacts with HS to dissoci- 298 K, the last 100 ps data in the trajectory are used for ate from the Mg2+ center (see Electronic Annex, Section analysis. 4 for this choice of reaction coordinate). Electronic energy For the Mg2+ with HS solution simulations, we use the is used to compute the dissociation energy barrier. The classical CHARMM force field, because of the lack of SCC- large size of the model clusters renders the calculations DFTB parameters for sulfur. The atomic charges for HS expensive, even with 8-CPU in parallel. are computed with the Merz-Singh–Kollman method (Singh and Kollman, 1984; Besler et al., 1990) at B3LYP/ 3. RESULTS AND DISCUSSION 6–311+G** level. A Nuclear Overhauser Effect (NOE) restraint is applied on sulfide with a maximum cutoff 3.1. Solution structures from MD simulations distance of 5.5 A˚ , to ensure that HS remains within the second solvation shell of Mg2+. The rest of the simulation To have a consistent comparison of solution structures setup is similar to the one for the Mg2+-only solution. for both solutions (without and with HS), up to 2 ns MD Additionally, in order to ensure a consistent comparison simulations with CHARMM force field are performed. of the solvent dynamics and structures for solutions with Solution structures are analyzed based on the last 1.4 ns pro- and without HS anion, the Mg2+-only solution is also sim- duction simulations. Radial distribution functions (g(r)) and ulated with the classical CHARMM force field. running coordination number (RCN) of water molecules around the Mg2+ center are computed (Fig. 2a). For 2.2. Reaction Path Ensemble (RPE) study with large cluster Mg2+ only solution, the first peak in g(r) is located at models 2.0 A˚ , which is consistent with previous experimental and computational results (Neilson and Enderby, 1989; We adopt large cluster models in order to take into Skipper et al., 1989; Kerisit and Parker, 2004). Along the account the effect of water molecules beyond the first solva- whole 2 ns simulation, the octahedral structure of the first tion shell, where the solvent structures are obtained from the solvation shell is stable. No water exchange is observed be- snapshots of the MD simulations. For the Mg2+-only mod- tween the first-shell water and water beyond, as reflected by els, we include water molecules within 5.0 A˚ from Mg2+. the sharp and narrow first peak in the g(r) plot and by the Water molecules within 4.0 A˚ from HS are included for zero-value region ranging from 2.0 A˚ to 3.6 A˚ of the RCN the Mg2+ with HS models. In order to explore the impact curve. Similar results were observed in an earlier theoretical of thermal fluctuations, 6 snapshots for the Mg2+-only solu- study of Mg2+ hydration structure (Obst and Bradaczek, tion and 4 snapshots for the Mg2+ with HS system are ran- 1996). domly selected from the MD simulation. In order to examine the effect of HS, the HS ion is The number of snapshots chosen is based on both prac- constrained to move only within 5.5 A˚ from the Mg2+ cen- tical and scientific reasons. For the Mg2+ with HS system, ter in the simulation, effectively restraining the HS within 2+ the MD simulations showed that occasions for HS to the two solvation shells of Mg . The g(r) for Mg–Owater directly interact with one water molecule in the Mg2+ first and RCN are almost identical in the presence of HS to solvation shell are dominant, with a probability of 72%. the pure Mg2+ system, within 4.0 A˚ from the Mg2+ center Encounters between HS and two water molecules have a (Fig. 2a). The first peak remains at 2.0 A˚ , which indicates 20% probability, and chances to interact with more water that HS does not weaken the interactions between Mg2+ molecules are negligible. We selected four model clusters in and first-shell water molecules in the reactant state. This re- order to reflect this probability distribution. In three of sult is consistent with the quantum mechanical calculations them, HS interacts with one water molecule in the first sol- on the small model clusters (Electronic Annex, Section 4). vation shell of Mg2+, and in the forth, HS interacts with The average Mg–S distance is 4.8 A˚ with a variation of two water molecule in the first solvation shell of Mg2+. 0.3 A˚ , and the shortest distance observed is 3.8 A˚ . Due to Thus, the choice of four clusters was based on scientific con- the stable first-shell solvation of Mg2+,HS constantly siderations. For the Mg2+-only system, the high expense of occupies the second solvation shell of Mg2+, and cannot the simulations even with 8-CPU in parallel, limited the penetrate the first water layer to form direct contact with number of snapshots. Taking the model of the Mg2+ with Mg2+. This explains the lack of any significant differences HS as an example, each single-point calculation takes observed between the two solutions beyond 4.0 A˚ (Fig. 2a). about 80 min CPU time. On average, 120–150 minimiza- The radial distribution function and RCN of water mol- tion steps are needed to satisfy the optimization threshold ecules around HS are also computed, where the S-Owater Y. Yang et al. / Geochimica et Cosmochimica Acta 88 (2012) 77–87 81

40 5 40 (a)18 (b) 16 2+ Mg 4 30 30 14 Mg2++HS- 12 RCN

3 RCN 10 20 20 g(r) g(r) 8 2 6 10 10 4 1 2 0 0 0 0 01234567 01234567 Mg-Owater distance (angstrom) S-Owater distance (angstrom)

Fig. 2. Radial distribution function (g(r), solid curves) and running coordination number (RCN, dashed curves) of water around (a) Mg2+ for solutions with and without HS and (b) of water around HS. distance is analyzed (Fig. 2b). Based on the g(r), the first solvation shell of HS ends at 3.7 A˚ , and there are 7.4 71.4 water molecules in the first solvation shell. According to the best of our knowledge, there are no previous detailed 57.1 computational or experimental studies in the literature for HS solution structure for bench-marking our results, so 42.9 we use studies of Cl solution. Chloride provides a reasonable comparison with HS, because both ions posses the same charge as and similar ra- 28.6 dii. The two ions also have similar interactions with water. Probability (%) Based on pulsed high-pressure mass spectrometry study, 14.3 Cl and HS show similar hydrogen-bonding energies (Meot-Ner, 1988). The interaction energy between HS 0.0 and one water molecule in the gas phase is 14.2 kcal.mol1, 0123 which is very close to that for Cl of 14.8 kcal.mol1.At Number of Water Molecules infinite dilution and temperature of 25C, Koneshan et al. (1998) studied Cl in solution using MD simulations with Fig. 3. The probability distribution of the number of water molecules which are located on the first solvation shell of Mg2+ the SPC/E water model (Berendsen et al., 1987). Results and directly interact with HS. showed that 7.2 water molecules occupy the first solvation shell of Cl at a distance of up to 3.8 A˚ (Koneshan et al., 1998; Chowdhuri and Chandra, 2001), similar to our results 3.2. Reaction path ensemble study with large cluster models for HS. Thus, our calculations characterize the local solvent structure around HS reasonably well. 3.2.1. Mg2+-only system The number of first-shell water molecules around Mg2+ Six snapshots of large model clusters of the Mg2+-only that directly interact with HS is analyzed along the simu- system without HS are obtained from MD simulations. lation trajectory. The probability distribution is shown in The interactions between Mg2+ and first-shell water mole- Fig. 3. A high probability of 72% exists for occasions cules of the optimized structures for the reactant state are where HS directly interact with a single first-shell around consistent with results from the small model cluster. In de- the Mg2+. Interactions between HS and two water mole- tail, six water molecules form an octahedral geometry sur- cules have a 20% probability, and encounters with more rounding the Mg2+ ion, with an average Mg–Ow distance water molecules are negligible. In contrast, gas phase results of 2.12 A˚ (36 Mg–Ow distances from all of the six large with small model clusters show interactions with three clusters are taken into account, and a variation 0.05 A˚ ). water molecules because the HS has no other choice One interesting observation is that the first-shell water mol- (See Electronic Annex Fig. S4a). In the large cluster models, ecules around Mg2+ coordinate asymmetrically to Mg2+ HS does not form stable interactions with three water through one of the oxygen lone pair orbitals (Fig. 4). The molecules in the first solvation shell of Mg2+ due to the asymmetric coordination was also obtained in a CPMD dynamical structure of solution and the full solvation of study to of Mg2+ hydration (Lightstone et al., 2001). Each the anion. Based on these results (Fig. 3), we focus on the first-shell water molecule forms 2–3 hydrogen bonds with situations for HS interacting with one or two water mole- the water molecules in the second solvation shell, which cules to address the solvent effects beyond the first solvation makes the observed asymmetric water orientations possible. shell. In contrast, the first-shell waters in the small cluster model, 82 Y. Yang et al. / Geochimica et Cosmochimica Acta 88 (2012) 77–87 coordinate symmetrically to Mg2+ by bisecting the two do not form a trigonal bipyramidal geometry at the end oxygen lone pair orbitals (Electronic Annex Fig. S3). point of the energy scan, even though the dissociating water We next compute the energetics for dissociation of a has escaped. Instead, small contractions are observed for first-shell water molecule around Mg2+. The MD simula- the two axial \O Mg O angles from 180° in the reactions of Mg2+ in aqueous solution show that the first shell tant state to 163° at the scan end point, with a variation of ˚ ends at Mg–Ow 3.5 A. Therefore, we define the Mg–Ow 6.8° (see a representative structure in Fig. 5b). The limited distance as the reaction coordinate and set 3.7 A˚ as the relaxation of the water molecules in the first solvation shell upper limit for the energy scans to ensure that the dissoci- occurs due to hydrogen bond interactions with second-shell ating water escapes from the first solvation shell. As stated water molecules. A similar result has been obtained previ- above, we assume that the transition from a six-fold hydra- ously (Evans et al., 2008). tion of Mg2+ to a five-fold geometry involves two elemen- Despite the lack of an energy barrier for five of the six tary steps (Ikeda et al., 2007). The first step involves scans, we believe that our computational approach is rele- removing one water molecule from the first solvation shell. vant, because the average value for the difference in energy Subsequently, the remaining first-shell water molecules re- between the end point of the scan and the reactant state . 1 lax structurally into a trigonal bipyramidal geometry due (EMg–Ow = 3.7 A˚ —EMg–Ow = 2.1 A˚ ) is 10.4 kcal mol , with to thermal fluctuations that would overcome the hydrogen a variation of 2.9 kcal mol1. The average energy difference bonding interactions between the first and second water is similar to the Gibbs free energy barrier of 10.5 kcal mol1 shells. The first step is an energy-increase process, and the obtained for water dissociation using the small cluster mod- subsequent structural relaxation for the five water mole- el with PCM solvation (see Electronic Annex Fig. S1). The cules is an energetically down-hill process. If both steps average energy difference is also similar to the single scan are captured in the simulation, then an energy barrier will that did show an energy barrier of 9.9 kcal mol1. A direct be obtained. If the water molecules are unable to relax then comparison of our calculated energies to experimental val- a monotonically increasing profile will be seen.The energy ues is not easy (e.g., potential energy versus free energy), 1 increases with increasing Mg–Ow distance for all the six but we report here a value of 9.5 kcal mol for water ex- 2+ 17 scans, but in only one of the scans, does the energy decrease change on Mg(H2O)6 at 300 K from O NMR experi- resulting in an energy barrier of 9.9 kcal mol1 (Fig. 5a). ment (Bleuzen et al., 1997). Our calculated values for The decrease in energy occurs because the five remaining both, the average of the six scans as well as the single scan first-shell water molecules relax and form a trigonal bipyra- which did show an energy barrier, are in fair agreement ˚ midal geometry at Mg–Ow 3.54 A. For five out of six with the experimental value. A similar barrier height of large model clusters, the energy scans show a monotonic 9 kcal mol1 was obtained using the molecular mechan- energy increase with the Mg–-Ow distance going up to ics-based potential of mean force calculations ((Kerisit 3.7 A˚ , no local energy minima or energy barriers are ob- and Parker, 2004). These considerations suggest that our tained (Fig. 5a). The lack of an energy barrier is ascribed RPE calculations are meaningful. to the fact that the five remaining first-shell water molecules 3.2.2. Mg2+ with HS system From the four optimized reactant state structures, we see that HS does not perturb the interactions between Mg2+ and the first-shell water molecules, which is consistent with our small cluster model results (see Electronic An- nex Figs. S3a and S4a). In detail, the average Mg–Ow distance is 2.12 A˚ with a variation of 0.03 A˚ . As observed in the Mg2+-only system, the first-shell water molecules coordinate asymmetrically to Mg2+ through one of the oxygen lone pair orbitals. This result is ascribed to preferred interactions with water molecules in the second solvation shell. In three of the large model clusters, HS interacts with a single first-shell water molecule around Mg2+. The average ˚ S–Hwater distance obtained is 2.34 A, where “Hwater” refers to the hydrogen atom of the water molecule that directly interacts with HS. For the fourth large model cluster, Fig. 4. A representative optimized structure for the reactant state HS interacts with two first-shell water molecules around 2+ ˚ ˚ based on the large model cluster calculation with no HS presence. Mg , with S–Hwater distances of 2.24 A and 2.36 A.In Water molecules on the first solvation shell (CPK representation all four cases, HS remains in the second solvation shell 2+ with hydrogen in white and oxygen in red) of Mg (CPK of Mg2+ with an average Mg–S distance of 4.8 A˚ . representation with green color) tend to asymmetrically coordinate The energy scan is set up similar to the Mg2+-only case. to Mg2+ through one of the oxygen lone pair orbitals, which are We set the Mg–Ow distance as the reaction coordinate with schematically shown as small purple circles. Water molecules ˚ beyond first solvation shell are in blue with licorice representation. 3.7 A as the upper limit for the energy scan to ensure that (For interpretation of the references to color in this figure legend, the dissociating water escapes from the first solvation shell 2+ the reader is referred to the web version of this article.) of Mg . Based on results of the small cluster study (see Y. Yang et al. / Geochimica et Cosmochimica Acta 88 (2012) 77–87 83

(a)18 (b) 16

14 ) -1 12 mol . 10 kcal 8

Energy ( 4

0 2.0 2.4 2.8 3.2 3.6 Mg-Owater distance (angstrom)

Fig. 5. (a) Energy scan proﬁles along the water dissociation with large cluster models with Mg2+ only. Only electronic energy is taken into account. (b) Representative structure at the ending point of an energy scan. The same representation scheme is adopted from Fig. 4. The dissociating water molecule is highlighted in pink color. (For interpretation of the references to color in this ﬁgure legend, the reader is referred to the web version of this article.)

Electronic Annex, Section 4), the water molecule which the remaining first-shell water molecules. Consequently, interacts directly with HS is defined to dissociate from the resulting penta-hydrated complex of Mg2+ cannot be the Mg2+ center. All four energy scans show monotonically stabilized effectively by HS. For the fourth large cluster increasing profiles as the Mg–Ow distance increases, similar model, HS directly interacts with two water molecules in to the Mg2+-only large cluster model (Fig. 6a). Interest- the first solvation shell of the reactant state. As one water ingly, the average energy difference between the end point molecule leaves, the interaction between HS and the sec- of the scan and the reactant state (EMg–Ow = 3.7 A˚ —EMg– ond water molecule becomes stronger, with the S-Hwater 1 ˚ Ow = 2.1 A˚ ) from the four scans is 14.3 kcal mol . This distance decreasing from 2.36 A in the reactant state to average energy difference value is much higher than the dis- 2.28 A˚ in the penta-hydrated complex. Even here, though, sociation barrier of 7.9 kcal.mol1 for the small cluster the HS-water stabilization is still much weaker than for model in the solution phase (see Electronic Annex Table the small model cluster, where two HS-water interactions . 1 ˚ EA1), and than the energy difference of 10.4 kcal mol exist and each S–Hwater distance is shorter than 2.00 A.In for the large cluster Mg2+-only system.Similar to the the small cluster model, the remaining first-shell water mol- Mg2+-only system, for all of the four scans, the five remain- ecules have no choice but to interact with HS, whereas ing first-shell water molecules do not gradually form a tri- those in the large cluster model have the ability to interact gonal bipyramidal geometry along the water dissociation with HS as well as with second-shell water molecules. Fur- pathway. The two axial \O Mg O angles contract from thermore, we note that the remaining first-shell water mol- 180° in the reactant state to 161° at the end of scans ecules are relatively far away from the HS ligand (the ˚ (Fig. 6b). minimum S–Ow distance is over 5 A). It is then reasonable The results of the present computational approach to assume that HS may not directly affect the structural indicate a large energy barrier for Mg2+ dehydration in rearrangement for the five remaining first-shell water the presence of HS (Fig. 6a), suggesting that HS did molecules. not facilitate water dissociation. The lack of structural In summary, the limited interactions between the remain- relaxation of first shell water molecules can be understood ing water molecules in the first solvation shell and HS by comparing the large cluster and the small cluster results. provide inadequate stabilization of the transition state, The ab initio small cluster calculations using the Natural which is mainly responsible for the large and monotonically Bond Orbital (NBO) method (Foster and Weinhold, 1980; increasing energy profiles in the presence of HS (Fig. 6a). Glendening et al., 2001) capture the intrinsic interactions The current computational result showing an apparent lack of ligands with first-shell water molecules around Mg2+ of any HS effect is consistent with our chemical intuition, without effects of solvation beyond the first shell (see Elec- and is supported by the small cluster studies showing no cor- tronic Annex Section 4.3). Those results show that the ma- relation between the intrinsic chemical properties of HS or jor lowering of the energy barrier (i.e., energy stabilization) other inorganic ligands and their ability to lower the Mg2+ for water dissociation by HS comes from the interactions dehydration behavior. between HS and the remaining first-shell water molecules around Mg2+. 3.3. Implications for dolomite formation In three out of four large cluster models, HS interacts only with one water molecule and when that molecule de- The elementary step of water leaving from the Mg2+ parts, there are no direct interactions between HS and center in the solution phase has previously been widely 84 Y. Yang et al. / Geochimica et Cosmochimica Acta 88 (2012) 77–87

(a)18 (b) 16

) 14 -1 12 mol . 10 kcal 8 6 Energy ( 4 2 0 2.0 2.4 2.8 3.2 3.6 Mg-Owater distance (angstrom)

Fig. 6. (a) Energy scan proﬁles along the water dissociation with large cluster models with Mg2+ and HS. Only electronic energy is taken into account. (b) Representative structure at the ending point of an energy scan. The same representation scheme is adopted from Fig. 4 and 5. HS is in CPK representation with white and yellow colors. (For interpretation of the references to color in this ﬁgure legend, the reader is referred to the web version of this article.)

2+ 2 accepted as the most critical step towards dolomite forma- Mg -CO3 ion interactions cannot be established, the prot- tion. According to our current study, and consistent with odolomite precursor will not be formed. Instead, separate our chemical intuition, it is unlikely that HS has a specific phases consisting of a calcium carbonate kernel and a hy- ability to promote Mg2+ dehydration in aqueous solution drated magnesium carbonate outer shell would be pro- via a dissociative mechanism. It is entirely possible, how- duced. Results of preliminary experiments in our ever, that HS may facilitate dolomite formation via other laboratories support these speculations, though detailed pathways. For instance, a concerted (interchange) mecha- work remains to be done (Chakraborty and C. S. Romanek, nism is conceivable, where a water molecule leaves the unpublished results). An anion-promoted interfacial mecha- 2+ 2 2+ Mg solvation shell and CO3 attacks the Mg center nism has also been proposed for barite formation, where simultaneously. Such a mechanism will be explored in Ba2+ desolvation was assisted by anions (inorganic ligands 2 future work. Alternatively, HS may promote cation like SO4 or biological ligands like aspartic acid) adsorbed desolvation at the interface of a solid precursor phase or on the crystal surface (Piana et al., 2006, 2007). We have pre- seed crystal. viously reported the formation of an amorphous, hydrated, The difficulty of dehydrating Mg2+ is supported by mixed anion phase at room temperature (Sahai et al., 2007). empirical observations that magnesite (MgCO3) is difficult While dolomite synthesis at Earth’s near-surface condi- to synthesize directly at low temperature and, a number of tions has been a fascinating challenge for geochemists over hydrated MgCO3 solid precursor phases are formed instead decades, the question remains as to whether any laboratory (Marschne, 1969; Fischbec and Muller, 1971; Garvie, 2003; experiments can capture the true geological process. As Romanek et al., 2009). A hydrated, amorphous CaCO3 solid noted in Hardie’s (1987) excellent and provocative review, precursor to calcite has also been reported in recent biomin- massive sedimentary dolomitization occurs over 100,000 eralization literature and depending on solution conditions time periods, so it is entirely plausible that completely dif- (Weiss et al., 2002; Politi et al., 2004; Politi et al., 2006; Politi ferent mechanisms operate over geologic time and space, et al., 2008). Static lattice energy minimization calculations and that given enough time, dolomitization may not be a have shown that a solid phase 50/50 mixture of (Ca/Mg) “problem”. CO3(H2O)6 is thermodynamically more stable than ikaite (CaCO3)(H2O)6 (de Leeuw and Parker, 2001). Since ikaite 4. CONCLUSIONS is a potential precursor of calcite (Ito, 1998), de Leeuw et al. proposed that the solid 50/50 mixture of (Ca/Mg) The “dolomite problem” has puzzled geochemists and 2+ CO3(H2O)6 may be a precursor to low-temperature dolo- sedimentologists for a long time. The difficulty of Mg mite. Although our computational approach does not indi- dehydration is deemed as the biggest hurdle toward dolo- cate a promoting effect of HS on Mg2+ dehydration in mite formation. Sulfide was proposed to play an active role bulk solution, Zhang et al. (2010) apparently did synthesize in promoting dolomite formation. Using our current dolomite in the presence of HS. computational approach, HS does not seem to have any We speculate, then, that HS or some organic ligands specific ability to promote Mg2+ dehydration in aqueous may promote Mg2+ dehydration at the surface of a solid solution via simple hydrogen-bond-like interactions. It is precursor phase resulting in (proto)dolomite. If no pro- entirely possible, however, that HS may facilitate dolomite moter anion is present, then it follows logically that a formation by some other mechanism(s). We propose that 2+ 2þ CaCO3 solid precursor will form first and hydrated Mg MgðH2OÞ6 associates with the surface of a calcium car- will be adsorbed to the precursor surface. Since direct bonate solid precursor phase (potentially amorphous and Y. Yang et al. / Geochimica et Cosmochimica Acta 88 (2012) 77–87 85

2þ hydrated), and HS promotes dehydration of MgðH2OÞ6 dynamical properties of ions and water molecules. J. Chem. at the solution–solid interface resulting in a “protodolo- Phys. 115, 3732–3741. mite” precursor that eventually transforms to dolomite. Criscenti L. J., Allen H. A., Chen C. C., Katz L. E., Larentzos J. P. and Xu M. (2008) Molecular modelling of metal speciation in ACKNOWLEDGEMENTS aqueous solution and at the mineral surface. Geochim. Cosmo- chim. Acta 72, A188. This research was funded by a National Scientific Foundation Cui Q., Elstner M., Kaxiras E., Frauenheim T. and Karplus M. CAREER Award (EAR 0346689), American Chemical Society (2001) A QM/MM implementation of the self-consistent charge Petroleum Research Fund (41777-AC2) to N.S., and a NASA density functional tight binding (SCC-DFTB) method. J. Phys. Astrobiology Institute grants to N.S. and C.S.R, and start-up Chem. B 105, 569–585. funds to N.S. from University of Akron. Partial post-doctoral sal- de Leeuw N. H. and Parker S. C. (2001) Surface-water interactions ary support to Y.Y. was provided by the Weeks Endowment, in the dolomite problem. Phys. Chem. Chem. Phys. 3, 3217– Department of Geoscience, University of Wisconsin. Y.Y. 3221. acknowledges start-up funding from Rowan University. We are Di Tommaso D. and de Leeuw N. H. (2008) The onset of calcium grateful to Prof. Huifang Xu and Mr. Fangfu Zhang for sharing carbonate nucleation: a density functional theory molecular their experimental synthesis results with us. Computational re- dynamics and hybrid microsolvation/continumn study. J. Phys. sources from the National Center for Supercomputing Applica- Chem. B 112, 6965–6975. tions (NCSA) at the University of Illinois, the Condor High Di Tommaso D. and de Leeuw N. H. 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