Letter pubs.acs.org/JPCL
Solution Structures and Acidity Constants of Molybdic Acid Xiandong Liu,*,†,‡ Jun Cheng,‡ Michiel Sprik,‡ and Xiancai Lu† †
State Key Laboratory for Mineral Deposits Research, School of Earth Sciences and Engineering, Nanjing University, 22 Hankou Road, Nanjing 210093, People’s Republic of China ‡ Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom S Supporting Information *
ABSTRACT: Experiment has not been able to discriminate between the oxo (MoO3· (H2O)3) and oxyhydroxide (MoO2(OH)2·(H2O)2) forms of molybdic acid. Using firstprinciples molecular dynamics based pKa calculation techniques, we identify that MoO2(OH)2.(H2O)2 is the true solution structure and its OH ligands are the acidic site. Simulations at elevated temperatures up to 573 K show an encouraging agreement between calculated and experimental pKa’s, which validates our method of prediction of subtle pH-dependent speciation in hydrothermal solutions. We find that molybdate species have highly volatile pH- and temperature-dependent coordinations, which is related with the experimentally observed variability in Mo coordination of polyoxometalates (POMs). These results form a physical basis for understanding the properties of Mo in numerous lab and natural processes ranging from formation of POMs to transport and deposition mechanisms in crustal fluids. SECTION: Molecular Structure, Quantum Chemistry, and General Theory report shows that pKa1’s increase with T,18 but recent studies indicate a decreasing trend.15,19 Undoubtedly, knowledge of the molecular-level structure and acid properties of molybdic acid is a prerequisite for resolving the open issues in the aqueous chemistry of Mo. Unfortunately, the exact aqueous structure of molybdic acid, that is, the most fundamental information, is still under debate. For the formula of H2MoO4, there are several possible solution structures, MoO3·(H2O)3 (oxo molybdic acid), MoO2(OH)2·(H2O)2 (the oxyhydroxide form), and Mo(OH)6 (the hydroxide form).20,21 On the basis of vibrational spectra measurements on deuterium-exchanged molybdic acid, Mo(OH)6 can be definitely ruled out because of the strong shift in vibrational frequency upon H/D exchange, contrary to experiment.20 Quantum chemistry studies also show that the Mo(OH)6 conformation is highly unstable.21 Static calculations21 and Car−Parrinello molecular dynamics (CPMD) simulation22 indicate that both MoO3·(H2O)3 and MoO2(OH)2 are stable in solution. While according to the Raman spectroscopy study of ref 20 the spectra of both structures fall within the uncertainty of quantum chemical calculations, MoO3·(H2O)3 gives the best agreement with experiment. In contrast, Ozeki et al. found the best agreement between calculated and measured electronic absorption spectra for MoO2(OH)2·(H2O)2.23 The present study addresses these questions using firstprinciples molecular dynamics (FPMD) simulations.24 Acidity constants are calculated by applying a combination of FPMD
O
xo anions are the common form of Mo6+ in aqueous solution.1 Upon acidification, simple aqueous oxalates can combine to form polyoxometalates (POMs). Due to their unique structural and electronic properties, POMs have attracted significant attention in several fields, including chemistry, materials, and biology.2−4 In particular, the formation mechanism of POMs has been the subject of intensive research starting with the pioneering study of refs 5 and 6. The condensation is a complex process, and a number of questions remain. Due to the interest in transport and deposition mechanisms of Mo in the crust, many studies have also been performed under elevated temperatures and pressures, mimicking the ore-forming conditions. Again, the exact complexation mechanism between Mo6+ and common ligands (e.g., F−/Cl−/S2−) is still ambiguous. For example, Tugarinov et al.7 suggested that Mo−F complexes could be important in acidic solutions under high temperatures, but later studies showed that F is not essential for the Mo concentration in geofluids.8−10 It is generally accepted that Mo−Cl complexation is weak, but it is still unclear if Mo-oxo-chloride complexes can form in solution at high salinity and low pH.11−13 Acid chemistry is a key for understanding the aqueous properties of Mo. It is well-known that molybdic acid has very similar first and second acidity constants, pKa1 = 3.61−4.0 and pKa2 = 3.89−4.37,14−16 and therefore, MoO42− is dominant in neutral and near-basic solutions, whereas H2MoO4 and HMoO4− are present only in acidic environments. Experiments agree that the second acidity constants of molybdic acid increase with temperature.15,17,18 However, the first acidity constants at high T are still not well-documented; an early © 2013 American Chemical Society
Received: July 11, 2013 Accepted: August 14, 2013 Published: August 14, 2013 2926
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and free-energy perturbation methods, as outlined in an earlier technical publication (see the Supporting Information for computational details).25 Tests on acids and bases spanning a 20 pK unit interval prove that this technique can achieve an accuracy of 2 pKa units.25−28 We have computed the pKa’s of candidate structures of molybdic acid and through comparison with experiment show that MoO2(OH)2·(H2O)2 should be the real structure in solution. In addition, we examine the temperature dependence of structure and acidity constants for temperatures varying from ambient to 573 K. The calculated acidity constants are supported by recent spectrophotometric measurements.15 We interpret this agreement as a validation of the use of FPMD as a computational tool in the study of the subtle pH-dependent speciation of metals in hydrothermal fluids, giving us confidence in the detailed information on the structure obtained from analysis of the molecular dynamics trajectories. The FPMD results on molecular structure and acidity presented here are therefore directly relevant for the understanding of a variety of chemical processes, for example, formation of POMs, the transport and deposition mechanism of Mo, and adsorption of Mo-containing complexes on mineral surfaces. The acidic sites of the MoO3·(H2O)3 conformation are the H2O ligands. The calculated acidity constant is 9.3 (Table 1).
Figure 1. Time evolution of Mo−OH2 distances after deprotonation of a H2O ligand of MoO3·(H2O)3 (blue curves), a H2O ligand of MoO2(OH)2·(H2O)2 (red curve), and a OH ligand of MoO2(OH)2· (H2O)2 (black curves).
pKa2 = 7.21, and pKa3 = 12.67. For molybdic acid, because the two H2O ligands leave, the decrease in repulsion by Mo6+ is not as severe; therefore, the pKa2 is not significantly higher. Our calculations suggest therefore that the dehydration of the monoanion is responsible for the similarity in pKa1 and pKa2 values of molybdic acid. The calculated and experimental pKa’s of molybdic acid at high T−P conditions are plotted in Figure 3. At 473 K, the predicted pKa1 and pKa2 are 1.3 and 4.9, which is comparable to the experimental results of 0.99 and 6.1.15 This agreement is further support for the proposed solution conformation of molybdic acid. At 573 K, the pKa1 and pKa2 reported in ref 15 are 0.44 and 7.79. These estimates are not directly obtained from experimental measurement but are extrapolations from the data at lower temperatures using the Van’t Hoff equation. They are in reasonable agreement with our calculated pKa’s (pKa1 = 0.6 and pKa2 = 5.7). These comparisons confirm the peculiar temperature dependence of the acidity constants of molybdic acid; as pointed out in ref 15, pKa1’s decrease whereas pKa2’s increase with T. The implication is that as the temperature increases, the molecular form is gradually replaced by the bimolybdate. The radial distribution functions (RDFs) and coordination numbers (CNs) characterizing the molecular structures of molybdic acid and deprotonated forms at the three temperatures are also given in Figure 2. Under ambient conditions, the RDFMo−O of MoO2(OH)2·(H2O)2 exhibits two sharp peaks at around 1.74 and 1.95 Å, corresponding to MoO and Mo− OH bonds, respectively (left panel in Figure 2A). The broad band at around 2.40 Å marks the Mo−OH2 bonds. These three peaks add up to 2 on the CN curve. As the snapshot shows, the OH2 and OH ligands donate H-bonds to hydrating water, and the oxygens of OH and O ligands accept H-bonds from water (right panel in Figure 2A). At 473 K, the RDF peak for Mo− OH2 becomes weaker. The corresponding running CN is only 0.5, which means that the complex is nearly four-foldcoordinated and can formally be written as MoO2(OH)2· (H2O)0.5. It can be seen that the peak position of the MoO bonds stays where it was at lower temperature, but the Mo− OH peak shifts inward to 1.89 Å, strengthened due to the loss of H2O ligands. At 573 K, the H2O peak almost disappears, and therefore, molybdic acid is actually MoO2(OH)2 at this temperature. Bimolybdate keeps its tetrahedral structure for all simulated temperatures (Figure 2B). The Mo−OH bond (1.79 Å) is
Table 1. pKa’s for MoO3·(H2O)3, Mo2(OH)2·(H2O)2, and MoO3(OH)− at Ambient Conditionsa
a
MoO3· (H2O)3
Mo2(OH)2·(H2O)2 OH as acid
Mo2(OH)2·(H2O)2 H2O as acid
Mo3(OH)−
9.3
4.7
10.6
4.5
See the Supporting Information for more details.
MoO2(OH)2·(H2O)2 has two kinds of proton-donating ligands, that is, OH and H2O, for which we predict pKa’s of 10.6 and 4.7, respectively. Clearly, the pKa of the H2O ligands of MoO3· (H2O)3 and MoO2(OH)2·(H2O)2 is much higher than the experimental estimate of 3.61−4.0. The difference is well outside of the error margin of our methodology (2 pKa units). In contrast, the pKa of the OH ligand of MoO2(OH)2·(H2O)2 is consistent with that from experiment. This result strongly suggests that MoO2(OH)2·(H2O)2 rather than MoO3·(H2O)3 is the true solution structure of molybdic acid and its OH ligand is the acidic proton donor. Deprotonation of the OH ligand of MoO2(OH)2·(H2O)2 is followed almost immediately by spontaneous expulsion of the two H2O ligands, as shown by the trajectories in Figure 1. A similar dehydration is also found after deprotonation of a H2O ligand of MoO3·(H2O)3 and MoO2(OH)2·(H2O)2 (Figure 1). The acid dissociation induced dehydration of MoO2(OH)2· (H2O)2 can be expected to decrease the effective volume of the conjugate base, which is consistent with conclusions derived from experiment.29 As the structural data and snapshots show (Figure 2), acid dissociation has a drastic effect on the geometry of the oxyhydroxide complex, transforming from a six-fold-coordinated structure to a tetrahedral form, that is, MoO3(OH)−. The calculated acidity constant of this product species (i.e., pKa2 of molybdic acid) is 4.5, which is in good agreement with the experimental range of 3.89−4.4. For acids with a stable coordination under deprotonation, the pKa2 can be expected to be higher than the pKa1 due to the weaker repulsion from the central cation after loss of the first proton. For example, phosphoric acid (PO(OH)3) has pKa1 = 2.12, 2927
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Figure 2. Radial distribution functions (RDFs) and coordination numbers (CNs) for Mo−O in (A) MoO2(OH)2·(H2O)2, (B) MoO3(OH)−, and (C) MoO42− at the three temperatures. In the snapshots, some water molecules are removed for clarity, and H = white, O = red, and Mo=cyan. The numbers in the snapshots denote H-bond lengths.
As molybdic acid gradually transforms from MoO2(OH)2· (H2O)2 to MoO2(OH)2 with increasing temperature, the dissociating proton feels an increasing repulsion by Mo6+. In contrast, the repulsion in the bimolybdate ion remains because the four-fold structure holds at all temperatures. Therefore, as the temperature increases, the difference between pKa1 and pKa2 becomes more obvious, as shown in Figure 3. Molybdate species are the basic building blocks of Mocontaining POMs. Their molecular structures and acidity
slightly longer than the MoO bond (1.76 Å). Even though bimolybdate is an anion, its OH ligand donates a H-bond to the hydrating waters, as illustrated in the snapshot in the right panel of Figure 2B. The oxygen atoms all accept H-bonds from water. The structure of MoO42− is tetrahedral, with an average Mo O bond length of 1.79 Å, consistent with the EXAFS measurement.11 Figure 2C shows that this structure is stable from ambient to high temperature (Figure 2C). Again, the oxygen sites act as H-bond acceptors from hydrating waters. 2928
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structure of Mo complexes adsorbed on mineral surfaces,32−34 which, in principle, can be revealed by in situ experiments complemented with FPMD simulations. 35 We see the encouraging agreement between the calculated and experimental acidity constants at elevated temperatures as a validation of FPMD-based free-energy perturbation methods in the study of aqueous speciation of elements in hydrothermal solutions, which is a new developing area in geochemistry.36−38
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ASSOCIATED CONTENT
* Supporting Information S
Methodology including systems, FPMD details, and pKa calculation techniques, and the results including vertical energy gap data, deprotonation free energies, and pKa’s. This material is available free of charge via the Internet at http://pubs.acs.org.
Figure 3. Calculated and measured15 pKa’s for molybdic acid at 300, 473, and 573 K and the corresponding saturated vapor pressure. See the Supporting Information for more details.
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AUTHOR INFORMATION
Corresponding Author
constants are crucial for understanding the formation mechanism of POMs. The pKa’s indicate that at near-neutral and basic pH’s, the majority species is MoO42−, and with gradual acidification, MoO3(OH)−, MoO2(OH)2·(H2O)2 and MoO42− can coexist in solution. Our simulations show that molybdic acid tends to lose its H2O ligands at higher temperature, changing to four- and five-coordinate forms. According to experiment, four-, five-, and six-fold coordination are all possible in POMs.3,22 This suggests that the volatile coordination of molybdate species observed in the simulation may be related to the variability in coordination in Mo POMs. Indeed, experiments have shown that the formation of these POMs is strongly sensitive to pH and temperature. 3 Manipulation of the pH, T, Mo concentration, and counterions produces numerous permutations of species with different building block populations, which can explain the diversity of POM structures. FPMD-based free-energy calculation techniques have provided essential clues for uncovering the mechanisms of POM formation on the basis of reasonable evaluation of the free energy of bond breakage/formation.4,22,30,31 Here, we have shown that our pKa calculation technique can be used to obtain sufficiently accurate estimates of deprotonation constants over a wide range of temperatures. As proton transfer is a key process in POM formation, our methodology has therefore added an important tool in the computational study of the formation mechanism of POMs. In summary, using FPMD-based free-energy perturbation techniques, we have presented strong evidence for the structure of aqueous molybdic acid. Comparison between calculation and experiment suggests that the true structure should be MoO2(OH)2·(H2O)2 rather than MoO3·(H2O)3. Furthermore, we investigated the structure and acidity of molybdic acid over a range of temperatures up to 573 K. The results show that molybdate species have a highly volatile coordination, strongly affected by the environmental pH and temperature. Simulation can provide structural and thermodynamic data that are not yet accessible to experiments, in particular, in complex environments or under nonambient conditions in the Earth’s interior. The results of this study are therefore directly relevant for the unraveling of the relation between the chemical properties of Mo and processes such as formation of POMs, isotopic fractionation, and transport and deposition in high T−P crustal fluids. In geochemistry, it is believed that fractionation of Mo isotopes can be used to reconstruct the paleoenvironment, and understanding isotopic processes requires knowledge of the
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We acknowledge the National Science Foundation of China (Grants 41002013, 41273074, and 41222015), the Newton International Fellow Program, and financial support from the State Key Laboratory for Mineral Deposits Research. We are grateful to the High Performance Computing Center of Nanjing University for use of the IBM Blade cluster system.
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REFERENCES
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