DFT Study on Characterization of Hydrogen Bonds in the Hydrates of

Article pubs.acs.org/JPCC

DFT Study on Characterization of Hydrogen Bonds in the Hydrates of MgSO4 Eldhose Iype,† Silvia V. Nedea,† Camilo C. M. Rindt,*,† Anton A. van Steenhoven,† Herbert A. Zondag,† and A. P. J. Jansen‡ †

Department of Mechanical Engineering (Energy Technology), Eindhoven University of Technology, Den Dolech 2, 5612 AZ Eindhoven, The Netherlands ‡ Department of Chemical Engineering, Eindhoven University of Technology, Den Dolech 2, 5612 AZ Eindhoven, The Netherlands ABSTRACT: Magnesium salt hydrates are potential thermo-chemical energy storage materials considering their high energy storage density and their availability. However, in practical applications, these materials suffer from low efficiency due to their sluggish kinetics and significant structural changes during hydration and dehydration. A DFT PW91-TZ2P level optimization is performed on the various hydrates of magnesium sulfate molecules to study their structural properties. The study identifies a wide network of hydrogen bonds that is significantly influencing the chemical structure of the molecules. These hydrogen bonds appear to cause distortions in the hydrated structures and even hinder the coordination of water with magnesium, resulting in lower-energy isomers. In the case of hexahydrated isomers, the hydrogen bond stabilizes a conformation that has only four coordinated water molecules and is energetically more stable than the conformation with six coordinated water molecules. The sluggish hydration kinetics in magnesium sulfate is attributed to the strong hydrogen bond network present in the crystals. In addition, the hexahydrated structure exhibits an intramolecular proton-transfer reaction. This suggests that the strong hydrogen bond interactions potentially dissociate water molecules during hydration.

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INTRODUCTION Magnesium salt hydrates are potential candidate materials for storing energy in seasonal heat storage systems. Hydration and dehydration reactions in MgSO4 are accompanied with considerable amounts of energy exchange (approximately 2.8 GJ/m31). These salt hydrates are abundant in nature, and thus they are characterized as excellent thermo-chemical heat storage materials. However, experiments have shown that thermo-chemical heat storage systems, using salt hydrates, suffer from low efficiency due to the low extent of hydration under normal atmospheric conditions.2 To attain full hydration (six water molecules per MgSO4), the water vapor pressure should be significantly higher than the normal atmospheric conditions.2 This requirement poses a challenge in regenerating stored energy from hydrated MgSO4 systems. Chipera et al.3 have suggested that the hydration processes in MgSO4 crystals are characterized by the presence of metastable states and slow kinetics, which increases the complexity of the heat storage process. A molecular-level investigation into the process involved seems to be necessary in order to understand the dynamics in detail and to identify the factors limiting the extent of hydration and diffusion through surface layers. Crystalline structures of various hydrates of MgSO4 are widely studied in the literature.4−9 The presence of the extensive network of hydrogen bonds in MgSO4·7H2O is investigated by Zalkin et al.10 Significant delocalization of hydrogen atoms within the hydrogen bonds is reported in this study. Investigation of © 2012 American Chemical Society

molecular structures of up to trihydrates of MgSO4 reveals the presence of isomeric structures, which are stabilized by the formation of hydrogen bonds.11 These findings lead us to the conclusion that hydrogen bonds in MgSO4 might play a crucial role in its structural and dynamic properties. The current study will focus on investigating the molecular structures of various hydrates of MgSO4 and the characterization of hydrogen bond networks present in them. Chemical structures of hydrated Mg2+ ions in aqueous media are studied experimentally as well as theoretically.12−14 In aqueous media, Mg2+ ions tend to form complexes with six water molecules oriented toward the six corners of a regular octahedra. All the water molecules are situated at an equal distance from the Mg2+ ions. However, studies also indicate that the orientation of water molecules changes depending on the nature of the environment. In perfect hydrated crystals, the water molecules are directed toward the corners of octahedra surrounding the Mg 2+ ions, and they do not remain indistinguishable.4,10 Even the possibility of the formation of a contact ion pair with the sulfate anion is also predicted by Cory,12 which has been confirmed in our study. In this study, we report various optimized structures of MgSO4 hydrates and their corresponding DFT energies. The Received: March 16, 2012 Revised: July 2, 2012 Published: August 17, 2012 18584

dx.doi.org/10.1021/jp3025649 | J. Phys. Chem. C 2012, 116, 18584−18590

The Journal of Physical Chemistry C

Article

octahedral structure of [Mg(H2O)6]2+ is representative of a gasphase molecule14 or a perfect crystalline structure with suitable anionic groups, such as (SO4)2−9 or (Cl2)2−.15 In aqueous solutions, the average Mg−O distance decreases significantly (approximately by 0.07 Å) due to the formation of a strong hydrogen bond network.14 Several hydrogen bonds present in the structures are identified in this study. The effect of such a hydrogen bond network on the structure of MgSO4·xH2O is also investigated in this work.

of multiple isomers was high, the starting geometries for x = 1− 3 hydrates were chosen to be similar to the ones reported in the literature.11 A six-coordinated hexahydrate of magnesium sulfate has been obtained by binding SO2− tetrahedra to 4 [Mg(H2O)6]2+ octahedra. The presence of hydrogen bonds has been identified by checking the distance between nonbonded O···H pairs. When this distance is between 1.2 and 2.1 Å, we classify those O···H interactions as hydrogen bonds, which is consistent with the study of Grabowski.18−20 A Bader charge21 analysis is performed on the optimized structures to study the charge distributions. This method is chosen since the results will then be independent of the choice of basis set used in the DFT method.22

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METHODOLOGY AND VALIDATION Molecular structures of various hydrates (0, 1, 2, ...6) of MgSO4 were optimized using the density functional level theory using the PW91 generalized gradient approximation (GGA) functional implemented in the Amsterdam Density Functional (ADF) program with the double-polarized triple-ζ basis set. A spin-restricted Kohn−Sham method was used by keeping the integration accuracy to the maximum throughout the calculation. The applicability of GGA to study hydrogenbonded systems has already been established in the literature.16 Figure 1 shows the optimized structure of the [Mg(H2O)6]2+ system. The equilibrium bond lengths obtained for [Mg-

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RESULTS AND DISCUSSION Energies of hydration in the Mg2+ ion are in the range of 30−80 kcal/mol,14 and energy exchange in the formation of a strong hydrogen bond, X−H···Y, is on the order of 10−17 kcal/ mol.23,24 This suggests that systems involving large numbers of hydrogen bonds can possibly disturb the Mg−O bond in Mg2+containing salts. This has been investigated in the following sections where we discuss optimized structures of MgSO4·xH2O molecules. Molecular Structures of Various Hydrates of Magnesium Sulfate. Equilibrium structures of magnesium sulfate (0−3) hydrates have been investigated by Galina et al.11 They found two stable conformations for each hydrate: One in which all the water molecules were attached to the Mg atom, and the second set in which at least one water molecule, which may or may not be bonded to Mg, was stabilized by forming intramolecular hydrogen bondings. In all the instances, the energy differences between both of the conformations were less than 12 kcal/mol. Our optimized structures correspond to one of these two conformers for 0−3 hydrates and, in most cases, to the lowest-energy isomers. The optimized structures are shown in Figures 2−9, and the corresponding DFT energies are given in Table 1. All the distances are shown in angstroms. Table 1. Number of Hydrogen Bonds and Energies of Various Configurations molecule

2+

Figure 1. Optimized structure of [Mg(H2O)6] .

MgSO4·1H2O MgSO4·2H2O MgSO4·3H2O MgSO4·4H2O MgSO4·5H2O MgSO4·6H2O MgSO4·6H2O

(H2O)6]2+ from our calculation (Mg−O: 2.09 and O−H: 0.97) are in good agreement with other high-level electronic structure calculations (Mg−O: 2.10; O−H: 0.97)12 as well as experiments (Mg−O: 2.09).17 This result reiterates the applicability of the PW91 functional to such systems. The structures of various hydrates of MgSO4·xH2O, where x = {0.1−6}, are optimized. Solvation effects are not taken into account in this work, and thus the systems in this study correspond to molecules in the gas phase. A complete analysis to study the hydration in salt hydrates requires the modeling of periodic lattices, which is computationally demanding. Nevertheless, the assumption to treat this problem in the gas phase is satisfactory, as the focus is more on hydrogen bonds, and the theories of hydrogen bonds may be generalized irrespective of whether the system is in the condensed phase or not. Structural optimization is performed in all the geometries discussed in this study. A frequency analysis is also done to confirm the absence of imaginary frequencies. Since the possibility for the formation

(Figure (Figure (Figure (Figure (Figure (Figure (Figure

3) 4) 5) 6) 7) 8) 9)

number of hbs

energy (kcal/mol)

binding energy (ΔE) (kcal/mol)

0 2 3 4 5 6 4

−1096.2666 −1457.4938 −1818.8178 −2166.1394 −2516.2105 −2863.8574 −2848.0336

−33.8458 −65.19514 −96.64124 −114.0849 −134.2781 −152.0471 −136.2233

Anhydrous and Monohydrated Magnesium Sulfate. In the MgSO4 structure (Figure 2), the SO2− 4 tetrahedra is connected to the Mg atom via two Mg−O bonds. The presence of Mg in the system elongates the S−O bond by 0.17 Å in the SO2− tetrahedra. In the case of MgSO4·1H2O (Figure 3), 4 however, there are no significant changes in the bond lengths, compared to the anhydrate, due to the presence of a water molecule. The Bader charges of Mg, S, and O atoms in MgSO4·1H2O are seen to be only slightly larger than those in MgSO4, whereas the natural bond orbital (NBO) charges did not show significant variation between the two molecules.11 18585



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Figure 2. Structure of MgSO4. Bond lengths and Bader charges are also shown.

Figure 4. Structure of MgSO4·2H2O. Bond lengths and Bader charges are also shown.



Magnesium Sulfate Dihydrate. The structures of higher hydrates are characterized by the presence of hydrogen bonds of varying bond lengths. In our optimized structures (Figures 4−9), the presence of hydrogen bonds are identified by measuring the distances of O···H interactions. MgSO4·2H2O, in Figure 4, has two hydrogen bonds, hb1 and hb2. The hydrogen bond lengths are 1.85 Å each, and the O−O bond lengths in these hydrogen bonds are 2.58 Å. These hydrogen bonds cause a slight elongation in one of the O−H bonds in the water molecules by roughly 0.03 Å, but they do not cause much structural deformation in the SO2− 4 tetrahedra. Additionally, the presence of two water molecules increases the Mg−O and Mg− S distances by approximately 0.07 Å. This may be connected with the decreased negative charges in the hydrogen-bondacceptor O atoms. Magnesium Sulfate Trihydrate. Our structure of MgSO4·3H2O (Figure 5) has three hydrogen bonds (hb1, hb2, and hb3). According to Jeffrey,25 a hydrogen bond is regarded as strong when the O−O distance is less than 2.5 Å.

We give the bond lengths of all the hydrogen bonds in our systems. It can be seen that the O−O distances in hb2 is 2.5 Å, and thus it may be classified as a strong hydrogen bond. Additionally, it causes clear elongations in the O−H(0.13 Å) bond in water (W2) as well as in the S−O(0.06 Å) bond connected to this hydrogen bond. In contrast, hb1 and hb3 appear to be relatively weaker hydrogen bonds because of the longer O−O bond lengths in these hydrogen bonds (>2.5). Moreover, these hydrogen bonds result in smaller elongations in O−H bond lengths in the water molecules (W1 and W3) associated with these bonds. Another noticeable deformation in the MgSO4·3H2O structure includes the overall displacement of the O atoms connecting Mg and S atoms toward the S atom. This may be due to the increased positive charges in Mg and S atoms as the degree of hydration increases. Magnesium Sulfate Tetrahydrate. As the number of water molecules is increased to four (Figure 6), the number of hydrogen bonds is also increased to four (hb1, hb2, hb3, and hb4). Among these, hb1 and hb3 are, comparatively, on the 18586



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probably due to the increased Coulombic repulsion. One of the significant observations in the MgSO4·4H2O structure is the absence of coordination of W4 with the Mg atom (Figure 6). The measured distance between W4 and Mg is 2.23 Å, and this water molecule is stabilized by forming two hydrogen bonds (hb3 and hb4) within the system. Magnesium Sulfate Penta- and Hexahydrates. The molecular structures of penta- and hexahydrates show significant distortions in their molecular structures, which is caused by the formation of an extensive hydrogen bond network. Figure 7 shows the optimized structure of

Figure 6. Structure of MgSO4·4H2O along with bond lengths and Bader charges. Unlike in all the previous hydrates, this structure contains one uncoordinated water molecule, W4. This water molecule is stabilized by the formation of hydrogen bonds.

weaker side of the hydrogen bond strength spectrum with O− O distances being above 2.6 Å (Table 2) and the corresponding Table 2. Hydrogen Bond Parameters in the Conformations molecule MgSO4·2H2O MgSO4·3H2O

MgSO4·4H2O

MgSO4·5H2O

MgSO4·6H2O 1

MgSO4·6H2O 2

hydrogen bond name

O−H (Å)

H···O (Å)

O−O (Å)

∠OHO (deg)

hb1 hb2 hb1 hb2 hb3 hb1 hb2 hb3 hb4 hb1 hb2 hb3 hb4 hb5 hb1 hb2 hb3 hb4 hb5 hb6 hb1 hb2 hb3 hb4

1.00 1.00 0.98 1.10 1.00 0.98 1.07 0.98 1.02 1.02 0.98 1.03 1.00 0.99 1.02 1.03 1.02 1.00 1.03 1.03 1.02 1.07 1.04 1.09

1.85 1.85 2.04 1.41 1.83 1.96 1.48 2.02 1.65 1.63 2.00 1.60 1.66 1.89 1.57 1.58 1.57 1.72 1.59 1.55 1.63 1.41 1.54 1.37

2.58 2.58 2.66 2.50 2.57 2.63 2.53 2.64 2.53 2.60 2.66 2.60 2.62 2.66 2.56 2.58 2.57 2.63 2.61 2.55 2.48 2.48 2.58 2.47

126.47 126.43 119.65 165.06 128.18 123.18 164.36 118.11 141.62 158.32 121.61 161.44 154.82 132.22 159.32 160.92 164.89 149.49 170.09 163.40 136.24 171.71 177.36 174.04

Figure 7. Structure of MgSO4·5H2O along with bond lengths and Bader charges. This structure contains four coordinated water molecule and one uncoordinated water molecule, W4.

MgSO4·5H2O. Five hydrogen bonds are identified in the structure (hb1−hb5). All the O−O bond lengths are larger than 2.6 Å, which suggests that they do not belong to the category of strong hydrogen bonds.25 The average radius of the coordination sphere and the distance between Mg and S, in MgSO4·5H2O, are increased to 2.11 and 2.65 Å, respectively. It is interesting to note that hb4 and hb5 have the same hydrogen-bond acceptors, and this causes an elongation of the bonds connected to this oxygen atom from both Mg and S. In the case of MgSO4·6H2O, we have arrived at two stable conformations with an energy difference of 15.82 kcal/mol. Figure 8 shows the first conformation in which four water molecules (W1, W2, W5, and W6) are coordinated with Mg, and the remaining two water molecules (W3 and W4) are stabilized by the formation of hydrogen bonds. Altogether, there are six hydrogen bonds in the conformation, and none of them can be strictly classified as strong hydrogen bonds according to the convention used in this study. The average radius of the coordination sphere is 2.04 Å, and the distance between Mg and S atoms is 3.14 Å. The second conformation is obtained by introducing an 2+ SO2− 4 tetrahedra to a fully hydrated [Mg(H2O)6] ion (Figure 1). This ensures that all the water molecules are coordinated with the Mg atom. Unlike the previous conformation, this structure has only four hydrogen bonds. However, two of them (hb2 and hb4) are strong hydrogen bonds with bond lengths of 1.41 and 1.37 Å, respectively. The average radius of the

elongation of O−H bond lengths by roughly 0.03 Å. On the other hand, hb2 and hb4 are relatively on the stronger side of the spectrum, with O−O distances being closer to 2.5 Å, and O−H bond elongation being higher than 0.05 Å. The average radius of the coordination sphere of water to Mg increases from 2.02 to 2.09 Å, as the number of hydrated water molecules is increased from zero to four, and in the mean-time, the distance between Mg and S atoms is increased from 2.45 to 2.6 Å, 18587



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water molecule clearly reflects the different way it binds to the rest of the molecule. The addition of a fifth water molecule increases the number of hydrogen bonds to five as well as the degree of coordination by one (Figure 7) and results in an energy change of 20.2 kcal/mol. It is to be noted that, in this step, the strength of all the five hydrogen bonds decreases (O− O distances are ≥2.6 Å), and thus the overall energy change does not reflect the significant energy change due to the coordination of the fifth water molecule. The presence of another (sixth) water molecule increases the number of hydrogen bonds by one and the degree of coordination by one, but, in this case (8), one of the Mg− O−S bonds is replaced with a Mg−W5−O−S bond, accompanying an energy change of roughly 17.7 kcal/mol. This implies that the total number of bonds to the Mg atom does not change with the addition of the sixth water molecule, and the energy contribution is assumed to be coming from the formation of another strong hydrogen bond. Continuing in this line of argument, one can easily see that, in the fully coordinated hexahydrated structure (Figure 9), an energy

Figure 8. Structure of MgSO4·6H2O along with bond lengths and Bader charges. All the water molecules are not coordinated to the Mg atom, and still this conformation is energetically favorable to the fully coordinated MgSO4·6H2O. Proton transfer is observed through hydrogen bond hb5.

coordination sphere is 2.105 Å, and the distance between Mg and S atoms is 2.6304 Å. One of the striking observations in both of these structures is the swapping of the covalent bond and the hydrogen bond between O−H in W5 and its hydrogen bond with SO2− 4 . This subsequently results in a proton transfer from W5 to SO2− 4 tetrahedra. Hydrogen bonding is regarded as an incipient mechanism for a proton-transfer reaction.26 A detailed discussion on the hydrogen bonds and the proton-transfer processes in our systems is done in the following sections. Energy Contributions in Various Hydrates. The binding energies (defined as ΔE = EMgSO4·xH2O − (EMgSO4 + x × EH2O) for all the hydrates are given in Table 1. The energy of a separately optimized water molecule, EH2O, is used to calculate ΔE. It can be easily understood that the binding energy of the monohydrate (Figure 3) represents the energy of hydration, which is roughly −33.84 kcal/mol. The addition of another water molecule (Figure 4) increases the magnitude of the total binding energy by roughly 31.3 kcal/mol. The latter includes contributions from hydration of a second water molecule as well as from the formation of two hydrogen bonds (relatively weaker). Addition of a third water molecule also liberates an equivalent amount of energy (roughly 31.4 kcal/mol) with contributions from hydration of the third water molecule as well as from the formation of another hydrogen bond. It is interesting to note that the total energy change per addition of water molecules is almost constant irrespective of the number of hydrogen bonds formed in these three hydrates. This implies that the interaction between the Mg atom and the water molecules is dominantly electrostatic. A similar analysis of the fourth hydrate (considering the fact that there is no further coordination of water) reveals that the binding energy (which is roughly −17.4 kcal/mol) of the fourth water molecule is coming purely from the formation of an additional hydrogen bond (hb4 in Figure 6), which, from the perspective of the energy change, should belong to the category of strong hydrogen bonds. The smaller binding energy of the fourth

Figure 9. Structure of MgSO4·6H2O along with bond lengths and Bader charges. This conformation has all the six water molecules coordinated to the Mg atom. Proton transfer is observed through hydrogen bond hb3.

increase of 15.8 kcal/mol is attributed to both an increase in the number of water coordination by one as well a decrease in the number of hydrogen bonds by two. Thus, the breaking of two hydrogen bonds dominates the energy contribution compared to the increase in degree of hydration. From a different perspective, one can argue that Figure 9 is formed by coordinating two additional water molecules to the structure, as shown in Figure 6. This leads us to the conclusion that an addition of two water molecules decreases the energy only by 22.1 kcal/mol. Thus, it can be argued that the major contribution to energy due to hydration is coming from the formation of strong hydrogen bonds within the system. This intermediate hydrogen bond network can, indeed, influence the rate of hydration significantly. This could possibly be one of the reasons for the sluggish hydration rates3 for MgSO4 crystals under normal atmospheric conditions. Hydrogen Bonds in MgSO4·xH2O Systems. A hydrogen bond is defined as a bond formed between two negatively 18588



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charged atoms, such as O, F, and N, with a hydrogen atom sitting in between them (Xδ−−Hδ+···Yδ−). The hydrogen atom interacts with both the negatively charged atoms, and one of the interactions is covalent in nature (X−H) and the other is electrostatic in nature (H···Y).20 The X−H group is considered as a proton donor, and the Y atom is called a proton acceptor, which has at least one lone pair of electrons.20 Hydrogen bond interactions include attractive electrostatic interactions at long distances, and polarization energy and charge transfer interactions at short distances. These attractive interactions compete against the exchange energy due to repulsive interactions.20 Figure 10 shows the variation of O−H bond lengths as a function of H···O distance of all the identified hydrogen bonds

Figure 11. Bond angles of hydrogen bond interactions.

bonds (SSHBs).28 Other SSHBs present in our structures include hb4 in Figure 6 and hb1 in Figure 9. However, ∠OHO in these bonds are 141.62° and 136.24°, respectively. The Bader charge analysis shows that the reason for a strong interaction in these hydrogen bonds is that the negative charges in O atoms involved in these hydrogen bonds are relatively on the higher side of the spectrum. It is worth mentioning that the two points in Figure 11, which are lying considerably below the linear fit, correspond to these two hydrogen bonds. Although there are some exceptions, like the strong hydrogen bonds and the proton transfer discussed in the next section, it seems that most of the hydrogen bonds are dominantly electrostatic with little covalent contribution. This can be seen in the additivity of the energy contributions of the first three water molecules, and Bader charges and bond lengths that show small to modest changes upon water addition. Intramolecular Proton Transfer in Hexahydrates. Another significant observation in the structures of MgSO4·6H2O shown in Figure 8 and Figure 9 is the protontransfer process from W5 to one of the O atoms in SO4 tetrahedra. Proton-transfer reactions in hydrogen-bonded systems are widely studied in the literature.19,29 In most cases, proton-transfer reactions are associated with systems that possess low barrier hydrogen bonds (LBHBs).26,30 LBHBs even cause quantum tunneling effects in such systems, and studies suggest that the rate of proton transfer is directly related to the barrier height.31 Grabowski et al.19 have shown that the protontransfer reaction is caused by the change in proton affinity values, pKa, between the hydrogen-bond donor and the hydrogen-bond acceptor. From a purely molecular structural perspective, it can be deduced that this proton transfer occurs subsequently after one of the two Mg−(SO4) bonds breaks as the degree of hydration increases. This enables us to connect this proton-transfer process with the relative increase in proton affinity of SO4 tetrahedra in MgSO4·6H2O structures. Although this type of proton transfer is not observed in experimental investigations of MgSO4 crystals, the implication of such a rearrangement might be significant in the process of hydration of MgSO4 crystals, which needs to be investigated further.

Figure 10. Bond lengths of hydrogen bond interactions. The hydrogen bond parameters seem to obey the bond valence model, which is shown as the continuous curve.

in our systems. Table 2 also gives an extensive list of the parameters of these hydrogen bonds. The data points in Figure 10 are in agreement with the valency conservation rule (eq 1) in the bond valence (BV) model,19 suggesting the idea that the hydrogen bond interaction in the O−H···O system can be generalized using this model.18 ⎛ r − rO−H ⎞ ⎛ r1 − rH···O ⎞ ⎟ + exp⎜ ⎟ = 1 exp⎜ 1 ⎝ ⎠ ⎝ ⎠ c c

(1)

The bond valence method conserves the valency (sum of bond numbers) of the H atom by adjusting the bond numbers of both the O−H bond as well as the O···H bond18 in the hydrogen bonds. The parameters in eq 1 (r1 = 0.957 Å and c = 0.379428 Å) are in accordance with the study of Dunitz.27 Thus, in most cases, the O−H bond length increases as the H···O bond length decreases and vice versa for each hydrogen bond, as the degree of hydration changes. Figure 11 shows the O−H···O bond angle as a function of H···O distance. The figure shows a linear trend between the O−H···O angle and the H···O distance. Hydrogen bond lengths in our systems vary from 1.37 to 2.04 Å (Figure 10). The strength of the hydrogen bonds can be directly related to the closeness of the hydrogen-bond donor to the acceptor atom. Short hydrogen bonds are seemingly probable when the acceptor O atom has just one other bond associated with it (hb2 in Figure 5, hb2 in Figure 6, hb3 in Figure 7, hb6 in Figure 8, and hb2 and hb4 in Figure 9). These hydrogen bonds can be regarded as strong, given the fact that ∠OHO in all of these bonds are above 160°, due to the complete availability of the lone pairs in the O for the antibonding O−H orbital overlap.20 The O−O distances in the above-listed hydrogen bonds are close to the limit of 2.5 Å, and for this reason, they can be considered as short strong hydrogen

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CONCLUSION To analyze the structure and chemical interactions involved, a density functional theory study has been conducted in various hydrates of MgSO4 molecules. The presence of an extensive network of hydrogen bonds in the molecules has been identified in the study. The study confirms the formation of multiple isomers for hexahydrates with varying numbers of hydrogen bonds and numbers of coordination bonds. Among the two isomers, the lowest-energy isomer appears to be stabilized by the formation of six hydrogen bonds and a low 18589



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(18) Grabowski, S. J. J. Mol. Struct. 2000, 552, 153−157. (19) Sobczyk, L.; Grabowski, S. J.; Krygowski, T. M. J. Chem. Rev. 2005, 105, 3513−3560. (20) Fuster, F.; Grabowski, S. J. J. Phys. Chem. A 2011, 115, 10078− 10086. (21) Bader, R. Atoms in Molecules: A Quantum Theory; Oxford University Press: NewYork, 1990. (22) Henkelman, G.; Arnaldsson, A.; Jónsson, H. Comput. Mater. Sci. 2006, 36, 354−360. (23) Grabowski, S. J. Chem. Rev. 2011, 111, 2597−2625. (24) Chen, Y.; Dennenberg, J. J. J. Comput. Chem. 2011, 32, 2890− 2895. (25) Jeffrey, G. A. An Introduction to Hydrogen Bonding; Oxford University Press: Oxford, U.K., 1997. (26) Grabowski, S. J.; Ugalde, J. M. Chem. Phys. Lett. 2010, 493, 37− 44. (27) Dunitz, J. D. X-ray Analysis and the Structure of Organic Molecules; Cornell University Press: Ithaca, NY, 1979. (28) Remer, L. C.; Jensen, J. H. J. Phys. Chem. A 2000, 104, 9266− 9275. (29) Grabowski, S. J.; Krygowski, T. M. Chem. Phys. Lett. 1999, 305, 247−250. (30) Cleland, W. W.; Frey, P. A.; Gerlt, J. A. J. Biol. Chem. 1998, 273, 25529−25532. (31) Schuster, P.; Zundel, G.; Sandorfy, C. The Hydrogen Bond: Revent Development in Theory and Experiments; North-Holland Publishing Company: Amsterdam, 1976; Vol. 1.

coordination number (four) against the expected octahedral coordination. This could result in the formation of metastable states and sluggish kinetics, as reported in the literature for magnesium sulfate hydrates.3 The presence of hydrogen bonds significantly influences the structures of the hydrates. The presence of strong hydrogen bonds is also identified in the molecules. One of the observations is the proton-transfer process that occurs in hexahydrated structures. This gives significant insights into the possibilities of the breaking or formation of covalent bonds during hydration or dehydration processes in these crystals, although most hydrogen bonds show very little covalency. The present study is only limited to magnesium sulfate molecules representative of the gas phase. Thus, it may not give a complete picture into the dynamics of the hydration and dehydration process. However, it provides a clear understanding about the various chemical interactions that will play a role in the process of hydration and dehydration. More detailed information on the crystalline structures requires further investigations involving periodic lattices of various hydrates of magnesium sulfates.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We would like to acknowledge the European Graduate School on Sustainable Energy (DTU,TU/E,TUM) for providing us with the necessary funding for this project.

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REFERENCES

(1) N’Tsoukpoe, K. E.; Liu, H.; Pierrés, N. L.; Luo, L. Renewable Sustainable Energy Rev. 2009, 13, 2385−2396. (2) van Essen, V.; Zondag, H.; Gores, J. C.; Bleijendaal, L.; Bakker, M.; Schuitema, R.; van Helden, W.; He, Z.; Rindt, C. C. M. J. Sol. Energy Eng. 2009, 131, 041014. (3) Chipera, S. J.; Vaniman, D. T. Geochim. Cosmochim. Acta 2006, 71, 241−250. (4) Ferraris, G.; Jones, D. W.; Yerkess, J. J. Chem. Soc., Dalton Trans. 1973, 816−821. (5) Aleksovska, S.; Petrusevski, V. M.; Soptrajanov, B. Acta Crystallogr., Sect. B 1998, B54, 564−567. (6) Fortes, A. D.; Wood, I. G.; Vočadlo, L. V.; Brand, H. E. A.; Knight, K. S. J. Appl. Crystallogr. 2007, 40, 761−770. (7) Rentzeperis, P. J.; Soldatos, C. T. Acta Crystallogr. 1958, 11, 686. (8) Baur, W. H. Acta Crystallogr. 1964, 17, 863. (9) Batsanov, A. S. Acta Crystallogr., Sect. C 2000, 56, e230−e231. (10) Zalkin, A.; Ruben, H.; Templeton, H. D. Acta Crystallogr. 1964, 17, 235−240. (11) Chaban, G. M.; Huo, W. M.; Lee, T. J. J. Chem. Phys. 2002, 117, 2532. (12) Pye, C. C.; Rudolph, W. W. J. Phys. Chem. A 1998, 102, 9933− 9943. (13) Vinogradov, E. V.; Smirnov, P. R.; Trostin, V. N. Russ. Chem. Bull., Int. Ed. 2003, 52, 1253−1271. (14) Pavlov, M.; Siegbahn, P. E. M.; Sandström, M. J. Phys. Chem. A 1998, 102, 219−228. (15) Sugimoto, K.; Dinnebier, R. E.; Hanson, J. C. Acta. Crystallogr., Sect. B 2007, 63, 235−242. (16) Ireta, J.; Neugebauer, J.; Scheffler, M. J. Phys. Chem. A 2004, 108, 5692−5698. (17) Marcus, Y. Chem. Rev. 1988, 88, 1475−1498. 18590


DFT Study on Characterization of Hydrogen Bonds in the Hydrates of

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