A DFT-based comparative equilibrium study of thermal dehydration and hydrolysis of CaCl2 hydrates and MgCl2 hydrates for seasonal heat storage

Salt hydrates store solar energy in chemical form via a reversible dehydration–hydration reaction. However, as a side reaction to dehydration, hydrolysis (HCl formation) may occur in chloride based salt hydrates (specially in MgCl 2 hydrates), affecting the durability of the storage system. The mixture of CaCl 2 and MgCl 2 hydrates has been shown experimentally to have exceptional cycle stability and improved kinetics. However, the optimal operating conditions for the mixture are unknown. To understand the appropriate balance between dehydration and hydrolysis kinetics in the mixtures, it is essential to gain in-depth insight into the mixture components. We present a GGA-DFT level study to investigate the various gaseous structures of CaCl 2 hydrates and to understand the relative stability of their conformers. The hydration strength and relative stability of conformers are dominated by electrostatic interactions. A wide network of intramolecular homonuclear and heteronuclear hydrogen bonds is observed in CaCl 2 hydrates. Equilibrium product concentrations are obtained during dehydration and hydrolysis reactions under various temperature and pressure conditions. The trend of the dehydration curve with temperature in CaCl 2 hydrates is similar to the experiments. Comparing these results to those of MgCl 2 hydrates, we find that CaCl 2 hydrates are more resistant towards hydrolysis in the temperature range of 273–800 K. Specifically, the present study reveals that the onset temperatures of HCl formation, a crucial design parameter for MgCl 2 hydrates, are lower than for CaCl 2 hydrates except for the mono-hydrate.


Introduction
Solar thermal energy can be stored in three forms: sensible heat, latent heat, and in thermochemical form.In a thermochemical storage system, energy is stored by bond breaking and reformation in a reversible reaction. 1Compared to sensible or latent heat, the energy storage density is higher in thermochemical form. 2 This explains the enormous interest in thermochemical materials (TCMs) for seasonal heat storage applications. 3TCMs offer compact solar energy storage suitable for household applications.TCMs are widely available and inexpensive, and therefore appear to be an attractive material for seasonal heat storage.The cost of TCM is 30% of the total investment in the thermochemical heat storage system. 3Thus, the selection of TCMs is a key aspect in designing the heat storage system.
Salt hydrates are one class of TCMs.Upon charging, these materials absorb solar energy and disintegrate into a lower hydrated or anhydrous form.Upon discharging, these dried salt hydrates recombine with H 2 O, forming hydrates while dissipating energy.
The forward reaction is endothermic while the backward reaction is exothermic.The major challenge in selection of these salt hydrates is to find materials with high storage capacity, cycle stability and fast kinetics.MgSO 4 hydrates have a high storage capacity (2-3 GJ m À3 ).However, MgSO 4 hydrates have sluggish hydration kinetics due to the presence of strong hydrogen bonds (H-bonds). 4hloride based salt hydrates (MgCl 2 ÁnH 2 O, CaCl 2 ÁnH 2 O, n = 0, 1, 2, 4, and 6) are also promising TCMs for seasonal heat storage.They have high storage capacity (2-3 GJ m À3 ).However, hydrolysis is reported for chloride based salt hydrates.This is an irreversible endothermic reaction which competes with dehydration reaction, according to MgCl 2 hydrates have faster kinetics but also have the problem of hydrolysis as a side reaction. 5Hydrolysis affects the cycle stability of the storage system and generates HCl gas, which is harmful and corrosive.This poses a challenge for the application of MgCl 2 hydrate as a TCM.
Hydrolysis can be avoided in TCMs by mixing with other halides. 6Rammelberg et al. 7 examined the performance of various salt mixtures.They observed that the mixture of CaCl 2 hydrates and MgCl 2 hydrates shows good cycle stability and improved kinetics compared to MgCl 2 and CaCl 2 hydrates alone.They have not described the chemical explanation for this extra stability.To assess the performance of the mixture of CaCl 2 hydrates and MgCl 2 hydrates, it is essential to investigate the dehydration and hydrolysis behavior of CaCl 2 hydrates and compare these to MgCl 2 hydrates.
][10][11] It has a very high crystalline energy storage density (2.82 GJ m À3 ), is readily available, inflammable and has high temperature lift during hydration. 3,8,12CaCl 2 hydrates are also used in mobile storage of industrial waste. 13In domestic heat storage systems, TCMs are used in the temperature range of 300-500 K while in mobile storage of industrial heat, a much higher temperature range is used.Thus, it is important to investigate the equilibrium products of dehydration and hydrolysis reactions of CaCl 2 hydrates over a wide temperature range.Next to the kinetics of dehydration/hydrolysis, the onset temperature of HCl formation in chloride based salt hydrates is a crucial parameter in designing heat storage systems.
Rammelberg et al. 10 and Zondag et al. 9 examined the kinetics of dehydration of CaCl 2 hydrates using Thermogravimetric analysis (TGA) and did not observe hydrolysis.Fraissler et al. 14 observed that the formation of HCl gas from the hydrolysis of CaCl 2 occurs in a certain temperature range (683-1013 K).In these temperature regimes the preference of hydrolysis over dehydration reaction is ambiguous from experiments.
6][17][18] The hydration of Ca 2+ ions has been successfully investigated using Density Functional Theory (DFT), 19,20 molecular dynamics simulations 18,21 and validated by experiments. 22,23Iype et al. 4 characterized the H-bonds present in MgSO 4 hydrates using DFT calculations.They observed that strong H-bonds affect the hydration kinetics of MgSO 4 hydrates.Smeets et al. 15 computationally investigated the dehydration and hydrolysis reactions for MgCl 2 hydrates.They have reported the equilibrium curves for dehydration/hydrolysis of MgCl 2 hydrates.We have explored the relative stability of various conformers of CaCl 2 hydrates, ideal operating conditions of CaCl 2 hydrates and compared them with MgCl 2 hydrates. 15Nevertheless, to the best of our knowledge, currently no computational studies exist on the hydrolysis reaction of CaCl 2 hydrates, the onset temperature of HCl formation and their comparison with MgCl 2 hydrates.The system level complexity of salt hydrate mixtures like grain boundaries, grain sizes and their effect on the reaction kinetics could be addressed by multiscale integration of DFT results to the system level. 24n the present study, we would like to understand by means of DFT calculations, the temperature and pressure conditions under which hydrolysis precedes over dehydration.First we examine the molecular structure and vibrational frequencies of CaCl 2 hydrates and their conformers.We investigate the strength of H-bonds present in CaCl 2 hydrates, since strong H-bonds can result in sluggish hydration kinetics.We characterize the H-bonds using the Bond Valence (BV) sum rule.The BV sum rule is frequently used to correlate the structural properties of H-bonds and crystal structure determination. 4,25,26he enthalpy of the dehydration and hydrolysis reactions of CaCl 2 hydrates is obtained from DFT calculations and compared to MgCl 2 hydrates.The change in Gibbs free energy for dehydration and hydrolysis of all hydrates is obtained, followed by the equilibrium product concentration.The equilibrium properties obtained from the present DFT calculations can be used to calculate safety limits for thermal degradation of CaCl 2 hydrates.These safety limits are compared with MgCl 2 hydrates.

Density functional theory calculations
The molecular structures of various CaCl 2 hydrates, their conformers, HCl, H 2 O, and CaOHCl are fully optimized in DFT using the Perdew-Wang exchange and correlation functional (PW91) under generalized gradient approximation (GGA) 27 implemented in the Amsterdam Density Functional (ADF) program 28 with the double-polarized triple-z basis set.A spin restricted Kohn-Sham method is used thus keeping the maximum integration accuracy.6][17] Iype et al. 4 showed the applicability of GGA-DFT to study the H-bonds present in hydrates of MgSO 4 .

Model validation
To validate the applicability of GGA-DFT using the PW91 functional, we have examined the binding enthalpy, Ca-O coordination length and vibrational frequency of [Ca(H 2 O) 6 ] 2+ ions.The successive binding enthalpy of hexahydrated Ca 2+ ions DH 6;5 is defined as The optimized structure of [Ca(H 2 O) 6 ] 2+ is shown in Fig. 1.We estimated the successive binding enthalpy of [Ca(H 2 O) 6 ] 2+ ions from GGA-DFT to be 26.26kcal mol À1 , which is in close agreement with previous DFT calculations (26.37 kcal mol À1 ) 20 and experimental results (25.3 kcal mol À1 ). 22n the present DFT study, the average coordination length of Ca-O in the first hydration shell of Ca 2+ is 2.39 Å, which is in excellent agreement with past DFT results (2.37 Å), 19 high order Car-Parrinello molecular dynamics results (2.41 Å) 21 and experimental results (2.39 Å, XRD). 29

Methodology
The harmonic frequencies of each optimized geometry are calculated to quantify the vibrational contribution of energy and entropy.The information of vibrational spectra, ground state geometry and Gibbs free energy (G) of all reactants and products are essential to calculate DG of dehydration and hydrolysis reaction. 30In the present study, we are interested in the following dehydration and hydrolysis reactions of CaCl 2 hydrates: The change in the Gibbs free energy of above reactions is expressed as The equilibrium product concentration of dehydration and hydrolysis reactions can be obtained by equating DG to zero.For the DG calculation, the physical state of each reactant and product is important.Experimentally, CaCl 2 hydrates remain in the solid phase, and H 2 O and HCl exist in the gaseous phase.However, the precise frequency calculation, subsequently the Gibbs free energy of solid CaCl 2 hydrates over a wide temperature range, is computationally challenging.2][33][34][35] Due to the large size of Ca and Cl atoms and a large number of atoms in unit cell, the Gibbs free energy calculation of the crystalline phase is expensive.Weck et al. 36 obtained the Gibbs free energy of solid MgCl 2 hydrates under quasi-harmonic approximation (QHA) from GGA-DFT calculations.The Gibbs free energy of the crystalline phase obtained from QHA may breakdown at higher temperature.Despite the fact that these calculations were done for another solid salt hydrates (MgCl 2 ÁnH 2 O), it should also be valid for CaCl 2 ÁnH 2 O. Nevertheless, the solid reactant and product do not always remain in the crystalline phase and hydrolysis is expected to occur in the liquid phase. 15Thus for a solid-gas reaction, DG can be estimated by Gibbs free energy of the gaseous phase (G gas ).The equilibrium product concentration obtained under gas assumption will be considered as the safety limit of these reactions in seasonal heat storage systems.
In this paper, the DG in dehydration and hydrolysis reactions is computed under ideal poly-atomic gas assumption 30 assuming each reactant and product to be in the gaseous state.Gibbs free energy of a gaseous molecule at given temperature T and absolute pressure p can be given as The partition function of an ideal poly-atomic gas can be expressed as 30 q = q trans q rot q vib q elec (9)   where q is the partition function and q trans , q rot , q vib , and q elec are their translational, rotational, and electronic contributions.
Internal energy U of poly-atomic gas can be expressed as where R is the gas constant, Y vib,j is vibrational temperature (hn/k b ) of the jth atom, n is the frequency of the vibrational mode, h is Planck's constant, k b is the Boltzmann constant and U gr is the ground state energy of the molecule.The entropy (S) of poly-atomic gas can be expressed as  where M is the total atomic mass and S rot is the rotational contribution of entropy and can be expressed for the asymmetrical top molecule as 30 where I a , I b , and I c are three principle moments of inertia and s is the symmetry number of the molecule, which is the number of rotational modes of the molecule.From the optimized geometry of the molecule, we have obtained the U gr , principle moment of inertia and frequency of its vibrational mode.Eqn ( 7) and ( 8) are used to calculate DG of a particular dehydration or hydrolysis reaction at given T and p.
The H-bonds of CaC 2 hydrates are analyzed in the gaseous phase.This is a valid analysis as the locus of H-bond parameters can be generalized irrespective of the system being in a condensed phase or the gaseous phase. 4The presence of H-bonds is identified by the non-bonded XÁ Á ÁH (X = Cl and O) distance.When the non-bonded distance between O and H varies from 1.5 Å to 2.0 Å, we classify these H-bonds as OHO homonuclear type H-bonds, which is consistent with Iype et al. 4 Similarly, when the non-bonded distance between Cl and H varies from 1.9 Å to 2.5 Å, we classify these H-bonds as a OHCl heteronuclear type H-bond.Bader charges on various atoms in the molecule are calculated to understand the charge distribution.We compared the charge distribution in all hydrates to observe charge transfer, the effect of Coulombic interactions on their stability and enthalpy of dehydration.

Results and discussions
The gaseous structures of CaCl 2 hydrates are investigated to understand the H-bond network, relative stability of conformers and enthalpy change in the hydrolysis and dehydration reactions.The optimized structures are used to obtain vibrational frequencies, and their entropic and energy contribution from DFT calculations.In this section, we present the optimized structures of CaCl 2 hydrates and their conformers.3e.The planar symmetric structure does not form a H-bond between H and Cl atoms while its conformer (non-planar) does.The intramolecular H-bonds provide extra stability of 4.78 kcal mol À1 to the non-planar structure (Fig. 3d) over the planar structure (Fig. 3e) and are responsible for the loss in symmetry of the non-planar molecule.The Bader charge on Cl differs by 0.04 in planar and non-planar structures due to the presence of a H-bond.The average Ca-O coordination length is the same (2.36Å) in both of these structures, which is in good agreement with the Ca-O coordination length (2.32 Å) in the experimental crystalline structures. 31[33][34] We have chosen the initial structure of CaCl 2 Á4H 2 O from these three crystalline phases and observed three stable structures shown in Fig. 4a-c.The optimized structure (ground state energy (U gr ) = À1628.66kcal mol À1 ) obtained from an a phase crystal has a slightly distorted octahedral geometry with four H-bonds.The average Ca-O coordination length is 2.42 Å, in good agreement with the a phase crystalline structure (2.42 Å). 32 The average Ca-Cl coordination length is 2.67 Å, in agreement with the a phase crystalline structure (2.8 Å). 32 The Bader charge on the Ca atom of the tetrahydrate (Fig. 4a) is 0.027 more positive than the Bader charge on the Ca atom of the dihydrate (Fig. 3d).
CaCl 2 Á4H 2 O also exists in the b polymorph phase. 33The initial molecular structure is chosen close to the b phase structure.The optimized structure is shown in Fig. 4b.The optimized geometry is a distorted octahedral with 1.62 kcal mol À1 more stable than the a phase optimized geometry (Fig. 4a).The average Ca-O coordination length in the b phase optimized gaseous tetrahydrate is 2.405 Å, which is in agreement with the experimental b phase crystalline structure (2.46 Å). 33 Similarly, the average Ca-Cl coordination of the gaseous phase tetrahydrate is 2.68 Å, which is in close agreement with the b phase crystalline structure (2.74 Å). 33 There are two relatively strong H-bonds (OHCl) observed in the b phase optimized geometry compared to the a phase optimized geometry.There are intermolecular H-bonds (OHCl type) present in the b phase of the experimental crystalline structures, 33 while intramolecular H-bonds are observed in the gaseous molecule.This is the reason for the slight discrepancy in the structure of a gaseous molecule and the b phase crystalline structure.
CaCl 2 Á4H 2 O also occurs in the g phase. 34The initial molecular structure is chosen close to the g phase structure.The optimized structure is symmetrical and has almost a planar structure as shown in Fig. 4c.This structure is 19.24 kcal mol À1 less stable than the b phase optimized geometry.The average Ca-O coordination length is 2.26 Å in the g phase optimized structure, which is in agreement with the g phase crystalline structures (2.33 Å). 34 The two H atoms of surrounded the average Ca-Cl coordination length is 2.72 Å.This optimized hexahydrate molecule (Fig. 5a) has four OHCl H-bonds (heteronuclear type) and three OHO H-bonds (homonuclear type).The average intramolecular H-bond length (2.19 Å) is in close agreement with the average intermolecular H-bond length (2.27 Å) present in the experimental g phase crystalline structures. 35aCl 2 Á6H 2 O exists experimentally in the g phase. 35There are OHCl type intermolecular H-bonds present in the g phase crystalline structures. 35Those H-bonds are between the H of the H 2 O of the hexahydrate and the Cl of the neighboring molecule of the hexahydrate in the crystal.The initial molecular structure is chosen close to the g phase crystalline structure.In the optimized structure, the H 2 O forms an octahedral with the Ca as shown in Fig. 5b.The optimized structure (Fig. 5b) forms six H-bonds (2.00 Å) of OHCl type.The average Ca-O coordination length of g phase optimized CaCl 2 Á6H 2 O is 2.37 Å.The average Ca-Cl coordination length is 3.84 Å.There is a discrepancy of 26.6% in the Ca-Cl coordination length of the gaseous hexahydrate and the g phase crystalline hexahydrate.There are intramolecular H-bonds present in the gaseous g phase of hexahydrate (Fig. 5b) while intermolecular H-bonds in the g phase crystalline structures, 35 which explains the discrepancy.
The second stable conformer of the optimized CaCl 2 Á6H 2 O is shown in Fig. 5c.This conformer is 4.12 kcal mol À1 less stable than the first conformer (Fig. 5a) and 4.41 kcal mol À1 less stable than the g phase optimized structure (Fig. 5b).The average Ca-O coordination length is 2.45 Å.There are five intramolecular OHCl H-bonds (heteronuclear type) and one OHO type H-bond present in this conformer (Fig. 5c).Three H 2 O molecules are forming H-bonds (OHCl type) with one Cl, one H 2 O forms a H-bond (OHO type) with one of these H 2 O molecules and two H 2 O molecules form H-bonds with the other Cl atom.The average HÁ Á ÁCl H-bond length is 2.05 Å in the second stable conformer (Fig. 5c) while in the more stable g phase optimized structure (Fig. 5b) it is 2.00 Å and 2.19 Å in the first conformer (Fig. 5a).The average OÁ Á ÁH H-bond length is 1.88 Å in the second conformer (Fig. 5c) and in the first conformer, it is 1.83 Å.The OÁ Á ÁH H-bonds are stronger in the first conformer, which explains the extra stability of the first conformer over the second conformer.The detailed explanation of H-bonds will be discussed in the section ''Hydrogen bond in CaCl 2 hydrate system''.
No conformer for MgCl 2 Á4H 2 O and MgCl 2 Á6H 2 O has been reported from DFT calculations. 15To rationally compare the structure of CaCl 2 hydrates with MgCl 2 hydrates, the average Bader charge on each atom is compared in

Reaction enthalpies of CaCl 2 hydrates
For reaction enthalpy calculations, we have considered the structure having minimum energy and no imaginary frequency.Table 2 describes the electronic ground state energy and various energy terms for all the studied hydrates.The binding energy (DE Binding ) of a hydrate is defined as The enthalpy change during the dehydration reaction (DE Dehydration ) is defined as Similarly, the enthalpy change during the hydrolysis reaction (DE Hydrolysis ) is defined as The H 2 O and HCl molecules are separately optimized using GGA-PW91 and TZ2P basis sets.The binding energy of CaCl 2 hydrates and their conformers depends on the Ca-Cl, Ca-O distance and on the strength of the intramolecular H-bond formed.The binding energy is the energy released on hydration per mole of salt, whereas the dehydration enthalpy is per mole of H 2 O.For the monohydrate, the binding energy is the same as the enthalpy change in dehydration, but opposite in sign, and it is equal to À21.9 kcal mol  2) thus, CaCl 2 hydrates are more resistant to hydrolysis reaction.

Hydrogen bond in the CaCl 2 hydrate system
CaCl 2 hydrates have the OHCl type heteronuclear H-bond and the OHO type homonuclear H-bond.The strong H-bond has a predominant covalent character while the moderate H-bond has mostly electrostatic character. 38The H-bond energy is a strong function of r X-H , r XÁ Á ÁH , and r X-Y in XHX and XHY H-bonded systems. 39The Cl atom is larger in size compared to O and less electronegative thus the availability of the lone pair for H-bond formation is lower compared to the O. Thus the OHO type H-bond is stronger than the OHCl type H-bond. 39n the present study, we observe the OHO type homonuclear H-bond in CaCl 2 Á6H 2 O isomers (Fig. 5a and c).The strength of H-bonds depends on the distance between the donor H and the acceptor O distance (H-bond distance) and the +O-HÁ Á ÁO (H-bond angle).The +O-HÁ Á ÁO above 1651 provides the complete lone pair availability in the O for the anti-bonding O-H orbital overlap 4,40 therefore stabilizing the H-bond.The non-bonded OÁ Á ÁH distance varies from 1.64 Å to 1.95 Å and +O-HÁ Á ÁO 135.921 to 165.481.The lengthening of the O-H bond varies from 0.017 Å to 0.041 Å.These OHO type H-bonds are moderate in strength and predominantly electrostatic in nature. 38In the first A similar bond length of H-bonds is observed in organic and organometallic crystals. 41Tommaso et al. also observed the OHCl type H-bond in the hydration of Ca 2+ ions in salt solution. 18The bond valence is proportional to the electron density.The bond valence of the atom is distributed between the bonds which it forms.Each bond involves the same number of electrons.The BV sum rule is described as In heteronuclear H-bonds, the BV sum rule (eqn ( 17)) has four parameters (two of O-H and two of HÁ Á ÁCl).From Fig. 6, it is evident that heteronuclear H-bonds follow the BV sum rule in close agreement (R 2 = 0.98).Therefore, the BV sum rule is applicable for this class of H-bonds.The bond parameters R respectively.This suggests that the formation of strong H-bonds in CaCl 2 Á4H 2 O could form metastable states and may result in sluggish hydration kinetics.

Equilibrium product concentrations
The DG of a system is a function of pressure, temperature, and the system characteristics.At chemical equilibrium, the DG (from eqn (7)) should be zero and this will provide information about the equilibrium concentration of products.
3.4.1 Dehydration reaction of CaCl 2 hydrates and their comparison with MgCl 2 hydrates.In the dehydration reaction, the higher hydrate absorbs energy and disintegrates into lower hydrates and H 2 O molecules.In the experimental dehydration set-up only the water vapor pressure ( p H 2 O ) and the HCl pressure ( p HCl ) are the controlled variables.The partial pressure (concentration) of hydrates is not important.In the present study, the partial pressure of water and system temperature are the control variables, while the partial pressure of hydrates is kept constant at 1 atm.The equilibrium water vapor pressure depends on the system temperature for all dehydration reactions of both hydrates (CaCl 2 and MgCl 2 ) as shown in Fig. 7.It is recognizable from Fig. 7 that dehydration from hexahydrate to tetrahydrate is easier (favored at lower temperature) than from tetra to dihydrate and from dihydrate to monohydrate for CaCl 2 and MgCl 2 hydrates.This trend of dehydration of various CaCl 2 hydrates is similar to the experimental results 9,10 and outlined as well by the enthalpy of dehydration in Table 2, where the enthalpy of dehydration increases from hexa to monohydrate.
In the present study, we observed 30% conversion of CaCl 2 Á6H 2 O to CaCl 2 Á4H 2 O only at around 340 K.There is an offset of 4 K is observed.The effect of temperature on the equilibrium dehydration curve of CaCl 2 Á6H 2 O (slope = 0.035) is in agreement with the experiments (slope = 0.032) 9,42 as shown in Fig. 7.An offset of 20 K is observed in the low vapor regime (o0.03 atm) for CaCl 2 Á6H 2 O.The offset may be a consequence of the ideal polyatomic gas phase assumption.Another reason could be that the equilibrium product concentrations obtained from DG (DFT calculations) reports the static equilibrium properties while the experimental (TGA/DSC)  Hydrolysis starts at higher temperature (4396 K) in comparison to dehydration for all the hydrates of CaCl 2 , which is consistent with the enthalpy change in hydrolysis (38.93 kcal mol À1 to 121.68 kcal mol À1 ) and dehydration (21.9 kcal mol À1 to 14.56 kcal mol À1 ) as given in Table 2.
The equilibrium vapor pressure of 1 atm is observed from CaCl 2 Á6H 2 O at 350.5 K and hydrolysis above the safety limit ( p HCl = 1 Â 10 À3 atm) starts at 396 K.There is no overlapping temperature region between hydrolysis and dehydration for CaCl 2 Á6H 2 O.The CaCl 2 Á4H 2 O dehydrates into CaCl 2 Á2H 2 O at 490.5 K ( p H 2 O = 1 atm) while hydrolysis starts (above safety limit, p HCl 4 1 Â 10 À3 atm) at 475.8 K.There is an overlap of around 14.7 K (from Fig. 7 and 8).Similarly the overlap for the CaCl 2 Á2H 2 O is around 32.5 K. Fraissler et al. 14 9.For any temperature (o761 K), MgCl 2 will always have high partial pressure of HCl ( p HCl ) compared to CaCl 2 hydrates.The slope of the equilibrium hydrolysis curve (Fig. 9) decreases from the hexahydrate to the monohydrate for both CaCl 2 and MgCl 2 hydrates.The slope of CaCl 2 is slightly lower than analogous MgCl 2 hydrates.Hence, the HCl concentration could be better controlled with temperature in CaCl 2 hydrates over MgCl 2 hydrates.
For a given change in partial pressure of HCl ( p HCl ), the temperature changes maximum for the monohydrate.The reason for the change in the slope of the hydrolysis curve can be explained by the stoichiometric ratio between HCl and H 2 O.The stoichiometric ratio of HCl to H 2 O increases from 0.2 to 1 for the hexahydrate to the monohydrate.Thus, the molar ratio between HCl and H 2 O decreases from mono to hexahydrate, therefore, temperature varies maximum for the monohydrate for a given change in p HCl .The similar trend of slope is observed for MgCl 2 hydrates.

Conclusions
To understand the equilibrium product concentrations of the dehydration and hydrolysis reactions of CaCl 2 ÁnH 2 O in comparison to MgCl 2 ÁnH 2 O, DFT calculations have been carried out.
The structural properties of CaCl 2 hydrates along with their atomic charges are analyzed.This study reveals the formation of many conformers due to the presence of various H-bonds.The relative stability of a conformer and dehydration enthalpy is dominated electrostatic attraction and strength of H-bond formed.We observed a homonuclear H-bond (OHO) and a heteronuclear H-bond (OHCl) in the various hydrates of CaCl 2 .Most of the H-bonds (B77%) in CaCl 2 hydrate are of moderate strength.CaCl 2 Á2H 2 O has two conformers due to the presence of an OHCl type H-bond.Similarly, three conformers of CaCl 2 Á4H 2 O, and CaCl 2 Á6H 2 O are observed.The most stable conformers are non-planar CaCl 2 Á2H 2 O (Fig. 3d), b phase optimized CaCl 2 Á4H 2 O (Fig. 4b), and g phase optimized CaCl 2 Á6H 2 O (Fig. 5b).These conformers are 4.78, 19.24, and 4.41 kcal mol À1 more stable than their lowest stable conformer.The relatively strong OHCl H-bonds provide 4.41 kcal mol À1 stability compared to its lowest stable conformer in CaCl 2 Á6H 2 O.The H-bonds in CaCl 2 Á4H 2 O destabilize the g phase optimized structure by 19.24 kcal mol À1 compared with the b phase optimized structure.This implies that CaCl 2 Á4H 2 O could form a metastable stage, and may have a sluggish hydration kinetics.Both CaCl 2 Á2H 2 O and CaCl 2 Á6H 2 O have less stable conformers, consequently they do not form metastable stages.Thus, the H-bonds should not markedly affect their hydration kinetics.The BV sum rule parameters for OHCl type H-bonds are 0.96 Å, 0.80 Å (for HÁ Á ÁCl pair) and 0.97 Å, 0.38 Å (for HÁ Á ÁO pair).These parameters can be used to characterize the OHCl H-bonded system.
The enthalpy change in the dehydration and hydrolysis reactions of CaCl 2 hydrates is obtained from DFT and compared with MgCl 2 hydrates.The equilibrium composition of dehydration and hydrolysis reactions is obtained by equating the DG to zero over a wide range of temperature and pressure conditions.The trend in the dehydration reaction is similar to the experiments for all the CaCl 2 hydrates.The effect of temperature on the dehydration of CaCl 2 Á6H 2 O (slope = 0.035) is in close agreement with experiments (slope = 0.032). 9,10We compared the equilibrium composition of dehydration and hydrolysis reactions for CaCl 2 and MgCl 2 hydrates.The CaCl 2 Á6H 2 O dehydrates at lower temperature (as shown in Fig. 7) compared with MgCl 2 Á6H 2 O while CaCl 2 Á4H 2 O and CaCl 2 Á2H 2 O dehydrates at higher temperature when compared to their analogous MgCl 2 hydrates.The CaCl 2 hydrates have better temperature control with the partial pressure of the products ( p HCl , p H 2 O ) when compared to the MgCl 2 hydrates.We investigated hydrolysis and dehydration at different temperature, pressure regimes for CaCl 2 and MgCl 2 hydrates.The CaCl 2 hydrates have better hydrolysis resistance over MgCl 2 hydrates in the temperature range 273 to 800 K, which explains the higher stability in the mixture of CaCl 2 and MgCl 2 hydrates.Hydrolysis is very rare for CaCl 2 Á6H 2 O because the onset of hydrolysis reaction at the safety limit ( p HCl = 1 Â 10 À3 atm) is higher than the dehydration temperature of CaCl   treated as the safety limit range for hydrolysis reactions.The CaCl 2 hydrates could be mixed with MgCl 2 hydrates to improve the hydrolysis resistance and therefore durability of the system.

Fig. 2
Fig. 2 The calculated IR spectra of the ground state structure of [Ca(H 2 O) 6 ] 2+ .The represents the IR peak position of [Ca(H 2 O) 6 ] 2+ ions, as reported by Lei and Pan.20

3. 1
Molecular structures of CaCl 2 hydrates and their conformers 3.1.1Anhydrous CaCl 2 , CaOHCl, and CaCl 2 ÁH 2 O.The gaseous anhydrous CaCl 2 molecule is optimized with many initial configurations and all converged into the final CaCl 2 structure as shown in Fig. 3a.The structure of CaCl 2 is linear with the Ca-Cl bond length being 2.45 Å.The structural properties of CaCl 2 are in agreement with the experimental crystalline structures of CaCl 2 . 37The optimized structure of CaOHCl is shown in Fig. 3b.CaOHCl is a non-linear molecule with Ca-Cl and Ca-O bond lengths of 2.49 Å and 1.99 Å.The optimized structure of CaCl 2 ÁH 2 O is shown in Fig. 3c.The Ca-O coordination length is 2.33 Å.The hydrated H 2 O forms a H-bond with one of the Cl atoms of CaCl 2 and stretched the Ca-Cl distance by 0.08 Å.The Bader charge of a Cl atom participating in H-bonding differs by 0.02 to that of a Cl atom not participating.
0 and b for HÁ Á ÁCl are 0.96 Å, 0.80 Å and for the H-O pair 0.97 Å, 0.38 Å, which is in agreement with the literature. 4,25The strength of the H-bond is inversely related to the HÁ Á ÁCl distance.The nonbonded HÁ Á ÁCl distance depends on +O-HÁ Á ÁCl, which varies from 166.91 to 1231 in CaCl 2 hydrates.The larger +O-HÁ Á ÁCl (41651) facilitates anti-bonding ClÁ Á ÁH orbital overlap and favors hydrogen bonding.Most of these (B77%) OHCl type H-bonds are moderate and weak in strength and are dominated by electrostatic interactions and dispersion. 38In CaCl 2 Á4H 2 O, the H-bonds destabilize the structure by 19.24 kcal mol À1 while stabilize the CaCl 2 Á6H 2 O and CaCl 2 Á2H 2 O by 4.41 kcal mol À1 and 4.78 kcal mol À1

Fig. 6
Fig. 6 Correlation of HÁ Á ÁCl bond length (non-bonded interaction) with OH bond length of surrounding H 2 O in all the hydrates of CaCl 2 .The nonbonded ClÁ Á ÁH distance versus OH bond length obeys the BV sum rule, which is shown as a continuous curve.

Fig. 7
Fig.7Equilibrium vapor pressure for the dehydration reactions of CaCl 2 hydrates (green) at various temperatures and constant partial pressure of hydrate, p 0 = 1 atm.The dashed red lines represent the dehydration curves of MgCl 2 hydrates.15The inset graph shows the comparison of enthalpy change during the dehydration reactions of CaCl 2 and MgCl 2 hydrates.

Fig. 8
Fig.8Equilibrium vapor pressure for the hydrolysis reactions of CaCl 2 hydrates (green) at various temperatures and fixed HCl pressure p HCl = 1 Â 10 À3 atm and p 0 = 1 atm.The dashed red lines represent the hydrolysis curves of MgCl 2 hydrates.15The inset graph shows the comparison of enthalpy change during the hydrolysis reactions of CaCl 2 and MgCl 2 hydrates.

Fig. 9
Fig. 9 Equilibrium vapor pressure for the hydrolysis reactions of CaCl 2 hydrates (green) at various temperatures and fixed H 2 O pressure p H 2 O = 4 Â 10 À3 atm and p 0 = 1 atm.The dashed red lines represent the hydrolysis curves of MgCl 2 hydrates. 15The inset graph shows the comparison of enthalpy change during the hydrolysis reactions of CaCl 2 and MgCl 2 hydrates.

Fig. 10
Fig. 10 Equilibrium water vapor pressure for hydrolysis and dehydration reactions at different temperatures.p HCl is varied from 10 À7 to 10 À2 atm and p 0 = 1 atm.
Furthermore, we have calculated the vibrational frequencies of [Ca(H 2 O) 6 ] 2+ .The IR peak position obtained from present calculations are in close agreement with Lei and Pan 20 as shown in Fig. 2. Published on 10 March 2016.Downloaded by Eindhoven University of Technology on 23/05/2016 10:58:14.

Table 1 .
The Bader charges on Ca and Cl atoms of CaCl 2 are lower in magnitude when compared with Mg and Cl in their analogous MgCl 2 hydrates.The Bader charge on Ca and Mg atoms increases monotonically with the hydration number.The magnitude of the Bader atomic charge on Cl in CaCl 2 hydrates decreases with hydration number whereas it increases from MgCl 2 to MgCl 2 Á2H 2 O and decreases till MgCl 2 Á6H 2 O.The magnitude of average Bader atomic charges on O and H in CaCl 2 hydrates is lower than MgCl 2 hydrates.The Ca-Cl, Ca-O distance in CaCl 2 hydrates is higher than MgCl 2 hydrates.Thus, electrostatic attractions Á6H 2 O is easier than the removal of the two H 2 O molecules from CaCl 2 Á4H 2 O and so on.The enthalpy change in the hydrolysis reaction is very high for CaCl 2 Á6H 2 O compared to the enthalpy change in dehydration as given in Table 2.The enthalpy change in hydrolysis decreases from higher hydrates to lower hydrates.The enthalpy change during the dehydration and hydrolysis reaction of CaCl 2 hydrates is compared with MgCl 2 hydrates, as shown in Table 2.The dehydration enthalpy of CaCl 2 Á6H 2 O, CaCl 2 Á4H 2 O, and CaCl 2 ÁH 2 O is slightly lower than analogous MgCl 2 hydrates.The dehydration enthalpy for CaCl 2 Á2H 2 O is 26.8% higher than MgCl 2 Á2H 2 O, thus CaCl 2 Á2H 2 O dehydrates at higher temperature compared with MgCl 2 Á2H 2 O.The CaCl 2 hydrates (except mono hydrate) have high enthalpy of hydrolysis compared to MgCl 2 hydrates (as given in Table

Table 1
15mparison of the Bader charge on various hydrates of CaCl 2 and MgCl 215(only the lowest energy conformers are considered).An average charge is reported for many atoms of the same element in a molecule

Table 2
15ergy of various hydrates and enthalpy change in dehydration and hydrolysis reactions (only the lowest energy conformers are considered).The parentheses value refers to analogous MgCl 2 hydrates15This journal is © the Owner Societies 2016 conformer of CaCl 2 Á6H 2 O (Fig.5a), three H-bonds of this type are present while in the second conformer of CaCl 2 Á6H 2 O (Fig.5c) only one H-bond is present.The first conformer of CaCl 2 Á6H 2 O has one relatively strong but moderate strength H-bond (1.64 Å) thus provides 4.12 kcal mol À1 stability over the second conformer.The CaCl 2 hydrates have mostly OHCl type heteronuclear H-bonds.The H atoms of the hydrated CaCl 2 ÁXH 2 O molecule are attracted by adjacent Cl atoms and form OHCl type H bonds.In the present case, the ClÁ Á ÁH distance varies from 1.82 Å to 2.48 Å and the Cl-O distance varies from 2.86 Å to 3.15 Å.The lengthening of the OH bond varies from 0.01 Å to 0.08 Å.
reported experimentally from TGA measurements that the HCl formation from thermal decomposition of CaCl 2 salt hydrates occurs in the temperature range of 683À1013 K.We observe the starting point ( p HCl = 1 Â 10 À3 atm, onset) of HCl formation for CaCl 2 Á2H 2 O and CaCl 2 ÁH 2 O at 660 K and 845 K ( p H 2 O = 1 Â 10 À3 atm) respectively.CaCl 2 Á4H 2 O and CaCl 2 Á6H 2 O will not be present in this temperature range.The offset in the onset of HCl formation temperature may be the consequence of the dynamic and static equilibrium comparison and the effect of the ideal polyatomic gas assumption.The hydrolysis of CaCl 2 ÁH 2 O is independent of the H 2 O vapor pressure as shown in Fig. 8. Hydrolysis of MgCl 2 hydrates starts at lower temperature in comparison to CaCl 2 hydrates for hexa, tetra, and dihydrates, which is consistent with the enthalpy change in hydrolysis of MgCl 2 and CaCl 2 hydrates as given in Table 2.The slope of the MgCl 2 hydrate hydrolysis curve is slightly higher compared to the CaCl 2 hydrates so the hydrolysis of CaCl 2 hydrates has a longer operating temperature range.Hydrolysis in MgCl 2 Á6H 2 O, MgCl 2 Á4H 2 O and MgCl 2 Á2H 2 O starts at 388, 446, and 616 K ( p H 2 O = 1 Â 10 À3 atm) respectively, which is lower than analogous CaCl 2 hydrates.Hydrolysis in CaCl 2 ÁH 2 O starts at lower temperature (845 K) than MgCl 2 ÁH 2 O (976 K).Thus, CaCl 2 hydrates have improved hydrolysis resistance if the operating temperature is less than 800 K. Furthermore, the partial pressure of HCl ( p HCl ) is plotted with their equilibrium temperature at fixed H 2 O vapor pressure ( p H 2 O = 4 Â 10 À3 atm) for MgCl 2 and CaCl 2 hydrates in Fig.