Gaseous Metal Hydrides MBeH_{3} and M_{2}BeH_{4} (M = Li, Na): Quantum Chemical Study of Structure, Vibrational Spectra and Thermodynamic Properties
Awadhi Shomari^{*}, Tatiana P. Pogrebnaya, Alexander M. Pogrebnoi
Department of Materials, Energy Science and Engineering, the Nelson Mandela African Institution of Science and Technology (NM–AIST), Arusha, Tanzania
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To cite this article:
Awadhi Shomari, Tatiana P. Pogrebnaya, Alexander M. Pogrebnoi. Gaseous Metal Hydrides MBeH_{3} and M_{2}BeH_{4} (M = Li, Na): Quantum Chemical Study of Structure, Vibrational Spectra and Thermodynamic Properties. International Journal of Materials Science and Applications. Vol. 5, No. 1, 2016, pp. 5-17. doi: 10.11648/j.ijmsa.20160501.12
Abstract: The theoretical study of complex hydrides MBeH_{3} and M_{2}BeH_{4} (M = Li, Na) have been carried out using DFT MP2 methods with basis set 6-311++G (d, p). The optimized geometrical parameters, vibrational spectra and thermodynamic properties of the hydrides and subunits MH, M_{2}H^{+}, M_{2}H_{2}, BeH_{2}, BeH_{3}^{−} have been determined. Two geometrical configurations, cyclic (C_{2v}) and linear (C_{∞v}), were found for pentaatomic MBeH_{3} molecules, the cyclic isomer being predominant. Three isomers of M_{2}BeH_{4} molecules were revealed of the following shapes: two-cycled (D_{2d}), polyhedral (C_{2v}) and hexagonal (C_{2v}). Among these structures polyhedral isomer was found to have the lowest energy. The relative abundance of the M_{2}BeH_{4} isomers in saturated vapour was analyzed. The enthalpies of formation ∆_{f}H°(0) of complex hydrides in gaseous phase were determined (in kJ×mol^{-1}): 105 ± 26 (LiBeH_{3}), 63 ± 37 (Li_{2}BeH_{4}), 121 ± 27 (NaBeH_{3}), and 117 ± 39 (Na_{2}BeH_{4}). The thermodynamic stability of the hydrides was examined through Gibbs free energies for heterophase decomposition.
Keywords: Complex Hydrides, Geometrical Structure, Vibrational Spectra, Enthalpy of Dissociation, Enthalpy of Formation, Heterophase Decomposition, Hydrogen Storage Materials
1. Introduction
Fossil fuels as the main source of energy worldwide are depleting, unsteady in terms of price, and have a negative impact to both the environment and humans beings [1]. Hydrogen shows a promising interest as a synthetic fuel. In order to use hydrogen as the source of energy and replacement of fossil fuels; it has to overcome three technical challenges associated with the production, storage and use [2]. Chater reported that the problem of hydrogen storage remains as the most challenging [3].
The large-scale deployment of vehicular fuel cells is hindered by the absence of a commercially feasible hydrogen storage technology. A selection of comparatively lightweight, low-cost, and high-capacity hydrogen storage devices must be available in a variety of sizes to meet different energy needs [4]. The use of hydrogen as fuel in transport offers the greatest challenge towards system design. The criteria for a practical hydrogen store for mobile applications have been outlined by the U. S. Department of Energy [5].
Complex metal hydrides studied recently considered as promising materials for hydrogen storage [6]. When Bogdanović and Schwickardi [7] announced the reversibility of the catalyzed sodium alanate NaAlH_{4} in hydrogen desorption and absorption reactions at ambient condition, several researches [8-12] have been focused on alkali complex hydrides particularly in the kinetics viewpoint. The complex hydrides Li_{2}MH_{5} (M = B or Al) were previously studied theoretically and it was shown that these materials are stable at low temperatures and suggested to be potential for hydrogen storage purposes [13]. The prediction and synthesis of hydride compound with sufficient amount of hydrogen contents were done in [14]. A lithium–hydride bonding in complexes HMgHLiX with different ligands X including hydrogen was studied theoretically at MP2/6-311++G (d, p) level [15]. Vajeeston [16] investigated the atomic arrangements, electronic structures, and bonding nature within the MMgH_{3} (M = Li, Na, K, Rb, Cs) series so as to determine the stability of these materials for hydrogen storage applications.
The decomposition of the complex metal hydrides such as the alkali metal tetrahydroborides to release hydrogen gas was reported in [17] to proceed in the following two channels:
MBH_{4} → MH + BH_{3} (1)
MBH_{4} → MH + B + 3/2H_{2} (2)
Theoretical investigation of structural, electronic and thermodynamic properties of crystalline Na_{2}BeH_{4 }and the structural transition from α- to β-Na_{2}BeH_{4} has been performed in [18].
This study aims at theoretical investigation of complex hydrides MBeH_{3} and M_{2}BeH_{4} (M = Li, Na) in gaseous state implying a potential application for hydrogen storage. The content of hydrogen is 15.8% (LiBeH_{3}), 8.6% (NaBeH_{3}), 14.8% (Li_{2}BeH_{4}), and 6.8% (Na_{2}BeH_{4}). The targets are to determine the structure, geometrical parameters, vibrational spectra and thermodynamic properties of the complex hydrides and subunits they composed of and examine the thermodynamic stability of the hydrides with respect to different channels of decomposition. Therefore, our work will provide useful information on the structural and thermodynamic properties of the species and contribute to an exploration of the hydrides for hydrogen storage application.
2. Computational Details
The calculations were carried by implementing density functional theory (DFT) with hybrid functional B3PW91 [19], and second-order Møller–Plesset perturbation theory (MP2) with the basis set 6-311++G(d, p). In order to find out the accuracy of calculated results, the properties of the diatomic alkali metal hydride molecules were computed by using two different DFT hybrid functionals, B3P86 and B3PW91, and MP2 method together with the said basis set; the calculated properties were then compared with available experimental data. The optimization of geometrical parameters and vibrational spectra computations were performed using the PC GAMESS (General Atomic and Molecular Electronic Structure System) program [20], Firefly version 8.1.0 [21]. Geometrical structures and IR spectra were visualized using the wxMcMolPlt [22] and ChemCraft software [23]. The thermodynamic functions were determined in rigid rotator-harmonic oscillator approximation by using Open thermo software [24].
The enthalpies of dissociation reactions ∆_{r}H°(0) were computed using the formulae:
Δ_{r}H°(0) = ∆_{r}E + ∆_{r}ε (3)
∆_{r}ε = 1/2hc(∑ω_{i prod} – ∑ω_{i react}) (4)
where ∆_{r}E is the energy of the reaction calculated through the total energies E of the species, ∆_{r}ε is the zero point vibration energy (ZPVE) correction, ∑ω_{i} _{prod} and ∑ω_{i react} are the sums of the vibration frequencies of the products and reactants respectively. The enthalpy of formation was computed by the underwritten equation:
∆_{r}H°(0)= ∑∆_{f}H°(0)_{prod }– ∑∆_{f}H°(0)_{react} (5)
where ∑∆_{f}H°(0)_{prod} and ∑∆_{f}H°(0)_{react} are enthalpies of formation of products and reactants, respectively. The values of ∑∆_{f}H°(0)_{react} were taken from Ivtanthermo Database [25]. The thermodynamic stability of the complex hydrides was examined through Gibbs free energy ∆_{r}G°(T) of dissociation reactions. The values of ∆_{r}G°(T) were calculated by the formula:
∆_{r}G°(T) = ∆_{r}H°(T) - T∆_{r}S°(T) (6)
where Δ_{r}H°(T) and Δ_{r}S°(T) are the enthalpy and entropy of the reaction at temperature T.
3. Results and Discussion
3.1. Subunits of Complex Hydrides
Diatomic molecules, NaH, LiH and H_{2}. Two DFT hybrid functionals, B3P86 and B3PW91, together with MP2 were used to calculate molecular parameters: equilibrium internuclear distance, normal vibrational frequency, and dipole moment (Table 1). To test an accuracy of the calculated results a comparison with the available experimental data has been done. The calculated parameters do not contradict to the experimental values [26-29]. Among two DFT methods, B3PW91 and B3P86, the former provided a bit more accurate results. Thereby the results for other species considered are represented as found by DFT/B3PW91 and MP2 methods.
Notes: here and hereafter in Tables 2–7, R_{e} is the equilibrium internuclear distance in Å, E is the total energy in au, ω_{e} is the vibrational frequency in cm^{–1}, μ_{e} is the dipole moment in D.
Triatomic molecule BeH_{2} and ions M_{2}H^{+} (M = Li, Na).
The characteristics of the BeH_{2} molecule are summarized in Table 2. The values obtained through the two methods are generally in agreement with each other and reference data [25]. The values of equilibrium internuclear distance by DFT and MP2 are slightly shorter, by 0.007 Å and 0.014 Å, than the experimental value, while the valence asymmetric frequency ω_{2} is overrated by 3.2% (DFT) and 5.5% (MP2) respectively compared to experimental magnitude. The structure of the triatomic ions M_{2}H^{+} is linear of D_{∞h} symmetry (Fig. 1 a); the results are displayed in Table 3. The experimental reference data are not available.
Note: the parenthesized values near frequencies are the IR intensities in D^{2} amu^{–1} Å^{–2}.
The properties calculated follow the trend of that for the diatomic molecules MH (Table 1). It is worth mentioning that the internuclear distance R_{e}(Li-H) in Li_{2}H^{+} is longer by ~ 0.05 Å compared to that in LiH and R_{e}(Na-H) in Na_{2}H^{+} is longer by ~0.08 Å than that in NaH. The vibration frequencies calculated by two methods are in a good agreement between each other, respectively.
Tetraatomic ion BeH_{3}^{–} and molecules M_{2}H_{2} (M= Li, Na).
The properties of the tetraatomic species are displayed in Tables 4 and 5; their structures are shown in Figs. 1 b, c. The tetraatomic ion BeH_{3}^{–} has the planar equilibrium configuration of the D_{3h} symmetry. The values obtained through two methods are generally in agreement with each other. For the M_{2}H_{2} molecules, the values of internuclear distances, valence angles, and vibrational frequencies calculated by DFT and MP2 fairly match with each other respectively and with the theoretical results obtained previously [31]. The calculated enthalpy of dimerization for Li_{2}H_{2} is in agreement within uncertainty limit with the experimental magnitude by Wu et al. [32].
Note: Here and hereafter α_{e} is bond angle in degrees; the values ∆E_{dim} and ∆_{r}H°(0)_{dim} are the energies and enthalpies of dimerization reactions 2MH = M_{2}H_{2} in kJ mol^{–1}.
(a) (b) (c)
3.2. Geometrical Structure and Vibrational Spectra of Pentaatomic Molecules LiBeH_{3} and NaBeH_{3}
Two possible geometrical configurations, cyclic (C_{2v}) and linear (C_{∞v}), were considered for pentaatomic MBeH_{3} molecules (Fig. 2). The calculated equilibrium geometrical parameters and vibrational frequencies for cyclic isomer are shown in Table 6. The binding in the cyclic isomer may be considered through an attachment of M^{+} cation to BeH_{3}^{–} anion. Within the MBeH_{3} molecules, the fragment BeH_{3} is distorted compared to free BeH_{3}^{–} anion. In the latter the bond lengths and angles are equivalent, R_{e}(Be-H) ≈ 1,42 Å (Table 4) while in the MBeH_{3} molecules the bridge distances R_{e}(Be-H) are elongated to 1.44-1.45 Å; and the terminal distance is shortened to ~1.35 Å; the bond angles become also non-equivalent, the angle β_{e}(H_{4}-Be_{1}-H_{5}) decreases to 104° in LiBeH_{3} and 110° in NaBeH_{3}. Thus the BeH_{3} moiety looks alike in both LiBeH_{3} and NaBeH_{3} molecules.
The IR spectra of MBeH_{3} (C_{2v}) molecules are presented in Fig. 3. The similarity of the vibrational bands is observed for LiBeH_{3} and NaBeH_{3}. For instance the most intensive bands correspond to the Be-H stretching vibrations at 1528 cm^{–1} (LiBeH_{3}) and 1555 cm^{–1} (NaBeH_{3}). The highest vibration frequencies correspond to the Be_{1}-H_{3} stretching vibrations at 2029 cm^{–1} (LiBeH_{3}) and 1980 cm^{–1} (NaBeH_{3}). The bending vibration H-Be-H is observed at 849 cm^{–1} (LiBeH_{3}) and 833 cm^{–1} (NaBeH_{3}).
(a) (b)
(a) (b)
Note: Δ_{r}E_{iso} is the relative energy of linear isomer regarding cyclic, Δ_{r}E_{iso} = E_{lin} – E_{cycl}, in kJ mol^{–1}.
The properties of the MBeH_{3} molecules of linear configuration are shown in Table 7. The linear isomer MBeH_{3} may be represented through linkage of the MH and BeH_{2} molecules. Worth to mention that for lithium bonding complexes HMgH···LiH the linear structure was considered in [15], while existence of possible isomers had not been taken into account. Our results for MBeH_{3} show that the energy of the linear isomer appeared to be much higher compared to the cyclic one, i. e. by 165 kJ mol^{–1} (MP2, both for LiBeH_{3} and NaBeH_{3}). It is also worth to note a low frequency of vibration ω_{7} which corresponds to bending of the Li-H-Be fragment. Moreover when the parameters of the linear isomers were calculated using DFT/P3P86 method the imaginary frequency for LiBeH_{3} was revealed which indicates low stability of the linear structure with respect to bending deformation. Hence only this cyclic isomer was considered further in examination of thermodynamic properties of MBeH_{3} hydrides.
3.3. Geometrical Structure and Vibrational Spectra of Heptaatomic Li_{2}BeH_{4} and Na_{2}BeH_{4} Molecules
Several different geometrical shapes of the M_{2}BeH_{4 }molecules have been considered: bipyramidal one with a tail of C_{2v} symmetry; polyhedral (compact or hat-shaped), C_{2v}; two-cycles, D_{2d}; and hexagonal shape, C_{2v}. Among these four configurations the first one was found to be unstable as imaginary vibrational frequencies were revealed. The rest three structures were proved to correspond to the minima at the potential energy surface and therefore appeared to be isomers of M_{2}BeH_{4} molecules. Hereafter these isomers are denoted as I, II, and III, for C_{2v} compact, D_{2d}, and C_{2v} hexagonal, respectively; the equilibrium geometrical configurations are shown in Fig. 4 and the parameters are displayed in Tables 8-10.
The binding in the polyhedral and two-cycled structures may be considered through an attachment of two M atoms to a slightly distorted tetrahedral BeH_{4} moiety. In the first isomer there are two types of Be-H bonds with internuclear separations R_{e1}(Be-H) ≈ 1.53 Å and R_{e2}(Be-H) ≈ 1.42 Å; the averaged of these two values, 1.47 Å, is very close to the distance R_{e}(Be-H) in the D_{2d} isomer. The averaged valence angle H-Be-H in BeH_{4} fragment of the polyhedral isomers is about 109° that is almost equal to the tetrahedral angle. In the D_{2d} isomer, the angle H-Be-H is 104° (Li_{2}BeH_{4}) and 110° (Na_{2}BeH_{4}) that is also close to the tetrahedral angle. The hexagonal molecule may be considered through a combination of BeH_{3}^{–} and M_{2}H^{+} subunits. The geometrical parameters, the bridge Be-H bond lengths (~1.42 Å) and valence angle β_{e}(H-Be-H) ≈ 117°, of the hexagonal M_{2}BeH_{4} molecules are similar to the respective parameters in free BeH_{3}^{–} ion as well as in cyclic MBeH_{3} molecules.
(a) (b) (c)
Note: ∆_{r}E_{iso}(I-II) is the energy of isomerization reaction M_{2}BeH_{4} (I, C_{2v, comp})= M_{2}BeH_{4} (II, D_{2d}), ∆_{r}E_{iso}(I-II) = E(II) – E(I), in kJ×mol^{-1}.
The IR spectra of three isomers of Li_{2}BeH_{4 }and Na_{2}BeH_{4 }molecules are presented in Fig. 5. By comparing IR spectra of Li_{2}BeH_{4} and Na_{2}BeH_{4} molecules, alike features may be observed for the isomers of the same symmetry. For the polyhedral isomer I, the bands of high intensity at 1259 cm^{–1}, 1772 cm^{–1} (Li_{2}BeH_{4}) and 1207 cm^{–1}, and 1650 cm^{–1} (Na_{2}BeH_{4}) correspond to H-Be-H asymmetrical stretching vibrations of BeH_{4} moiety. For the two-cycled D_{2d} isomer, similar H-Be-H asymmetrical stretching vibrations of BeH_{4} moiety are observed at 1436 cm^{–1}, 1520 cm^{–1} (Li_{2}BeH_{4}) and 1408 cm^{–1}, 1440 cm^{–1} (Na_{2}BeH_{4}). The most intensive band in spectrum of Li_{2}BeH_{4} D_{2d} is seen at 1213 cm^{–1} and corresponds to the H-Li-H asymmetrical stretching mode, in Na_{2}BeH_{4} D_{2d} the similar vibration is observed at 1118 cm^{–1}. For the hexagonal isomer the most intense bands appear at 1764 cm^{–1} (Li_{2}BeH_{4}) and 1742 cm^{–1} (Na_{2}BeH_{4}) and are characterized by stretching modes of the BeH_{3} fragment. Other similarities may be noted between two hexagonal species as wagging vibrations at 444 cm^{–1} Li-H-Li, 794 cm^{–1} H-Be-H (Li_{2}BeH_{4}) and 344 cm^{–1} Na-H-Na, 797 cm^{–1} H-Be-H (Na_{2}BeH_{4}). The vibration of highest frequency at about 2000 cm^{–1}, both for Li_{2}BeH_{4} and Na_{2}BeH_{4}, corresponds to the terminal bond Be-H stretching mode, that is the highest frequency correlates with the shortest bond length R_{e}(Be-H) = 1.36 Å.
Note: ∆_{r}E_{iso}(I–III) is the energy of isomerization reaction M_{2}BeH_{4} (I, C_{2v, comp}) = M_{2}BeH_{4} (III, C_{2v, hex}), ∆_{r}E_{iso}(I–III) = E(III) – E(I), in kJ×mol^{-1}.
(a) (b)
(c) (d)
(e) (f)
The relative energies ∆_{r}E_{iso} of the isomers II and III regarding I given in Tables 9, 10 were calculated for the following isomerisation reactions:
M_{2}BeH_{4}(I, C_{2v, comp}) = M_{2}BeH_{4}(II, D_{2d}) (7)
M_{2}BeH_{4}(I, C_{2v, comp}) = M_{2}BeH_{4}(III, C_{2v, hex}). (8)
The values of Δ_{r}E_{iso} are positive: for reaction R1 15.5 kJ mol^{-1} (Li_{2}BeH_{4}), 15.7 kJ mol^{-1} (Na_{2}BeH_{4}), and for R2 30.1 kJ mol^{-1} (Li_{2}BeH_{4}), 17.4 kJ mol^{-1} (Na_{2}BeH_{4}) according to MP2 calculations. Therefore among three isomers, I, II, and III, the first one has the lowest energy, followed by D_{2d}, and the hexagonal: E(I) < E(II) < E(III) for both molecules. The energy difference between isomers II and III is 14.6 kJ mol^{-1} (Li_{2}BeH_{4}), and 1.7 kJ mol^{-1} (Na_{2}BeH_{4}) in favour of D_{2d}, thus worth to note the isomers II and III of the Na_{2}BeH_{4} molecule are comparable by energy.
To evaluate the relative concentration of the isomers in the equilibrium vapour, the thermodynamic approach was applied. The following equation was used:
(9)
where ∆_{r}H°(0) is the enthalpy of isomerisation of the reaction; T is absolute temperature; ∆_{r}Φ°(T) is the reduced Gibbs energy of the reaction, Φ°(T) = -[H°(T)-H°(0)-TS°(T)]/T; p_{A}/p_{B} is the pressure ratio between two isomers, that is p_{II}/p_{I} for reaction R1 and p_{III}/p_{I} for R2. The values of ∆_{r}H°(0) were calculated using isomerization energies ∆_{r}E_{iso} and the ZPVE corrections ∆_{r}ε by Eqs. (3) and (4). The relative concentrations p_{A}/p_{B} have been calculated for the temperature range between 500 and 2000 K; the plots are shown in Fig. 6. The graphs show that the relative concentrations of the isomers II and III increase with temperature increase for both molecules, for Li_{2}BeH_{4} the growth is slow compared to Na_{2}BeH_{4}. At 1000 K for Li_{2}BeH_{4} and Na_{2}BeH_{4} the values of p_{II}/p_{I} are equal to 0.6 and 5.2, respectively, while the ratios p_{III}/p_{I} are 2.5 and 30, respectively. Therefore the isomer I of Li_{2}BeH_{4} molecule is more abundant at moderate temperatures, but at higher temperatures its concentration is noticably decreasing. For Na_{2}BeH_{4} the hexagonal isomer is much more abundant compared to either isomers I and II. The fraction of each isomer of Na_{2}BeH_{4} was estimated as x_{i} = p_{i}/(p_{I} + p_{II} + p_{III}) where i stands for I, II, or III, the results for two selected temperatures are given in Table 11. Thus as seen the hexagonal isomer of Na_{2}BeH_{4} is predominant in a broad temperature range and its concentration is increasing with temperature raise.
3.4. Thermodynamic Properties of Complex Hydrides
3.4.1. The Enthalpies of Dissociation Reactions and Enthalpies of Formation of Molecules
Different dissociation reactions of the complex hydrides MBeH_{3} and M_{2}BeH_{4} have been examined; for the latter the polyhedral isomer of C_{2v} symmetry was considered as lowest by energy. The calculated energies and enthalpies of gas-phase reactions are represented in Tables 9 and 10; the results obtained by DFT/B3PW91 and MP2 methods. Two types of dissociation reactions of complex hydrides, MBeH_{3} and M_{2}BeH_{4} were considered: a partial dissociation and complete reduction of the hydride with hydrogen gas release. The values of ∆_{r}H°(0) show that all reactions proceed with the absorption of energy (endothermic). The partial dissociation of both penta- and heptaatomic hydrides requires much less energy than reaction with hydrogen formation. The most energy consuming reactions are those with H_{2} evolving (reactions 2 for MBeH_{3} and 6, 7 for M_{2}BeH_{4}) and dissociation into ionic subunits M_{2}H^{+} and BeH_{3}^{–} (reactions 8).
The enthalpies of formation ∆_{f}H°(0) of the complex hydrides were calculated through the enthalpies of the reactions and enthalpies of formation of the gaseous products, Li, Na, H_{2}, LiH, NaH [25] and BeH_{2} [27]. The enthalpies of formation of M_{2}H_{2} molecules involved in reactions 5 were obtained through the enthalpies of dimerization reactions (Table 5), the averaged values of ∆_{f}H°(0) between DFT/B3PW91 and MP2 methods were accepted: 90 ± 10 kJ×mol^{-1} (Li_{2}H_{2}) and 139 ± 10 kJ×mol^{-1} (Na_{2}H_{2}). The enthalpies of formation of the penta- and heptaatomic hydrides are presented in the far right column in Tables 12, 13. The enthalpies of formation of MBeH_{3} molecules are accepted as the averaged values found through the enthalpies of reactions 1 and 2; similarly for M_{2}BeH_{4} through reactions 3-7. Uncertainties were estimated as half-differences between maximum and minimum magnitudes. The accepted values of ∆_{f}H°(0) are gathered in Table 14.
Stability of the gaseous complex hydrides MBeH_{3} and M_{2}BeH_{4} regarding heterophase decomposition with hydrogen release were also considered. The enthalpies of the heterophase reactions were calculated and given in Table 12. The required enthalpies of formation of Be, LiH, NaH, Li, Na in condensed phase were taken from [25]. In the heterophase reactions considered, beryllium is in solid state, the alkali metal hydrides are in gas-phase (reactions 1, 4) or in condensed phase (reactions 2, 5); complete decomposition is described by reactions 3, 6. The results show that the reactions in which gaseous MH are among the products are endothermic, while the rest reactions are exothermic; the biggest energy being released in reactions 2 and 5 with MH_{(c)}.
3.4.2. Thermal Stability of the Complex Hydrides and Thermodynamic Favourability of the Reactions
The thermodynamic stability of the complex hydrides MBeH_{3} and M_{2}BeH_{4} was examined through Gibbs free energies for heterophase reactions shown in Table 15. The temperature dependences of Δ_{r}G° are presented in Figs. 7-9. For the reactions in which MH is in gaseous phase Δ_{r}G° are negative at moderate and elevated temperatures (Fig. 7); the decomposition reactions are thermodynamically favoured at temperatures above 350 K (NaBeH_{3}), 500 K (LiBeH_{3}), 800 K (Na_{2}BeH_{4}) and 1000 K (Li_{2}BeH_{4}). Thus the MBeH_{3} hydrides appeared to be less stable thermodynamically than M_{2}BeH_{4} and Na-containing hydrides are less stable compared to Li-hydrides.
For reactions in which both MH and Be are in condensed phase (Fig. 8) the values of Δ_{r}G°(T) are negative for whole temperature range considered. The Na-containing hydrides are slightly more stable than Li-hydrides as the values of Δ_{r}G°(T) for the former are less negative. The inflections on the curves correspond to phase change transition of the products, namely the melting points of LiH_{(c)} and NaH_{(c)} at 965 K and 911 K [25], respectively. The Gibbs free energy for the decomposition reaction of MBeH_{3} decreases with temperature raise, while for M_{2}BeH_{4} hydrides the values of Δ_{r}G° pass through maximum at temperatures of the phase transitions. Here the entropy has an impact on Δ_{r}G°(T): as a jump of entropy at phase transition of MH_{(c)} occurs hence the contribution of entropy factor TΔ_{r}S increases with temperature raise.
(a) (b)
(a) (b)
For the reactions with complete dissociation into alkaline metal and beryllium in condensed phase (Fig. 9) the Gibbs free energies are negative in the temperature range considered and decreasing with temperature increase, this indicates that the decomposition processes are spontaneous. In contrast to previous case (Fig. 8), the Na-containing hydrides are less stable than Li-hydrides as the values of Δ_{r}G°(T) are less negative for the latter.
For different channels of dissociation of the hydrides, a correlation between Δ_{r}G°(T) and Δ_{r}H°(0) values may be noted: the lower is the enthalpy of the reaction the more negative are Δ_{r}G°(T) and hence the more favourable the decomposition process. For instance, for the reactions with gaseous alkali hydrides MH the enthalpies ∆_{r}H°(0) are positive, ~20–30 kJ mol^{–1} (MBeH_{3}) and ~170–220 kJ mol^{–1} (M_{2}BeH_{4}); then the Gibbs free energies are positive at low and moderate temperatures and turn negative at certain temperatures said (Fig. 7). This implies that the reversibility of the reactions is able to be attained. For other heterogeneous reactions the ∆_{r}H°(0) values are negative, the Gibbs free energies are negative (Figs. 8, 9) that is the decomposition of the hydrides, both MBeH_{3} and M_{2}BeH_{4}, is spontaneous in the whole temperature range considered. The reaction with Li/Na and Be in condensed phase the reversibility may be achieved by pressure increase (Le Châtelier's principle). The reversibility of the decomposition reactions of hydrides is one of the requirements for hydrogen storage materials.
(a) (b)
4. Conclusion
The geometrical parameters, vibrational spectra and thermodynamic properties of the complex hydrides MBeH_{3} and M_{2}BeH_{4} (M = Li, Na) and subunits have been determined using DFT/B3PW91 and MP2 methods. The results obtained by both methods are in a good agreement between each other and with the reference data available for subunits MH, BeH_{2}, M_{2}H_{2}. The enthalpies of different gas-phase dissociation reactions were computed; the enthalpies of formation of the complex hydrides were found. The Gibbs free energies Δ_{r}G°(T) of heterophase decomposition of MBeH_{3} and M_{2}BeH_{4} with hydrogen release were analyzed. It was shown the reactions the products of which were gaseous alkaline metals and solid beryllium may be reversible at moderate temperatures. The reactions of complete decomposition (products are M_{(c)}, Be_{(c)}, H_{2}) were shown to be spontaneous at a broad temperature range; the reversibility of the reactions may be attained if certain conditions are provided. The complex hydrides MBeH_{3} and M_{2}BeH_{4} (M = Na or Li) may be considered as promising candidates for hydrogen storage applications as they showed the feasibility of hydrogen gas production.
Authors’ Contributions
Authors participated equally in all steps to the completion of this work.
Acknowledgment
The authors are very thankful to the government of Tanzania through The Nelson Mandela African Institution of Science and Technology for supporting and sponsoring this study.
References