Complex Hydrides Li2MH5 (M = B, Al) for Hydrogen Storage Application: Theoretical Study of Structure, Vibrational Spectra and Thermodynamic Properties
Melkizedeck Hiiti Tsere1, 2, *, Tatiana P. Pogrebnaya1, 2, Alexander M. Pogrebnoi1, 2
1The Nelson Mandela African Institution of Science and Technology (NM – AIST), Arusha, Tanzania
2Department of Materials, Energy Science and Engineering, the Nelson Mandela African Institution of Science and Technology (NM – AIST), Arusha, Tanzania
To cite this article:
Melkizedeck Hiiti Tsere, Tatiana P. Pogrebnaya, Alexander M. Pogrebnoi. Complex Hydrides Li2MH5 (M = B, Al) for Hydrogen Storage Application: Theoretical Study of Structure, Vibrational Spectra and Thermodynamic Properties. International Journal of Computational and Theoretical Chemistry. Vol. 3, No. 6, 2015, pp. 58-67. doi: 10.11648/j.ijctc.20150306.13
Abstract: Gaseous lithium complex hydrides Li2MH5 (M = B, Al) have been studied using DFT/B3P86 and MP2 methods with 6-311++G(d,p) basis set. High content of hydrogen by these materials accord them with good candidacy as a class of hydrogen storage materials. The optimized geometrical parameters, vibrational spectra and thermodynamic properties of the hydrides and the subunits LiH, Li2H+, Li2H2, MH3, MH4−, and LiMH4 have been determined. For the LiBH4 the equilibrium configuration was tridentate of C3v symmetry. For LiAlH4 two isomeric forms, bidentate (C2v) and tridentate (C3v), were confirmed to exist, and C2v isomer was shown to dominate in saturated vapor. For complex hydrides Li2MH5, different structural forms were considered but only one asymmetric form (C1) appeared to be equilibrium. Several possible channels of dissociation of Li2MH5 were considered; the enthalpies and Gibbs free energies of the reactions were computed. The enthalpies of formation ∆fH°(0) of the complex hydrides in gaseous phase were determined: -60 ± 10 kJ×mol-1 (Li2BH5) and 33 ± 10 kJ×mol-1 (Li2AlH5). Heterophase decomposition of the gaseous Li2MH5 with solid products LiH and B/Al and hydrogen gas release was shown to be spontaneous at ambient temperature. Production of hydrogen gas via gaseous decomposition is highly endothermic and achievable at elevated temperatures. The complexes Li2MH5 are therefore proposed to be useful hydrogen storage materials under appropriate conditions.
Keywords: Complex Hydrides, Hydrogen Storage, Geometrical Structure, Vibrational Spectra, Density Functional Theory, Møller–Plesset Perturbation Theory, Basis Set, Isomers, Thermodynamic Properties
Utilization of hydrogen as fuel energy is limited by lack of viable hydrogen storage materials . Application of hydrogen in fuel cells has an advantage due to the fact that hydrogen is environmentally benign with water as the only byproduct, renewable and has very high energy density compared to any known conventional fuel sources [2,3]. Also the substantial use of hydrogen as primary fuel energy would greatly reduce the emissions of greenhouse gases and dependence on fossil fuels . Materials suitable for hydrogen storage should have the characteristics such as high capacity to store large weight percent and volumetric fraction of hydrogen, good desorption/adsorption kinetics as a reversible mechanism [5,6]. Thermal decomposition of great number of hydrides regarding hydrogen storage application has been discussed in review .
Recently, complex hydrides of light weight metals have been reported as prospective materials for hydrogen storage . Thermal stability and reaction reversibility of these hydrides becomes the key barrier for the growth of hydrogen powered fuel cells . However, kinetics of dissociation and formation of these hydrides can be improved by catalytic additives . In 1996, Bogdanovic and Schwickardi  first reported on the adsorption and desorption isotherms of catalyzed NaAlH4 at the temperature of around 180°C to 210°C, this has unlocked the researchers’ interest towards lightweight complex metal hydrides as new candidates for hydrogen storage.
Among alkali metals, lithium possesses lowest atomic mass, thus lithium complex hydrides comprise high weight percent of hydrogen. For this reason, LiBH4 and LiAlH4 have been extensively studied as ideal hydrogen storage material . The extreme hydrogen content and decomposition temperature correlated with the electronegativity of metal have been the reason for the growth of the research interest on metal borohydrides . Lithium tetrahydroboride has been discovered by DTA technique in hydrogen at high pressure . Züttel et al.  proposed decomposition of LiBH4 in liberation of hydrogen gas as
LiBH4 → LiH + BH3 (1)
LiBH4 → LiH + B + 3/2H2 (2)
Orimo et al.  performed the experimental studies and confirmed desorption and rehydrogenation of the compounds mentioned in the Eqs: (1) and (2). The aim of this study is a theoretical investigation of lithium complex hydrides Li2MH5 (M = B, Al) in gaseous state. Based on the described decomposition of hydrides in literature [14-16] we suggest the decomposition of Li2MH5 to deliver hydrogen in the following reaction steps:
Li2MH5 → LiMH4 + LiH (3)
LiMH4 → LiH + M + 3/2H2 (4)
hence Eqs. (3) and (4) can be combined into overall dissociation reaction as shown below:
Li2MH5 → 2LiH + M + 3/2H2 (5)
We suggest the decomposition of Li2MH5 molecule with elimination of the dimer Li2H2 as well:
Li2MH5 → Li2H2 + M + 3/2H2 (6)
These overall reactions (5) and (6) give the theoretical yield of 10% wt of hydrogen gas when Li2BH5 is decomposed and 6.5% wt from decomposition of Li2AlH5. The structure, geometrical parameters, vibration spectra and thermodynamic properties of the lithium complex hydrides are to be determined.
2. Methods of Computation and Details of Calculations
Two quantum chemical methods were implemented: namely, density functional theory (DFT) with B3P86 functional and Møller-Plesset perturbation theory of the 2nd order (MP2). The basis set 6-311++G(d,p) was applied in both methods. The General Atomic and Molecular Electronic Structure System (GAMESS) software , Firefly version 8.1.0  was used to perform computations. The geometric parameters of the molecules and ions were optimized and the calculations of vibrational frequencies in the harmonic approximation were carried out by the methods implemented in the GAMESS program. Geometrical structures were analyzed using the ChemCraft software . The thermodynamic functions were determined by using OpenThermo software , the thermochemical reference data for calculations were taken from Ivtanthermo Database . The enthalpies of reactions ΔrH°(0) were determined through the energies of the reactions ∆rE and zero point vibrational energies (ZPVE) ∆rε:
ΔrH°(0) = ∆rE + ∆rε (7)
∆rε = 1/2hc(∑ωi prod – ∑ωi react) (8)
where ∑ωi prod and ∑ωi react are the sum of the vibration frequencies of the products and reactants respectively.
3. Results and Discussion
3.1. Subunits of the Lithium Boron/Aluminium Complex Hydrides
3.1.1. Diatomic Molecules, LiH, H2, and Triatomic Ion Li2H+
The calculated parameters, internuclear distances, ionization energies and the vibrational frequencies, have been calculated and compared with the available reference data so as to analyze the appropriateness of the methods used. The results obtained with both DFT and MP2 methods are in good agreement between each other as well as with the available reference data . As an example, for triatomic ion Li2H+ (D∞h) the calculated parameters, equilibrium bond length and vibrational frequencies, are given in Table 1. The MP2 method gives slightly shorter equilibrium internuclear distance and higher frequencies than DFT.
Note: Here and hereafter, Re are the internuclear distances, Å; E is the total electron energy, au; parenthesized values near frequencies are intensities of IR spectrum bands, D2 amu–1 Å–2, vibrational representation is Γ = ∑g+ + ∑u+ + Πu.
3.1.2. Tetraatomic Molecules Li2H2, BH3 and AlH3
The properties of tetraatomic molecules are presented in Tables 2 and 3, and structures are given in Fig. 1 a, b. For the Li2H2 molecule, the equilibrium structure is rhomb of D2h symmetry. Molecular parameters are presented in Table 2. Results of computations by DFT and MP2 methods fairly match with each other, and also they are in a very good agreement with quantum chemical data obtained from MP2/6-311++G** and QCISD/6-311++G** methods in . The calculated enthalpies of dimerization are in accordance within uncertainty with the experimental magnitude by Wu and Ihle. . The geometrical structure for BH3 and AlH3 is planar of D3h symmetry. For both molecules results obtained by two methods agree well with each other and do not contradict to available literature data [22,25,30].
Note: ∆Edim and ∆rH°(0)dim are the energy and enthalpy of dimerization reaction 2LiH = Li2H2, kJ mol–1; the vibrational representation for Li2H2 (D2h) is Γ = 2Ag + B1g + B1u + B2u + B3u.
3.1.3. Pentaatomic Ions, MH4−
The equilibrium geometrical structure of the ions BH4– and AlH4– is tetrahedral of Td symmetry as shown in Fig. 1 c; the properties are represented in Table 4. The calculated properties are also compared with available experimental  and theoretical data [32,33]. The values of Re(B-H) we obtained do not contradict with the theoretical magnitude 1.239 Å reported by Spoliti et al. . Our theoretical internuclear distance Re(Al-H) is slightly smaller by 0.003 Å (DFT) and 0.014 Å (MP2) than the reference value . The DFT and MP2 results on the frequencies fairly agree with each other with variations of less than 5%. One can note that DFT frequencies better correspond to the experimental values .
Note: The vibrational representation of molecules MH3 (D3h) is Γ = + + 2.
Notes: In , the values Re for BH4– and AlH4– were calculated by MP2/6-31+G*. The vibrational representation for MH4− (Td) is Γ = A1 + E + 2T2.
3.2. Lithium Tetrahydroboride Molecules, LiMH4
For lithium tetrahydroboride LiMH4 (M = B, Al), two geometrical configurations were considered; C3v and C2v symmetry (Fig. 2); the geometrical parameters were optimized and the results are given in Tables 5 and 6. By general observations, results obtained by DFT and MP2 are in good correspondence, following the trend inherited from lighter subunits. In a very small deviation, DFT overrates MP2 regarding internuclear distances, but underrates in case of frequencies and dipole moments. The geometrical structure of C2v symmetry for LiBH4 appeared to be not equilibrium as imaginary frequency ω9 (B1) was observed according to both DFT and MP2 results (Table 6). Therefore the only one equilibrium geometrical structure of C3y symmetry was confirmed for LiBH4 molecule.
As for LiAlH4, both structures, of C2v and C3v symmetry, were proved to correspond to minima at the potential energy surface. For the isomerization reaction
LiAlH4 (C3v) = LiAlH4 (C2v) (9)
the values of ΔrEiso are negative: -2.4 kJ mol–1 (DFT) and -3.2 kJ mol–1 (MP2), this implies that LiAlH4 (C2v) isomer is more stable energetically as compared to LiAlH4 (C3v) isomer. The enthalpy of isomerization reaction calculated using Eqs. (7), (8) are presented in Table 6.
Our results do not contradict with the data calculated by MP2/6-31G** and MP4/6-31G** methods by Spoliti et al. , whose findings indicated the imaginary frequencies for the boron complex of C2v symmetry and reported the equilibrium structure of C3v symmetry for LiBH4. The existence of two stable configurations of C2v and C3v for LiAlH4 molecule was found in  and shown that the C2v isomer was more stable energetically than C3v, the energy of separation between the two isomers was small, 1.6 kJ mol-1.
The IR spectra of LiMH4 molecules are presented in Figs. 3 and 4. Close observation of these spectra reveals common characteristic vibrational modes for the same isomers (C3v) of LiBH4 and LiAlH4 (Figs. 3 a, b). For example, the most intensive bands at 2220 cm–1 for LiBH4 and 1606 cm–1 for LiAlH4 are assigned to asymmetrical stretching H3-B-H4 and H3-Al-H4, respectively. On the other hand in spectrum of LiAlH4 modes of high intensity appear at the 954 cm–1 (Li-H2, Li-H3 and Li-H4) and the 779 cm–1 (H1-Al) in contrast to spectrum of LiBH4 where similar bands are not seen due to low intensities.
As for the IR spectrum of the C2v LiAlH4 isomer (Fig. 4), it looks quite different compared to that of C3v isomer. The former has many intensive bands, including symmetrical stretching at the 1897 cm–1 (H1-Al-H2), 1161 cm–1 (H3-Li-H4), asymmetrical stretching at the 1032 cm–1 (H3-Li-H4), scissoring at the 1556 cm–1 (H3-Li-H4), rocking at the 1441 cm–1 (H3-Li-H4) and wagging mode at the 810 cm–1 (H3-Li-H4).
Note: μe is the dipole moment in D; vibrational representation for molecules LiMH4 (C3v) is Γ = 4A1 + 4E.
To evaluate the relative content of the isomers of the LiAlH4 molecule, the thermodynamic approach was applied. The pressure ratio p(C2v)/p(C3v) of two isomers in the equilibrium vapour was determined using the equation
ΔrHº(0) = –RTln[p(C2v)/p(C3v)] + TΔrΦº(T) (10)
where ∆rH°(0) is the enthalpy of the isomerization reaction (9); T is absolute temperature; ∆rΦ°(T) is the reduced Gibbs energy of the reaction, Φ°(T) = -[H°(T)-H°(0)-TS°(T)]/T. The values of Φ°(T) and other thermodynamic functions were calculated using the optimized geometrical parameters and vibrational frequencies obtained by both DFT/B3P86 and MP2 method. The temperature effect on the concentrations of these isomers were also considered and plotted in Fig. 5. As is seen the isomer C2v is more abundant than that of C3v symmetry. For example, at 1000 K the p(C2v)/p(C3v) is about 3-3.5. As the temperature raises the ratio decreases, still the C2v isomer remains the prevailing for whole temperature range considered.
3.3. Geometrical Structure and Vibrational Spectra of Complex Hydride Molecules, Li2MH5
Two possible geometrical configurations of C2v and C1 symmetry were considered for octaatomic Li2BH5 and Li2AlH5 molecules. For the C2v structure, the imaginary frequencies were revealed through calculations using both methods DFT and MP2, and this structure was not taken for further consideration. Thus only one equilibrium configuration of the Li2MH5 molecules was proved to exist, namely the asymmetrical structure of the C1 point group (Fig. 6).
The geometrical parameters are given in Table 7. The results revealed a good agreement between two methods. The internuclear distances by DFT method overrate those by MP2; the difference is in the range 0.003–0.012 Å. These deviations are within the range depicted above for lower species whose parameters have been compared with reference data. The frequencies obtained by MP2 overrate those by DFT in accordance to the general trend as it was shown above for the lighter species. The IR spectra for the octaatomic complex hydrides Li2MH5 (M = B, Al) are shown in Fig. 7. In the spectrum of Li2BH5, the stretching modes of high intensities are observed at 1008 cm–1 and 2287 cm–1 and bending mode H3-Li-H5 at 452 cm–1.
In spectrum of Li2AlH5 molecule, high intensity peaks correspond to the stretching and wagging vibrational modes. The most intensive asymmetrical stretching modes appear at 1641 cm–1(H2-Al-H3), 832 cm–1 (H3-Li1-H4) and 1222 cm–1 (Li1-H5-Li2); symmetrical vibrations are observed at 1002 cm–1 (Li1-H5-Li2) and 1718 cm–1 (H3-Al-H4). Wagging vibrational modes appear at 461 cm–1 (Li-H5-Li2) and 773 cm-1 (H3-Al-H4). Worth to note the spectra of two molecules Li2BH5 and Li2AlH5 are not completely imposable and this signifies that the spectra exhibit specific features regardless the similarity of geometrical shape of the molecules.
3.4. The Enthalpies of Dissociation Reactions and Enthalpies of Formation of Complex Hydride Molecules Li2MH5
Several possible dissociation reactions of complex hydrides were considered. Theoretical enthalpies of reactions were determined according to Eqs. (7), (8). The reaction equations, energies, ZPVE corrections, enthalpies of the gaseous reactions and enthalpies of formation of the complex hydride molecules are presented in Table 8. A partial dissociation of Li2MH5 without release of hydrogen gas is described by reactions (i)-(iv) for Li2BH5 and (vi)-(ix) for Li2AlH5; while reactions (v) and (x) correspond to the complete reduction of boron or aluminium accompanied by hydrogen gas evolving. As is seen all dissociation reactions proceed with absorption of heat (endothermic reactions). For partial dissociation reactions leading to the formation of hydrides, LiH and LiMH4, lower energy is required than for other reactions.
Enthalpies of formation of complex hydrides in gaseous state were determined using the formula
∆rH°(0) = ∑∆fH°(0)prod -∑∆fH°react (11)
where ∆rH°(0) is the enthalpy of reaction, ∆fH°(0)prod and ∆fH°(0)react are enthalpies of formation of products and reactants, respectively. The values of ∆fH°(0)prod for gaseous LiH, BH3, AlH3, B, and Al were taken from Ivtanthermo Database . The enthalpy of formation of the gaseous Li2H2 molecule, ∆fH°(0) = 85.4 kJ mol-1 was estimated through the enthalpy of dimerization (-193.5 kJ mol-1, MP2, shown above in Table 2). The enthalpies of formation of the complex hydride molecules were calculated by both DFT and MP2 methods. For the hexaatomic molecules LiMH4, the enthalpies of formation were calculated through reactions (i) and (vi); the averaged values obtained by DFT and MP2 methods were: -27 ± 6 kJ mol-1 (LiBH4) and 74 ± 6 kJ mol-1 (LiAlH4). For each complex hydride molecule Li2MH5, three reactions were taken into account: (ii), (iii), (v) for Li2BH5 and (vii), (viii), (x) for Li2AlH5. The accepted averaged values of ∆fH°(0) were: -60 ± 10 kJ mol-1 (Li2BH5) and 33 ± 10 kJ mol-1 (Li2AlH5). Uncertainties were estimated as half-difference between maximum and minimum magnitudes.
The heterophase reactions were also considered. Using the reference datum of ∆fH°(LiH, c, 0 K)  and enthalpies of formation of the gaseous Li2MH5, the enthalpies of heterophase reactions were calculated (Table 9). Two types of the reactions may be seen. In the first one, where boron or aluminium is in solid state and LiH is in the gaseous phase, the enthalpies are positive. In the reactions of the second type where two products, LiH and B or Al, are in condensed phase, enthalpies are negative, i.e. these reactions are exothermic.
3.5. Thermal Stability of the Complex Hydrides, Li2MH5
The thermal stability of the complex hydrides was examined on the base of the Gibbs free energies for the dissociation reactions; the values of ∆rG°(T) were considered as a quantitative measure of the chemical processes favorability. The Gibbs free energies were calculated by using the expression:
∆rG°(T) = ∆rH°(T) - T∆rS°(T) (12)
The required thermodynamic functions have been computed using a rigid rotator-harmonic oscillator approximation, based on geometrical parameters and vibrational frequencies calculated by DFT/B3P86 method. Among several proposed partial dissociation channels (Table 8), two types of gas phase reactions were chosen for examination of Gibbs free energy temperature dependence. Reactions (ii) and (vii) in which the complexes Li2MH5 decompose into LiH and LiMH4, were chosen (Fig. 8 a) as they expected to be favorable due to lower enthalpies of the reactions. Another type of the processes relates to the reactions (v) and (x), in which Li2MH5 complex hydrides decompose into gaseous products LiH, M, and H2; the plots of ∆rG°(T) are shown in Fig. 8 b.
As is seen, the decomposition of Li2BH5 into LiH and LiBH4 is thermodynamically favored at temperature above
1300 K, while for Li2AlH5 the spontaneous partial dissociation into LiH and LiAlH4 occurs at 1700 K and above. This implies that, the formation of intermediate product LiBH4 is rather preferred compared to LiAlH4; this result is in accordance with lower value of enthalpy of dissociation of Li2BH5 compared to Li2AlH5. For gas phase channels with hydrogen evulsion, reactions become spontaneous at relatively elevated temperature, i.e. at about 2250 K for Li2BH5 and 1500 K for Li2AlH5, respectively (Fig. 8 b). Below these temperatures the systems favor the reverse reactions which lead to the formation of reactants Li2MH5.
It is worth to compare the two gas phase dissociation channels for the same complex hydride. For Li2BH5 the spontaneous decomposition into LiH and LiBH4 starts at 1300 while in the second type of decomposition, hydrogen gas is not evolved at temperature below ~2200 K. For Li2AlH5, the formation of intermediate products (LiH and LiAlH4) occurs at 1700 K which is relatively higher as compared to complete dissociation which becomes spontaneous at 1500 K. Therefore the results show both complexes, Li2BH5 and Li2AlH5, are stable for the partial decomposition and hydrogen evolving reactions in a broad temperature range.
Gibbs free energy ∆rG°(T) for heterophase reactions were also considered and shown in Figs. 9 a, b. First part of the graph (Fig. 9 a) represents the reactions where only one product (B or Al) is maintained in condensed state. The dissociation reactions become spontaneous at elevated temperatures ~1300 K (Li2BH5) and ~1000 K (Li2AlH5); below these temperatures the values of ∆rG°(T) are positive, thus reverse reactions are predicted to be spontaneous. For the reactions in which the products except hydrogen are kept in a solid form, the values of ∆rG°(T) are negative for whole temperature range considered (Fig. 9 b).
These graphs indicate that complex hydrides Li2MH5 can dissociate even at room temperature to produce hydrogen gas. For Li2AlH5 complex Gibbs energies are more negative than for Li2BH5, that relates to bigger exothermicity of dissociation reaction for the former: ∆rH°(0) equals to –204 kJ mol–1 (Li2AlH5) and –111 kJ mol–1 (Li2BH5). The inflection on both curves corresponds to the melting point of lithium hydride that is 965 K . If compare two heterogeneous channels it is evident that the reactions in which all products except hydrogen are solid, are more favorable for hydrogen gas evolving due to the spontaneity of the process.
Compared to gas phase dissociation, heterophase reactions are more appropriate for the purpose of producing hydrogen gas. The complex hydrides decompose spontaneously into solid products and hydrogen gas at standard conditions. On the other hand the thermal instability of the Li2MH5 species turns into a disadvantage of these materials because the reverse reaction seems difficult to be carried out. The stabilization of the complex hydrides Li2MH5 may be achieved by applying special technique e.g. matrix isolation  or increasing the pressure in the system.
The geometrical parameters, vibrational frequencies and thermodynamic properties of the complex gaseous hydrides Li2BH5 and Li2AlH5 have been theoretically determined using DFT/B3P86 and MP2 methods. The same methods were applied to compute the properties of the lower species considered as subunits of the complexes. The results obtained by DFT and MP2 methods are in good correspondence between each other; also good accordance was observed in the reference data available for lower species. The different possible channels of Li2MH5 decomposition have been examined. The enthalpies and Gibbs energies of dissociation reactions were calculated and analyzed. High stability of these complex hydrides regarding the decomposition into gaseous products was shown. However, spontaneous dissociation was revealed for the heterophase decomposition into solid products LiH and B/Al and hydrogen gas evolving. From our speculations based on a thermodynamic approach we can suggest the complexes Li2BH5 and Li2AlH5 may be potential materials for hydrogen storage application, provided the stabilization of them and reversibility of dehydrogenization process are achievable.
The authors are grateful to the British Gas Company through The Nelson Mandela African Institution of Science and Technology for supporting this study.
Authors participated equally in all steps to the completion of this work.