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Characteristics of Chemical Bond in Perovskite-Type Hydrides
CHAPT ER
19 Characteristics of Chemical Bond in Perovskite-Type Hydrides Yoshifumi Shinzato*, Kenji Komiya*, Yoshitaka Takahashi*, Hiroshi Yukawa*, Masahiko Morinaga* and Shinichi Orimo**
Contents
Abstract
1. Introduction 2. Calculation Procedure 3. Results and Discussion 3.1 Partial density of states 3.2 Chemical bond 3.3 Enthalpy changes in the dehydrogenation reactions, DH 3.4 Relationship between enthalpy change of perovskite-type hydrides and binary hydrides 4. Summary Acknowledgments References
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The electronic structure of typical perovskite-type hydrides, MMgH3 (M ¼ Na, K, Rb), CaNiH3 and SrPdH3, are simulated to understand the nature of the chemical bond between constituent ions in them using the DV-Xa molecular orbital method. For MMgH3, it is found that the valence band consists mainly of the H 1s and Mg 3s, 3p components, and the M s, p components are distributed over the empty conduction band. Thus, the covalent bond still remains between Mg and H ions, but the ionic bond is rather strong between them. The chemical bond between M and H ions is further ionic in character. On the other hand, for CaNiH3 and SrPdH3, covalent bond is dominant between Ni (or Pd) and H ions. Also, the enthalpy change in the dehydrogenation reaction, DH, is estimated for several reaction paths, using the plane-wave pseudopotential
* Department of Materials Science and Engineering, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan Corresponding author. E-mail: [email protected] ** Institute for Materials Research, Tohoku University, Katahira, Sendai 980-8577, Japan Advances in Quantum Chemistry, Vol. 54 ISSN 0065-3276, DOI 10.1016/S0065-3276(07)00019-6
r 2008 Elsevier Inc. All rights reserved
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method. For example, in the NaMgH3 system, DH is estimated to be 72.9 kJ/molH2 in the reaction, NaMgH3-NaH+Mg+H2, and 82.6 kJ/molH2 in the reaction, NaH-Na+1/2 H2. In agreement with these calculated results, NaMgH3 dehydrides in these two-step reactions at about 673 K according to recent experiments.
1. INTRODUCTION There are many perovskite-type hydrides being composed mainly of the 1A group elements and the 2A group elements in the periodic table. The crystal structure of perovskite-type hydride, KMgH3 is illustrated in Figure 19.1. In particular, the Mg-based perovskite-type hydrides, MMgH3 (M ¼ Na, K, Rb), are expected to be one of the materials for hydrogen storage because of their higher capacities of hydrogen than metal hydrides. However, any systematic investigations have not been carried out for the perovskite-type hydrides consisting of both the 1A group elements such as Li, Na, K, Rb, Cs and the 2A group elements such as Be, Mg, Ca, Sr, Ba in the periodic table. In addition, there are perovskitetype hydrides containing a transition metal (e.g., CaNiH3), but detailed information on the chemical bond remains unknown in these hydrides. The purpose of this study is to make clear the characteristics of the nature of the chemical bond in the perovskite-type hydrides, MMgH3 (M ¼ Na, K, Rb), CaNiH3, and SrPdH3, with the aid of electric structure calculations.
2. CALCULATION PROCEDURE The hydrogen positions in the perovskite-type hydrides are sometimes difficult to be determined experimentally. So, in this study, the crystal structure of the perovskite-type hydrides are optimized by the total energy minimization.
Figure 19.1 Schematic illustration of the perovskite-type hydride, KMgH3.
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For this purpose, the first-principles calculations based upon the density function theory (DFT) are performed with the generalized gradient approximation (GGA) [1]. The implementation of DFT employed here combines a plane-wave basis set with the total energy pseudopotential method, as is embodied in the CASTEP code [2]. The present calculations are based upon the ultrasoft pseudopotentials proposed by Vanderbilt [3]. The plane-wave cutoff energy is chosen to be 380 eV. This cutoff energy is found to achieve the convergence of the total energies within 0.03 eV/atom relative to the results with the cutoff energies up to 600 eV. The sampling in the reciprocal space is done with k-points grids of 6 6 6 for orthorhombic NaMgH3 [4], 6 6 6 for cubic KMgH3 [5], 5 5 2 for orthorhombic RbMgH3 [6], 8 8 8 for cubic CaNiH3 [7] and 8 8 8 for cubic SrPdH3 [8]. All the ions in the unit cell are allowed for full relaxation. The enthalpy change in the dehydrogenation reactions DH are also estimated by the total energy calculations, assuming several reaction paths for the dehydrogenation. The DV-Xa cluster method [9,10] is used for investigating the nature of the chemical bond between ions in the perovskite-type hydrides. This is a molecular orbital method, assuming the Hartree–Fock–Slater (HFS) approximation. In this method, the exchange-correlation between electrons is given by the Slater’s Xa potential. The matrix elements of Hamiltonian and the overlap integrals are calculated by a random sampling method. The molecular orbitals are constructed by a liner combination of numerically generated atomic orbitals (LCAO). The cluster models consisting of about 100 ions are constructed by using the optimized structure. For a characterization of the electronic structures and chemical bonding in the cluster, the bond order between ions and the ionicity (i.e., net charge) of each element in the cluster are estimated according to the Mulliken population analysis [11]. Here, the bond order is a measure of the strength of the covalent bond between ions in the hydride.
3. RESULTS AND DISCUSSION 3.1 Partial density of states As an example of perovskite-type hydrides, the partial density of states is shown in Figure 19.2 for cubic KMgH3. This is obtained after the geometry optimization using the pseudopotential method. It is found from this figure that the valence band consists mainly of the H 1s and Mg 3s, 3p components. The K 4s, 4p components are distributed over the empty conduction band. Thus, the covalent bond nature still remains between Mg and H ions. In Table 19.1, the result of the chemical bond for cubic KMgH3 is compared with that for Mg–H and K–H diatomic molecules. It is apparent that the covalent bond between Mg and H ions is much weaker in cubic KMgH3 than in the Mg–H diatomic molecule, instead the ionic bond is more enhanced. Additionally, the chemical bond between K and H ions is ionic in character. In other words, the ionic bonds between Mg and H ions and between K and H ions are stronger in KMgH3 than the corresponding
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5
Partial density of status
4 H-1s Mg-3d
3 Mg-3p 2 Mg-3s 1
K-4p 0
-15
-10
-5
0
5
10
15
K-4s Energy (eV)
Figure 19.2 Partial density of state for cubic KMgH3. Table 19.1 Comparison of the bond order and ionicity of elements between KMgH3 and diatomic molecules (K–H, Mg–H) Bond order
KMgH3
Diatomic molecule
Mg–H ˚) (2.00 A K–H ˚) (2.83 A Mg–H ˚) (1.76 A K–H ˚) (2.27 A
Ionicity
0.19
Mg
+1.08
0.03
K
+0.70
0.39
Mg
+0.55
0.20
K
+0.75
bonds in the Mg–H and K–H diatomic molecules, owing to the differences in the interionic distance among them. Similar trends are also seen in other perovskitetype hydrides such as NaMgH3 and RbMgH3. As an example of perovskite-type hydrides containing a transition element, the partial density of state for CaNiH3 is shown in Figure 19.3. The Fermi energy level falls on the Ni 3d band and there is a large overlap between the Ni 3d band and the H 1s band, resulting in the strong covalent interaction operating between Ni and H ions.
3.2 Chemical bond The DV-Xa molecular orbital calculations are performed with the cluster models constructed using the geometrically optimized crystal structures. The calculated
Partial density of state
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Ni-3d H-1s
Ni-4p
Ca-4p
Ca-4s Ni-4s
-15
-10
-5
0
5
10
15
Energy (eV)
Figure 19.3
Partial density of state for cubic CaNiH3.
lattice parameters agree with the experimental ones within 0.5% difference. Following the Mulliken population analysis, the ionicity of elements and the average bond order between ions in MMgH3 (M ¼ Na, K, Rb) are estimated and the results are shown in Figure 19.4a and b, respectively. The ionicitiy of H is similar among MMgH3 (M ¼ Na, K, Rb) and the value is about 0.6, which is negatively larger than the value of about 0.2 for H in typical metal hydrides. This means that the ionic character is more enhanced in the nature of the hydrogen–metal bond in MMgH3 than in metal hydrides. Also, as shown in Figure 19.4b, the Mg–H bond order is much larger than the M–H bond order in MMgH3 (M ¼ Na, K, Rb), indicating that the Mg–H covalent bond is stronger than the M–H covalent bond in MMgH3. By combining these results, it is evident that the Mg–H bond is rather ionic, but covalent interaction still remains. Also, the ionic interaction is dominant between K and H ions.
3.3 Enthalpy changes in the dehydrogenation reactions, DH The enthalpy changes in the dehydrogenation reactions, DH, are calculated for the perovskite-type hydrides MXH3 (M ¼ Na, K, Rb, Li, X ¼ Mg, Be). Here, LiBeH3 is assumed to have a cubic perovskite-type structure. According to ˚, the total energy calculation, the lattice parameter of LiBeH3 is about 3.15 A which satisfies the Westlake criterion that the H–H interaction should be longer ˚. than 2.1 A
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1.5 1.0
Mg
(a) M
Ionicity
0.5 Ionicity of H ion in the typical metal hydride
0.0 -0.5
H
-1.0 0.20 (b)
Mg-H
Bond order
0.15 0.10
M-H
0.05 M-Mg 0.00 NaMgH3
KMgH3
RbMgH3
MMgH3
Figure 19.4 (a) Ionicity of elements and (b) the bond order in the perovskite-type hydrides, MMgH3 (M ¼ Na, K, Rb).
The calculated results are shown in Figure 19.5. In this figure, the desirable range of DH is indicated by a narrow band to control the dehydrogenation temperature to be less than 400 K. In most cases, the calculated DH is out of this range, so the dehydrogenation temperature must be high. Here, the three different dehydrogenation reactions are simulated for MXH3. They are MXH3MH+X+H2, MXH3-M+XH2+1/2H2 and MXH3-M+X+3/2H2. For example, for the NaMgH3 system, DH is estimated to be 72.9 kJ/molH2 for the reaction (1): NaMgH3-NaH+Mg+H2, and 77.3 kJ/molH2 for the reaction (2): NaMgH3Na+Mg+3/2H2. So, DH becomes 86.2 kJ/molH2 for the reaction (3): NaHNa+1/2H2. In agreement with these calculated results, NaMgH3 dehydrides in the two-step reaction of (1) and (3) at 673 K according to recent experiments [12,13]. In the KMgH3 system, DH is estimated to be 99.1 kJ/molH2 for the reaction, KMgH3-K+Mg+3/2H2. In agreement with this calculated result, KMgH3 dehydrides in the one-step reaction according to recent experiment [13]. For the RbMgH3 system, DH is estimated to be 87.2 kJ/molH2 for the reaction, RbMgH3Rb+Mg+3/2H2. Judging from the calculation, RbMgH3 is expected to dehydride in this one-step reaction, but RbMgH3 dehydrides in two-step reactions and hence its dehydrogenation path is uncertain according to recent experiment [13]. Also, for the LiBeH3 system, the enthalpy change in the dehydrogenation reaction, DH, is estimated to be 38.3 kJ/molH2 for the reaction, LiBeH3-Li+Be+3/2H2,
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The enthalpy change in the dehydrogenation reaction, ∆H/kJmo1H2
-50
0
+50
MXH3
MH+X+H2
+100 M+X+3/2H2
MXH3 +150
MXH3
M+XH2+1/2H2
+200 NaMgH3 (6.0wt%)
KMgH3 (4.6wt%)
RbMgH3 [LiBeH3] (2.7wt%) (15.8wt%)
MXH3
Figure 19.5 Enthalpy change in the dehydrogenation reaction, DH, for the perovskite-type hydrides, MMgH3 (M ¼ Na, K, Rb) and LiBeH3. The number (wt%) in the parenthesis shown in the horizontal axis is the total amount of hydrogen to be release during dehydrogenation.
so its dehydrogenation is expected to occur in the one-step reaction at relatively low temperatures, if LiBeH3 has the cubic perovskite-type structure. For the Li–Be– H ternary system, a few experimental data have been reported [14]. However, it remains still unclear whether it is the perovskite-type or not.
3.4 Relationship between enthalpy change of perovskite-type hydrides and binary hydrides The relationship between DH1 and DH2 is shown in Figure 19.6, where DH1 and DH2 are the enthalpy change for the reactions, MXH3-M+X+3/2H2 and (XHX+1/2H2 or XH2-X+H2), respectively. There is a clear trend that DH1 increases with increasing DH2 except for the pervoskite-type hydride containing transition elements such as CaNiH3 and SrPdH3. For example, LiBeH3 has the lowest DH1 because of the lowest DH2 for BeH2. In case of CaNiH3 and SrPdH3, DH1 values are large, namely, 182 kJ/molH2 for CaNiH3 and 164 kJ/molH2 for SrPdH3, indicating that the strong covalent interaction between Ni (or Pd) and H atoms is operating in CaNiH3 (or SrPdH3) as explained earlier. This indicates that the hydrogen state in these hydrides is very stable. This result is supported by our recent calculation using energy density analysis [15]. Interionic Mg–H distances resembles between perovskite-type hydrides, MMgH3 and MgH2. For example, ˚ ˚ for NaMgH3, 2.00 A the optimized average Mg–H interionic distances are 1.95 A ˚ ˚ for KMgH3, and 2.02 A for RbMgH3, which are close to 1.96 A for MgH2. This trend is seen in CaNiH3 and SrPdH3.
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Figure 19.6 Correlation between enthalpy change of the perovskite-type hydrides, DH1, and enthalpy change of the binary hydrides, DH2, in the dehydrogenation reaction.
4. SUMMARY The nature of the chemical bond between ions is investigated in the perovskite-type hydrides, MMgH3 (M ¼ Na, K, Rb), CaNiH3, and SrPdH3 by the DV-Xa molecular orbital method. Also, the enthalpy changes in the dehydrogenation reactions are calculated using the pseudopotential method. It is found that the Mg–H bond is rather ionic, but the covalent interaction still remains to some extent. On the other hand, the M–H bond is further ionic. In the perovskite-type hydrides containing a transition element, CaNiH3 and SrPdH3, strong covalent interaction is operating between the transition element and hydrogen. So, their enthalpy changes are higher as compared to those of the other perovskite-type hydrides being composed of the 1A group element and the 2A group element.
ACKNOWLEDGMENTS The authors express sincere thanks to the staffs of the Computer Center, Institute for Molecular Science, Okazaki National Institute for the use of super-computers. This study was supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology of Japan, by the Japan Society for the Promotion of Science, and also by the 21st Century COE program ‘‘Nature-Guided Materials Processing’’.
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REFERENCES [1] J.P. Perdew, K. Burke, Y. Wang, Phys. Rev. B 54 (1996) 16533–16539. [2] V. Milman, B. Winkler, J.A. White, C.J. Pickard, M.C. Payne, E.V. Akhmatskaya, R.H. Nobes, Int. J. Quantum Chem. 77 (2000) 895–910. [3] D. Vanderbilt, Phys. Rev. B 41 (1990) 7892–7895. [4] A. Bouamrane, J.P. Laval, J.-P. Soulie, J.P. Bastide, Mater. Res. Bull. 35 (2000) 545–549. [5] J.P. Bastide, A. Bouamrane, P. Claudy, J.M. Letoffe, J. Less-Common Metals 136 (1987) L1–L4. [6] F. Gingl, T. Vogt, E. Akiba, K. Yvon, J. Alloys Compd. 282 (1999) 125–129. [7] T. Sato, D. Noreus, H. Takeshita, U. Ha¨ussermann, J. Solid State Chem. 178 (2005) 3381–3388. [8] W. Bronger, G. Ridder, J. Alloys Compd. 210 (1994) 53–55. [9] C. Satoko, M. Tsukada, H. Adachi, J. Phys. Soc. Jpn. 45 (1978) 1333–1340. [10] M. Morinaga, N. Yukawa, H. Adachi, J. Phys. Soc. Jpn. 53 (1984) 653–663. [11] R.S. Mulliken, J. Chem. Phys. 23 (1955) 1833–1840. [12] K. Ikeda, Y. Kogure, Y. Nakamori, S. Orimo, Scripta Mater. 53 (2005) 319–322. [13] K. Komiya, N. Morisaku, R. Rong, Y. Takahashi, Y. Shinzato, H. Yukawa, M. Morinaga, J. Alloys Compd. in press, doi: 10.1016/j.jallcom.2006.11.116. [14] A. Zaluska, L. Zaluski, J.O. Strow-Clsen, J. Alloys Compd. 307 (2000) 157–166. [15] Y. Shinzato, H. Yukawa, M. Morinaga, T. Baba, H. Nakai, Adv. Quantum Chem. 54 (2007) 145–160.
19 Characteristics of Chemical Bond in Perovskite-Type Hydrides Yoshifumi Shinzato*, Kenji Komiya*, Yoshitaka Takahashi*, Hiroshi Yukawa*, Masahiko Morinaga* and Shinichi Orimo**
Contents
Abstract
1. Introduction 2. Calculation Procedure 3. Results and Discussion 3.1 Partial density of states 3.2 Chemical bond 3.3 Enthalpy changes in the dehydrogenation reactions, DH 3.4 Relationship between enthalpy change of perovskite-type hydrides and binary hydrides 4. Summary Acknowledgments References
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The electronic structure of typical perovskite-type hydrides, MMgH3 (M ¼ Na, K, Rb), CaNiH3 and SrPdH3, are simulated to understand the nature of the chemical bond between constituent ions in them using the DV-Xa molecular orbital method. For MMgH3, it is found that the valence band consists mainly of the H 1s and Mg 3s, 3p components, and the M s, p components are distributed over the empty conduction band. Thus, the covalent bond still remains between Mg and H ions, but the ionic bond is rather strong between them. The chemical bond between M and H ions is further ionic in character. On the other hand, for CaNiH3 and SrPdH3, covalent bond is dominant between Ni (or Pd) and H ions. Also, the enthalpy change in the dehydrogenation reaction, DH, is estimated for several reaction paths, using the plane-wave pseudopotential
* Department of Materials Science and Engineering, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan Corresponding author. E-mail: [email protected] ** Institute for Materials Research, Tohoku University, Katahira, Sendai 980-8577, Japan Advances in Quantum Chemistry, Vol. 54 ISSN 0065-3276, DOI 10.1016/S0065-3276(07)00019-6
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method. For example, in the NaMgH3 system, DH is estimated to be 72.9 kJ/molH2 in the reaction, NaMgH3-NaH+Mg+H2, and 82.6 kJ/molH2 in the reaction, NaH-Na+1/2 H2. In agreement with these calculated results, NaMgH3 dehydrides in these two-step reactions at about 673 K according to recent experiments.
1. INTRODUCTION There are many perovskite-type hydrides being composed mainly of the 1A group elements and the 2A group elements in the periodic table. The crystal structure of perovskite-type hydride, KMgH3 is illustrated in Figure 19.1. In particular, the Mg-based perovskite-type hydrides, MMgH3 (M ¼ Na, K, Rb), are expected to be one of the materials for hydrogen storage because of their higher capacities of hydrogen than metal hydrides. However, any systematic investigations have not been carried out for the perovskite-type hydrides consisting of both the 1A group elements such as Li, Na, K, Rb, Cs and the 2A group elements such as Be, Mg, Ca, Sr, Ba in the periodic table. In addition, there are perovskitetype hydrides containing a transition metal (e.g., CaNiH3), but detailed information on the chemical bond remains unknown in these hydrides. The purpose of this study is to make clear the characteristics of the nature of the chemical bond in the perovskite-type hydrides, MMgH3 (M ¼ Na, K, Rb), CaNiH3, and SrPdH3, with the aid of electric structure calculations.
2. CALCULATION PROCEDURE The hydrogen positions in the perovskite-type hydrides are sometimes difficult to be determined experimentally. So, in this study, the crystal structure of the perovskite-type hydrides are optimized by the total energy minimization.
Figure 19.1 Schematic illustration of the perovskite-type hydride, KMgH3.
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For this purpose, the first-principles calculations based upon the density function theory (DFT) are performed with the generalized gradient approximation (GGA) [1]. The implementation of DFT employed here combines a plane-wave basis set with the total energy pseudopotential method, as is embodied in the CASTEP code [2]. The present calculations are based upon the ultrasoft pseudopotentials proposed by Vanderbilt [3]. The plane-wave cutoff energy is chosen to be 380 eV. This cutoff energy is found to achieve the convergence of the total energies within 0.03 eV/atom relative to the results with the cutoff energies up to 600 eV. The sampling in the reciprocal space is done with k-points grids of 6 6 6 for orthorhombic NaMgH3 [4], 6 6 6 for cubic KMgH3 [5], 5 5 2 for orthorhombic RbMgH3 [6], 8 8 8 for cubic CaNiH3 [7] and 8 8 8 for cubic SrPdH3 [8]. All the ions in the unit cell are allowed for full relaxation. The enthalpy change in the dehydrogenation reactions DH are also estimated by the total energy calculations, assuming several reaction paths for the dehydrogenation. The DV-Xa cluster method [9,10] is used for investigating the nature of the chemical bond between ions in the perovskite-type hydrides. This is a molecular orbital method, assuming the Hartree–Fock–Slater (HFS) approximation. In this method, the exchange-correlation between electrons is given by the Slater’s Xa potential. The matrix elements of Hamiltonian and the overlap integrals are calculated by a random sampling method. The molecular orbitals are constructed by a liner combination of numerically generated atomic orbitals (LCAO). The cluster models consisting of about 100 ions are constructed by using the optimized structure. For a characterization of the electronic structures and chemical bonding in the cluster, the bond order between ions and the ionicity (i.e., net charge) of each element in the cluster are estimated according to the Mulliken population analysis [11]. Here, the bond order is a measure of the strength of the covalent bond between ions in the hydride.
3. RESULTS AND DISCUSSION 3.1 Partial density of states As an example of perovskite-type hydrides, the partial density of states is shown in Figure 19.2 for cubic KMgH3. This is obtained after the geometry optimization using the pseudopotential method. It is found from this figure that the valence band consists mainly of the H 1s and Mg 3s, 3p components. The K 4s, 4p components are distributed over the empty conduction band. Thus, the covalent bond nature still remains between Mg and H ions. In Table 19.1, the result of the chemical bond for cubic KMgH3 is compared with that for Mg–H and K–H diatomic molecules. It is apparent that the covalent bond between Mg and H ions is much weaker in cubic KMgH3 than in the Mg–H diatomic molecule, instead the ionic bond is more enhanced. Additionally, the chemical bond between K and H ions is ionic in character. In other words, the ionic bonds between Mg and H ions and between K and H ions are stronger in KMgH3 than the corresponding
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5
Partial density of status
4 H-1s Mg-3d
3 Mg-3p 2 Mg-3s 1
K-4p 0
-15
-10
-5
0
5
10
15
K-4s Energy (eV)
Figure 19.2 Partial density of state for cubic KMgH3. Table 19.1 Comparison of the bond order and ionicity of elements between KMgH3 and diatomic molecules (K–H, Mg–H) Bond order
KMgH3
Diatomic molecule
Mg–H ˚) (2.00 A K–H ˚) (2.83 A Mg–H ˚) (1.76 A K–H ˚) (2.27 A
Ionicity
0.19
Mg
+1.08
0.03
K
+0.70
0.39
Mg
+0.55
0.20
K
+0.75
bonds in the Mg–H and K–H diatomic molecules, owing to the differences in the interionic distance among them. Similar trends are also seen in other perovskitetype hydrides such as NaMgH3 and RbMgH3. As an example of perovskite-type hydrides containing a transition element, the partial density of state for CaNiH3 is shown in Figure 19.3. The Fermi energy level falls on the Ni 3d band and there is a large overlap between the Ni 3d band and the H 1s band, resulting in the strong covalent interaction operating between Ni and H ions.
3.2 Chemical bond The DV-Xa molecular orbital calculations are performed with the cluster models constructed using the geometrically optimized crystal structures. The calculated
Partial density of state
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Ni-3d H-1s
Ni-4p
Ca-4p
Ca-4s Ni-4s
-15
-10
-5
0
5
10
15
Energy (eV)
Figure 19.3
Partial density of state for cubic CaNiH3.
lattice parameters agree with the experimental ones within 0.5% difference. Following the Mulliken population analysis, the ionicity of elements and the average bond order between ions in MMgH3 (M ¼ Na, K, Rb) are estimated and the results are shown in Figure 19.4a and b, respectively. The ionicitiy of H is similar among MMgH3 (M ¼ Na, K, Rb) and the value is about 0.6, which is negatively larger than the value of about 0.2 for H in typical metal hydrides. This means that the ionic character is more enhanced in the nature of the hydrogen–metal bond in MMgH3 than in metal hydrides. Also, as shown in Figure 19.4b, the Mg–H bond order is much larger than the M–H bond order in MMgH3 (M ¼ Na, K, Rb), indicating that the Mg–H covalent bond is stronger than the M–H covalent bond in MMgH3. By combining these results, it is evident that the Mg–H bond is rather ionic, but covalent interaction still remains. Also, the ionic interaction is dominant between K and H ions.
3.3 Enthalpy changes in the dehydrogenation reactions, DH The enthalpy changes in the dehydrogenation reactions, DH, are calculated for the perovskite-type hydrides MXH3 (M ¼ Na, K, Rb, Li, X ¼ Mg, Be). Here, LiBeH3 is assumed to have a cubic perovskite-type structure. According to ˚, the total energy calculation, the lattice parameter of LiBeH3 is about 3.15 A which satisfies the Westlake criterion that the H–H interaction should be longer ˚. than 2.1 A
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1.5 1.0
Mg
(a) M
Ionicity
0.5 Ionicity of H ion in the typical metal hydride
0.0 -0.5
H
-1.0 0.20 (b)
Mg-H
Bond order
0.15 0.10
M-H
0.05 M-Mg 0.00 NaMgH3
KMgH3
RbMgH3
MMgH3
Figure 19.4 (a) Ionicity of elements and (b) the bond order in the perovskite-type hydrides, MMgH3 (M ¼ Na, K, Rb).
The calculated results are shown in Figure 19.5. In this figure, the desirable range of DH is indicated by a narrow band to control the dehydrogenation temperature to be less than 400 K. In most cases, the calculated DH is out of this range, so the dehydrogenation temperature must be high. Here, the three different dehydrogenation reactions are simulated for MXH3. They are MXH3MH+X+H2, MXH3-M+XH2+1/2H2 and MXH3-M+X+3/2H2. For example, for the NaMgH3 system, DH is estimated to be 72.9 kJ/molH2 for the reaction (1): NaMgH3-NaH+Mg+H2, and 77.3 kJ/molH2 for the reaction (2): NaMgH3Na+Mg+3/2H2. So, DH becomes 86.2 kJ/molH2 for the reaction (3): NaHNa+1/2H2. In agreement with these calculated results, NaMgH3 dehydrides in the two-step reaction of (1) and (3) at 673 K according to recent experiments [12,13]. In the KMgH3 system, DH is estimated to be 99.1 kJ/molH2 for the reaction, KMgH3-K+Mg+3/2H2. In agreement with this calculated result, KMgH3 dehydrides in the one-step reaction according to recent experiment [13]. For the RbMgH3 system, DH is estimated to be 87.2 kJ/molH2 for the reaction, RbMgH3Rb+Mg+3/2H2. Judging from the calculation, RbMgH3 is expected to dehydride in this one-step reaction, but RbMgH3 dehydrides in two-step reactions and hence its dehydrogenation path is uncertain according to recent experiment [13]. Also, for the LiBeH3 system, the enthalpy change in the dehydrogenation reaction, DH, is estimated to be 38.3 kJ/molH2 for the reaction, LiBeH3-Li+Be+3/2H2,
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The enthalpy change in the dehydrogenation reaction, ∆H/kJmo1H2
-50
0
+50
MXH3
MH+X+H2
+100 M+X+3/2H2
MXH3 +150
MXH3
M+XH2+1/2H2
+200 NaMgH3 (6.0wt%)
KMgH3 (4.6wt%)
RbMgH3 [LiBeH3] (2.7wt%) (15.8wt%)
MXH3
Figure 19.5 Enthalpy change in the dehydrogenation reaction, DH, for the perovskite-type hydrides, MMgH3 (M ¼ Na, K, Rb) and LiBeH3. The number (wt%) in the parenthesis shown in the horizontal axis is the total amount of hydrogen to be release during dehydrogenation.
so its dehydrogenation is expected to occur in the one-step reaction at relatively low temperatures, if LiBeH3 has the cubic perovskite-type structure. For the Li–Be– H ternary system, a few experimental data have been reported [14]. However, it remains still unclear whether it is the perovskite-type or not.
3.4 Relationship between enthalpy change of perovskite-type hydrides and binary hydrides The relationship between DH1 and DH2 is shown in Figure 19.6, where DH1 and DH2 are the enthalpy change for the reactions, MXH3-M+X+3/2H2 and (XHX+1/2H2 or XH2-X+H2), respectively. There is a clear trend that DH1 increases with increasing DH2 except for the pervoskite-type hydride containing transition elements such as CaNiH3 and SrPdH3. For example, LiBeH3 has the lowest DH1 because of the lowest DH2 for BeH2. In case of CaNiH3 and SrPdH3, DH1 values are large, namely, 182 kJ/molH2 for CaNiH3 and 164 kJ/molH2 for SrPdH3, indicating that the strong covalent interaction between Ni (or Pd) and H atoms is operating in CaNiH3 (or SrPdH3) as explained earlier. This indicates that the hydrogen state in these hydrides is very stable. This result is supported by our recent calculation using energy density analysis [15]. Interionic Mg–H distances resembles between perovskite-type hydrides, MMgH3 and MgH2. For example, ˚ ˚ for NaMgH3, 2.00 A the optimized average Mg–H interionic distances are 1.95 A ˚ ˚ for KMgH3, and 2.02 A for RbMgH3, which are close to 1.96 A for MgH2. This trend is seen in CaNiH3 and SrPdH3.
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Figure 19.6 Correlation between enthalpy change of the perovskite-type hydrides, DH1, and enthalpy change of the binary hydrides, DH2, in the dehydrogenation reaction.
4. SUMMARY The nature of the chemical bond between ions is investigated in the perovskite-type hydrides, MMgH3 (M ¼ Na, K, Rb), CaNiH3, and SrPdH3 by the DV-Xa molecular orbital method. Also, the enthalpy changes in the dehydrogenation reactions are calculated using the pseudopotential method. It is found that the Mg–H bond is rather ionic, but the covalent interaction still remains to some extent. On the other hand, the M–H bond is further ionic. In the perovskite-type hydrides containing a transition element, CaNiH3 and SrPdH3, strong covalent interaction is operating between the transition element and hydrogen. So, their enthalpy changes are higher as compared to those of the other perovskite-type hydrides being composed of the 1A group element and the 2A group element.
ACKNOWLEDGMENTS The authors express sincere thanks to the staffs of the Computer Center, Institute for Molecular Science, Okazaki National Institute for the use of super-computers. This study was supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology of Japan, by the Japan Society for the Promotion of Science, and also by the 21st Century COE program ‘‘Nature-Guided Materials Processing’’.
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