First-principles study of hydrogen vacancies in lithium amide doped with titanium and niobium

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 8 ( 2 0 1 3 ) 1 1 3 0 3 e1 1 3 1 2

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First-principles study of hydrogen vacancies in lithium amide doped with titanium and niobium Liping Cheng, Baoen Xu, Xuejing Gong, Xiaoyan Li*, Yanli Zeng, Lingpeng Meng* College of Chemistry and Material Science, Hebei Normal University, Road East of 2nd Ring South, Shijiazhuang 050024, China

article info

abstract

Article history:

The crystal and electronic structures, the formation energy of H vacancies, and the

Received 27 April 2013

diffusion path of the H atom (i.e., diffusion path of H vacancy) in unsubstituted and

Received in revised form

substituted LiNH2 crystal were investigated by periodic first-principles calculations. The

19 June 2013

bonding characters between atoms were studied by topological analysis of electron den-

Accepted 22 June 2013

sity. Our calculations reveal that substitution of the Li atom with Ti or Nb favors the for-

Available online 20 July 2013

mation of hydrogen vacancies adjacent to substitution, and the existence of an H vacancy and Ti or Nb substitution can cause weakening of nearby NeH bonds, which facilitates N

Keywords:

eH bond dissociation. The minimum energy paths of H diffusion show that the substitu-

Lithium amide

tion can reduce the energy barrier and thus favor H diffusion in the bulk phase of LiNH2.

Hydrogen storage

Copyright ª 2013, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.

Vacancy Substitution Diffusion path First-principles calculations

1.

Introduction

Energy is the material basis of the survival and development of human society. With the very rapid development of the global economy, the human demand for energy is increasing. However, oil reserves are declining, thus the ongoing search for alternative sources of energy is expected. Hydrogen is an ideal energy carrier because its use does not cause pollution and it has abundant reserves. Hydrogen as a green energy carrier has gained much attention. The wide use of hydrogen for producing clean energy of car fuel in the future has been forecasted [1]. However, the effective use of hydrogen as an energy carrier has been impeded by the difficulty of hydrogen storage.

Promising methods for storing hydrogen are pressurization of the gas, its conversion to a cryogenic liquid, adsorption on carbon nanotubes, and conversion to clathrate hydrates and other chemical forms [2e5]. The storage of hydrogen in various materials has been found to be more suitable for fuel applications because of its safety and efficiency and its ease of transport [6,7]. Hydrides of light metals come closest to meeting such practical requirements. Light-metal hydrides, such as Mg(NH2)2 [8], LiNH2 [9], LiBH4 [10,11], Ca(NH2BH3)2 [12,13], and Li4BN3H10 [14], which are among the onboard hydrogen storage candidates, have moderate gravimetric and volumetric storage capacity, low cost, and readily available sources. They have the highest potential for use as hydrogen storage materials [15].

* Corresponding authors. Tel./fax: þ86 311 80787427. E-mail addresses: [email protected] (X. Li), [email protected] (L. Meng). 0360-3199/$ e see front matter Copyright ª 2013, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijhydene.2013.06.099

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Since the first report by Chen et al. in 2002 [16], the thermodynamics and mechanisms of reversible hydrogen release by metal amides and imides have been extensively studied. In particular, LiNH2 has attracted considerable attention as a hydrogen storage material [17e19]. This compound releases H2 according to the following reaction [20]: LiNH2 þ LiH/Li2 NH þ H2

(1)

The theoretical hydrogen yield of this reaction is 6.5 wt% at typical operating temperatures of 150e350  C [21]. The reaction enthalpy is 67 kJ/(mol H2) [22,23], which is close to the theoretical value, 73.6 kJ/(mol H2) [24]. The reaction in Equation (1) has been shown to proceed in two steps: decomposition of LiNH2 to release NH3 and lithium imides, and reaction of NH3 with LiH to form H2 [25]. 2LiNH2 /Li2 NH þ NH3

(2)

NH3 þ LiH/LiNH2 þ H2

(3)

The first step (Equation (2)) has been reported to be the bottleneck of the entire reaction [26]. The conversion process of LiNH2 to Li2NH involves Li/H mass transport through bulk crystalline phase. David et al. [27] suggested that the reaction of the intermediates involve substoichiometric phases. Hazrati et al. [28] suggested that the dehydrogenation of lithium amide (LiNH2) þ lithium (LiH) system involves mass transport in the bulk (amide) crystal through lattice defects. Lithium/ hydrogen interstitials and vacancies play an important role in mass transport and ionic conduction between LiNH2 and Li2NH. Hoang et al. [29] propose that hydrogen interstitials and vacancies are responsible for forming and breaking NeH bonds, which is essential in the Li amide/imide reaction. Miceli et al. [30] noted that the interconversion of LiNH2 and Li2NH occurs by diffusion of the charged species Hþ and Liþ. Although LiNH2 has a high hydrogen storage capacity, its use still shows several problems such as high operating temperatures and poor dynamic performance. Much work has been done to render the hydrogenation or dehydrogenation process reversible under practical conditions. Strategies that have been explored include addition of metals, nonmetals, or other substances as catalysts [31e37]. By thermal desorption mass spectroscopy, Ichikawa et al. [32] studied the properties of LiNH2 with Ni, Fe and Co metals and TiCl3 dopants. They showed that substitution of Li with highly electronegative elements could reduce the decomposition temperature of LiNH2 and especially adding TiCl3 would facilitate the release of hydrogen at lower temperature. Liang et al. [33] used a gasesolid reaction method to synthesize a LieMgeNeH complex system. They found that partial substitution of Li by Mg could destabilize LiNH2, and the dehydriding temperature decreased with increasing Mg concentration. These observations have been verified by theoretical calculations [34]. A 2:1 mixture of LiNH2 and CaH2 under vacuum at 300  C can be used to prepare a LieCaeNeH complex that is able to absorb and desorb hydrogen at lower temperatures [35]. By comparing the formation energies of the dopants on the Li site, Hazrati et al. [28] reported that Mg and Ti can easily be incorporated into LiNH2, whereas incorporation of Sc and Ca is thermodynamically unfavorable. Gupta and Gupta [38]

calculated the change of reaction enthalpy with a Cu- or Nisubstituted LiNH2, and found that the values of reaction enthalpy decrease, and the influence of Ni is significant. Nakamori and Orimo [39] proposed that alloying elements are useful in changing the structural stability and improving the dehydrogenating properties of the LiNH2 system. Based on Hazrati and Ichikawa’s results [28,32], Ti has been found that it can easily be incorporated into LiNH2, and the addition of TiCl3 to LiNH2eLiH could facilitate the release of hydrogen at lower temperature. NbF5 and NbCl5 doping may lower the hydrogen desorption temperature and promote reversible hydrogen storage in Ca(BH4)2 [40]. Therefore, in this work, Ti and Nb were chosen for substitution in LiNH2. The effects of H vacancies due to doping of Ti or Nb into the bulk LiNH2 were also investigated. Here, we focused on clarifying the geometrical and electronic structures and interatomic bonding effect of H vacancies in Ti- or Nb-substituted LiNH2. We also explored the hydrogen diffusion process in unsubstituted and Ti- or Nb-substituted LiNH2 with H vacancies.

2.

Computational methods

The first-principles calculations adopted in the present study are based on density functional theory (DFT) [41] using the generalized gradient approximation with the Perdew and Wang (PW91) [42,43] exchange correlation function. We used the projector augmented wave method [44] embodied in the Vienna ab initio simulation program (VASP) [45]. The plane wave expansion of the KohneSham orbitals was employed. The cutoff energy was set to 470 eV to attain sufficient accuracy, and the Brillouin zone (BZ) k-point 2  2  2 grid was applied according to the MonkhorstePack scheme [46]. A 2  1  1 supercell was chosen to model the bulk material. The supercell was optimized in terms of volume and shape, and its internal atomic positions were fully relaxed. During the energy minimizations, the convergence criteria for energy and force were set to 1  106 eV and 0.05 eV A1, respectively. We did not consider the charge of atoms in the entire framework, that is, atoms were electrically neutral and no background charge was required. The atomic valence electrons considered in the calculations are H 1s1, Li 2s12p0, N 2s22p3, Ti 4s13d3, Nb 4p65s14d4. To obtain deeper insight into the bonding nature between atoms in LiNH2, we performed a topological analysis of the electron density using a cluster model. The cluster was the 2  1  1 supercell whose configuration had been optimized by VASP as mentioned above. The cluster was subjected to ab initio calculations at the B3LYP/6-31G(d,p) level using the Gaussian 03 package [47] to generate the wave functions and density matrix. Afterward, the AIM 2000 program [48] was used to perform the topological analysis of the electron density. The minimum energy path (MEP) of the hydrogen diffusion process was identified by using the climbing imageenudged elastic band method (CIeNEB) [49,50]. In this method, a chain of images are interpolated between the initial and the final states. By minimizing the energy of this string of images, the MEP is revealed.

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Fig. 1 e The optimized unit cell of LiNH2 crystal. Large deep blue, azure and pink spheres represent Li, N and H atoms, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

was used to replace the Li14 atom. Meanwhile, the H9 atom linked to N5 was removed to create an H vacancy. The formation enthalpy (Hform) is defined as the different between the total energy of a system and the energy of the individual atoms [7]. The Hform of each Ti/Nb-doped Li16N16H32 is negative, respectively 762.24 and 748.32 (kJ mol1 H2), implying that each Ti/Nb-doped Li16N16H32 is stable, and their absolute values are lower than that of undoped Li16N16H32 (785.96), showing that Ti/Nb-doped lithium amide hydrides are less stable than pure Li16N16H32. In another word, the doping of Ti and Nb can lower the temperature of dehydrogenation of Li16N16H32 and facilitate its decomposition. The substitution energies of Ti- or Nb-substituted system were calculated and are listed in Table 2. The substitution energies (Es) of Ti- or Nb-substituted system, respectively, are 3.93 and 6.24 eV, which suggest that Ti is favorable to replace Li in LiNH2. The formation energy of the H vacancy, that is, the energy cost to introduce the vacancy into perfect and defective lattice was calculated using the following expression: Ef ðHÞ ¼ Etot ðLi16 N16 H31 Þ þ 1=2EH2  Etot ðLi16 N16 H32 Þ Ef ðHÞ ¼ Etot ðLi15 MN16 H31 Þ þ 1=2EH2  Etot ðLi15 MN16 H32 Þ ðM ¼ Ti; NbÞ

3.

Results and discussion

3.1.

Crystal structure

LiNH2 crystallizes in a body-centered tetragonal symmetry with the I4 space group (No. 82) [51,52]. The optimized crystal structure of LiNH2 is shown in Fig. 1. The unit cell contains eight formulas of LiNH2, and there are four NH2 groups around every Li atom, and there are four Li atoms around every NH2 group. The optimized lattice parameters of LiNH2 are a ¼ b ¼ 4.997  A and c ¼ 10.285  A, which are consistent with the neutron-scattering experimental values of a ¼ b ¼ 5.034  A and c ¼ 10.255  A [52], and in reasonable agreement with other calculations (a ¼ b ¼ 5.026  A and c ¼ 10.255  A) [53]. The optimized fractional coordinates of the relaxed atoms Li, N, and H are listed in Table 1. For comparison, the experimental and other theoretical results are also given in Table 1.

3.2.

The H vacancy in the supercell

The next discussions are all based on the 2  1  1 supercell model, as shown in Fig. 2. Here, a transition metal (Ti or Nb)

(4)

(5)

where Ef (H) is the formation energy of the H vacancy, Etot(Li16N16H31) and Etot(Li16N16H32) are the total energies of a supercell with and without the vacancy, and Etot(Li15MN16H31) and Etot(Li15MN16H32) are the total energies of Ti- or Nbsubstituted system with and without the vacancy, and EH2 is the energy of the H2 molecule, which is calculated by placing a A. The H2 molecule in a cubic box with each side measuring 10  calculated formation energies of the H vacancies at various positions are listed in Table 2. It can be seen from Table 2 that the formation energies of H vacancies in the perfect supercell are about 2.88 eV, which is in good agreement with the reported results of Wang et al. [8]. The formation energies of the H vacancies are markedly lowered when Ti and Nb substitute the Li atom. In particular, the formation energy of the H vacancy near Ti and Nb atoms are lowered drastically. For instance, Ef(H9) and Ef(H23), which are values for H vacancies near the Ti atom, are 1.26 and 1.27 eV, respectively. However, these values are more negative (1.54 and 1.63 eV, respectively) for the vacancies near the Nb atom. These changes indicate that the substitution of Ti or Nb for the Li atom favor the formation of H vacancies, and thus aid H diffusion in the bulk phase of LiNH2. In addition, the effect of Nb substitution is greater than that of Ti substitution.

Table 1 e The optimized fractional coordinates of atoms in LiNH2. Atom Li

N H

This work

Experiment

Theoretical work

(0,0,0) (0,0.5,0.25) (0,0.5,0.0064) (0.2309,0.2462,0.1159) (0.2300,0.1150, 0.1929) (0.4147,0.3364,0.1243)

(0,0,0) (0,0.5,0.25) (0,0.5,0.0025) (0.2286,0.2499,0.1158) (0.2429,0.1285,0.1910) (0.3840,0.3512,0.1278)

(0,0,0) (0,0.5,0.25) (0, 0.5,0.0042) (0.2284,0.2452,0.1148) (0.2783,0.1816,0.2057) (0.3492,0.4056,0.1239)

Experimental data from Ref. [52], others Theoretical data from Ref. [53].

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Fig. 2 e The 2 3 1 3 1 supercell of LiNH2. (a) Li16N16H32. (b) Li16N16H31 with an H vacancy. (c) Ti-substituted Li15TiN16H31 with an H vacancy. (d) Nb-substituted Li15NbN16H31 with an H vacancy.

The NeH bond lengths in the perfect supercell are in the range of 1.0263e1.0281  A (Table 3) which are close to the Wang’s calculated value of 1.030 and 1.032  A [8]. They showed no apparent change even in the presence of a nearby H vacancy. An exception to this general observation is the bond length of N5eH11, which increased from 1.0263 to 1.0330  A; this bond is nearest to the H9 vacancy. Therefore, an H vacancy has less effect on more distant NH2 groups. Ti and Nb substitution has great effect on NeH bond around the substitution atom. All of NeH bond, which nearby Nb, are become longer, while in Ti substitution system, only part of NeH bond increase. The bond length changes caused by the Nb substitution are larger than those caused by Ti substitution. The increased bond length results reveal that Ti and Nb

Table 2 e The substitution energy of Ti/Nb and the formation energy of H vacancy in Li16N16H32, Li15TiN16H32 and Li15NbN16H32. Supercell

Etot

Li16N16H32 306.50 Li15TiN16H32 308.43 Li15NbN16H32 308.42

Es(Ti/Nb) Ef(H5) Ef(H9) Ef(H10) Ef(H23) e 3.93 6.24

2.87 0.27 0.08

2.89 1.26 1.54

2.89 0.45 0.31

2.88 1.27 1.63

substitution weakened the NeH bond, which favors hydrogen release. Moreover, in perfect LiNH2 system, the effects of substitution are larger than those of vacancy formation. When the vacancy exists, the effects of substitution become obviously increased.

3.3.

Electronic structure

The calculated total and partial density of states (DOS) of Li16N16H32, Li16N16H31, Li15TiN16H31, and Li15NbN16H31 are plotted in Fig. 3. For the total DOS of perfect Li16N16H32, there are four energy bands below the Fermi level (see Fig. 3(a)). The lowest energy band from 17 to 15 eV can be assigned to the mixture of N s and H s states. The second band from 8 to 6 eV is attributed to the N p and H s states. The band from 2.7 to 5 eV arises from the N s, p and H s states with slight contribution from the Li s and p states. The highest energy band in the valence region is mainly due to N p states and partially due to the Li p states. The analysis of the DOS suggests that the sp hybridization between N and H results in a strong covalent NeH bond, and the interactions involving Li show a highly ionic character. Fig. 3(b) shows the total and partial DOS of Li16N16H31. The results indicate an H vacancy present in Li16N16H31 that is near the H11 atom. All bands of the total DOS in Li16N16H31 are

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total DOS of Li15TiN16H31 and Li15NbN16H31 are relatively similar to that of Li16N16H31, but they are narrower in band gap and their bands are located in a lower energy region. There are slight contributions of the Ti or Nb s, p, and d electrons to the band at 16 to 15 eV, which indicate N5eH11 bonding interaction. The s, p, and d electrons of the Ti or Nb atom mainly contribute to the valence band states at 7.5 to 2.5 eV. Bader [54,55] proposed the topological analysis of electron densities in the theory of the atom in molecule (AIM). It is known that the electron density at the bond critical point (BCP), r(rc), is positively related to the strength of the bond. In general, the larger the value of r(rc), the stronger the chemical bond. In addition, the Laplacian of the electron density (V2r(rc)) can represent the characteristic of the bond. Values of V2r(rc) < 0 indicate the characteristics of a covalent bond, in which case the electron density is concentrated in the bond axis. Values of V2r(rc) > 0 show interactions of closed shells, in which case the electron density is dispersed [56]. In this section, we discuss the bonding character between atoms in LiNH2 on the basis of a cluster model and topological analysis of electron density. The clusters were the optimized 2  1  1 supercell of the LiNH2 crystal, as described in Section 2. In order to make the calculation model more close to ideal cell structure, we take the whole 2  1  1 supercell (Li16N16H32, Li16N16H31, Li15TiN16H31, and Li15NbN16H31) as the cluster model. The topological analysis of electron density is performed on the supercell and all of the topological

Table 3 e The interatomic distance (in Angstrom) in the perfect and Ti, Nb substituted supercell with and without the H vacancy. Supercell Li16N16H32 Li16N16H31 Li15TiN16H32 Li15NbN16H32 Li15TiN16H31 Li15NbN16H31

N5eH11

N2eH2

N6eH12

N12eH22

1.0263 1.0330 1.0305 1.0338 1.0402 1.0451

1.0280 1.0289 1.0480 1.0397 1.0657 1.0894

1.0263 1.0266 1.0278 1.0340 1.0309 1.0343

1.0281 1.0281 1.0295 1.0349 1.0287 1.0291

shifted to an energy level about 2 eV higher than that of the bands of Li16N16H32. The lowest energy band at around 15 eV is almost the same as that of defect-free Li16N16H32; therefore, this band should describe the general NeH bonding interaction. A remarkable feature in the DOS of Li16N16H31 is that a new band emerged at 13.7 to 12.5 eV; the height of the new band is very low compared with the heights of the lowest energy band. These changes are due to the interaction between the N5 s and H11 s states, and indicate that the NeH bond was weakened by the presence of the nearby H vacancy. These findings are consistent with the analysis of the NeH bond length in Section 3.2. The DOS of the Ti- and Nb-substituted systems, Li15TiN16H31 and Li15NbN16H31, in which H11 is the atom near the H vacancy, are shown in Fig. 3(c) and (d). The profiles of the

(a)

H11(1s)

0.1 0.0 1.5

N5(2s) N5(2p)

1.0 0.5

Li14(2s) Li14(2p)

-15

-10

-5 Energy/eV

(c)

40 30 20 10 0 0.5 0.4 0.3 0.2 0.1 0.0 2.0 1.5 1.0 0.5 0.0 0.3 0.2 0.1 0.0 4.5 3.0 1.5 0.0 -20

0

5

10

50 40 30 20 10 0 0.5 0.4 0.3 0.2 0.1 0.0 2.0 1.5 1.0 0.5 0.0 0.20 0.15 0.10 0.05 0.00 -20

EF Li15TiN16H31

H11(1s)

-1

-1

DOS/electrons.eV

0.2

0.0 0.20 0.15 0.10 0.05 0.00 -20

DOS/electrons.eV

Li16N16H32

-1

EF

DOS/electrons.eV

DOS/electrons.eV

-1

50 40 30 20 10 0 0.3

N5(2s) N5(2p) Ti1(4s) Ti1(3p) Ti1(3d) -15

-10

-5 Energy/eV

0

5

40 30 20 10 0 0.5 0.4 0.3 0.2 0.1 0.0 1.6 1.2 0.8 0.4 0.0 0.3 0.2 0.1 0.0 3.0

(b)

EF

Li16N16H31

H11(1s)

N5(2s) N5(2p)

Li14(2s) Li14(2p)

-15

-10

-5 Energy/eV

(d)

0

5

EF Li NbN H 15 16 31

H11(1s)

N5(2s) N5(2p) Nb1(5s) Nb1(4p) Nb1(4d)

1.5 10

0.0 -20

10

-15

-10

-5 Energy/eV

0

5

10

Fig. 3 e The total and partial density of states of Li16N16H32 (a), Li16N16H31 (b), Li15TiN16H31 (c), and Li15NbN16H31 (d).

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Table 4 e Topological properties at the BCPs of NeH and metal-N bonds in the fragments of LiN4H8, LiN4H7, TiN4H7 and NbN4H7. V2r(rc)

r(rc)

N5eH9 N5eH11 N2eH2 N2eH4 N11eH21 N11eH23 N16eH30 N16eH32 N5eLi14/Ti/Nb N2eLi14/Ti/Nb N11eLi14/Ti/Nb N16eLi14/Ti/Nb

LiN4H8

LiN4H7

TiN4H7

NbN4H7

LiN4H8

LiN4H7

TiN4H7

NbN4H7

0.3225 0.3243 0.3224 0.3246 0.3232 0.3243 0.3230 0.3250 0.0216 0.0216 0.0204 0.0203

e 0.3137 0.3211 0.3249 0.3226 0.3234 0.3240 0.3240 0.0269 0.0206 0.0198 0.0184

e 0.3063 0.2976 0.3242 0.3201 0.2897 0.3142 0.3220 0.1358 0.0672 0.0748 0.0617

e 0.3021 0.2820 0.3259 0.3226 0.3064 0.3140 0.3234 0.1514 0.0899 0.0599 0.0588

1.5208 1.5664 1.5200 1.5700 1.5380 1.5528 1.5356 1.5596 0.0996 0.1000 0.1004 0.1000

e 1.3920 1.4976 1.5680 1.5540 1.5420 1.5600 1.5424 0.1296 0.1004 0.1008 0.0932

e 1.3816 1.3104 1.5944 1.5352 1.3020 1.4952 1.5612 0.3452 0.2652 0.3044 0.2360

e 1.3668 1.1604 1.6176 1.5488 1.4416 1.4984 1.5724 0.3432 0.3612 0.2380 0.2144

properties are calculated. For conciseness, we present a part of molecular graph of the cluster only. This part contains some atoms around the substituted atom and the H vacancy. The topological properties, r(rc) and V2r(rc), and the AIM molecular graphs for the fragments of LiN4H8, LiN4H7, TiN4H7, and NbN4H7 are shown in Table 4 and Fig. 4. As shown in Fig. 4,

there is a BCP between each pair of N and H atoms and each pair of N and metal atoms. There is also a bond path linked between each pair of atoms. These results suggest that a chemical bond is formed between each pair of atoms. However, these bonds have different strengths and characteristics. It can be seen from Table 4 that the electron density r(rc) and

Fig. 4 e AIM molecular graphs of total electron density for the fragments of LiN4H8 (a), LiN4H7 (b), TiN4H7 (c) and NbN4H7 (d). Small red dots represent the BCPs. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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Table 5 e Topological properties at the BCPs of NeH and metal-N bonds in the fragments of TiN4H8 and NbN4H8. V2r(rc)

r(rc)

N5eH9 N5eH11 N2eH2 N2eH4 N11eH21 N11eH23 N16eH30 N16eH32 N5eLi14/Ti/Nb N2eLi14/Ti/Nb N11eLi14/Ti/Nb N16eLi14/Ti/Nb

TiN4H8

NbN4H8

TiN4H8

NbN4H8

0.3090 0.3211 0.3086 0.3214 0.3196 0.3065 0.3202 0.3057 0.0651 0.0650 0.0784 0.0782

0.3155 0.3186 0.3147 0.3184 0.3127 0.3189 0.3130 0.3186 0.0710 0.0709 0.0596 0.0597

1.4676 1.5872 1.4632 1.5896 1.5468 1.4708 1.5520 1.4644 0.2428 0.2424 0.2844 0.2844

1.5280 1.5672 1.5216 1.5656 1.4696 1.5452 1.4716 1.5432 0.2536 0.2532 0.2288 0.2288

the Laplacian V2r(rc) at the BCP of N5eH9 in defect-free LiN4H8 are 0.3225 and 1.5208, respectively, signifying a typical covalent bond. The values of r(rc) and V2r(rc) for all NeH bonds in LiN4H8 have no apparent difference, that is, the r(rc) values are about 0.32 and the V2r(rc) values are about 1.5. Thus, the NeH bonds in LiN4H8 are almost equivalent. In contrast, the r(rc) of the NeLi bond is only 0.0216, and V2r(rc) is a small positive number (0.0996). This difference indicates that the NeLi

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bonding results from an interaction of closed shells, that is, it is mainly ionic. The Nemetal bonds in LiN4H7, TiN4H7, and NbN4H7 are similar to that in LiN4H8. We also adopt the same method to calculate the topological properties of Ti and Nb substitution without vacancy (TiN4H8, and NbN4H8), listing in Table 5. From Table 5, it can be seen that in the substituted supercell, the electron densities at BCPs of one NeH bond decrease, which means that this NeH bond was weakened, and the effects of substitution is larger than those of vacancy formation (Table 4). But when the vacancy exists, the effects of substitution become obviously increased. These results are consistent with the change tendency of bond lengths. When a defect was introduced into the system, the bonds near the defect were influenced. For example, when H9 was removed from LiN4H8, forming LiN4H7, the r(rc) of N5eH11 decreased from 0.3243 to 0.3137, but the other bonds relatively far from the H vacancy were nearly unchanged. Therefore, the presence of an H vacancy weakens the bonds near it. This situation can be also seen in the Ti- and Nb-substituted systems, TiN4H7 and NbN4H7. The Ti or Nb substitution had a larger effect on the bonds around the metal atom. For instance, the r(rc) and V2r(rc) of N11eH23 changed from 0.3243 and 1.5528 (in LiN4H8) to 0.2897 and 1.3020 (in TiN4H7). In contrast, these values for N2eH2 changed from 0.3224 and 1.5200 (in LiN4H8) to 0.2820 and 1.1604 (in NbN4H7), respectively. In conclusion, the topological analysis of the

Fig. 5 e The diffusion path and energy curve of hydrogen diffusion in Li16N16H31. (The imagines (a)e(e) were cut from the structures of Li16N16H31 supercells.)

Fig. 6 e The diffusion path and energy curve of hydrogen diffusion in Li15TiN16H31.

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Fig. 7 e The diffusion path and energy curve of hydrogen diffusion in Li15NbN16H31.

electron density for the cluster model suggests that formation of H vacancy and the Ti or Nb substitution can weaken the NeH bonds in LiNH2, and thus facilitate dehydrogenation.

3.4.

The diffusion paths of the hydrogen atom

The MEP of the hydrogen diffusion was determined through the CIeNEB technique. We considered the migration of the H9 atom to the position of the H23 atom in the supercell of LiNH2 (see Figs. 2 and 5e7). This movement is equivalent to the transfer of the vacancy from H23 to H9. Hence, the H23 vacancy is defined as the initial state and the H9 vacancy is the final state. The H diffusion path in unsubstituted Li16N16H31 is displayed in Fig. 5, where the small gray sphere represents the moving H9 atom. From the initial state (a) to point (b), the NH2 group rotates first and then the N5eH9 bond gradually stretches and it breaks at (c) point, which corresponds to the highest energy of the MEP. The energy barrier for this diffusion path was found to be 1.13 eV, which is close to Miceli G’s results [30]. At point (d), the H9 atom moves toward the N11 atom, and N11eH9 bond formed with the distance of 1.0525  A. At this point the structure is not stable. Subsequently, the rotation of N11eH9 takes place and the bond length decreases and the final state (e) forms. The diffusion path of the H atom in the Ti/Nb-substituted LiNH2 is shown in Figs. 6 and 7. The diffusion paths of the H atom in both Li15TiN16H31 and Li15NbN16H31 are similar to that of unsubstituted Li16N16H31. It can be seen in Fig. 6 that N5eH9 bond ruptures at (b) point. The energy barrier of H diffusion in Li15TiN16H31 is 0.79 eV, which is smaller than that in Li16N16H31. From point (d) to (e), the NH2 group rotates to a favorable configuration. The energy barrier of H diffusion in Li15NbN16H31 is 0.66 eV, which is smaller than those in Li16N16H31 and Li15TiN16H31. Therefore, the substitution of Ti or Nb for Li favors H diffusion in the bulk phase.

4.

Conclusions

In summary, we performed periodic DFT calculations on unsubstituted and substituted LiNH2 to investigate their crystal and electronic structures, the formation energy of H vacancies, and the diffusion path of the H atoms (the diffusion path of H vacancies). To understand the bonding nature between atoms, we conducted a topological analysis of the

electron density using models that were abstracted from the cluster. The formation energies of the H vacancies indicate that the substitution of Ti or Nb for the Li atom favors the formation of H vacancy adjacent to substitution. Analysis of the DOS and the topological properties at the BCPs reveal that the NeH bonds are a typical covalent bonds and that the NeLi bond exhibits mainly ionic features. The analyses also suggest that the presence of an H vacancy and the substitution of Ti or Nb could cause the weakening of nearby NeH bonds in LiNH2, which favors dehydrogenation. Results on the MEP of H diffusion indicate that the substitution can reduce the energy barrier and thus facilitate H diffusion in the bulk phase. Therefore, the H vacancy plays an important role in H2 dissociation and diffusion, and Ti or Nb substitution (doping) is an effective technique for improving the performance of LiNH2 in hydrogenation or dehydrogenation.

Acknowledgments Thanks for International Science Editing to edit this paper. This project was supported by the National Natural Science Foundation of China (Contract No: 21171047, 21102033, 21073051), the Natural Science Foundation of Hebei Province (Contract No: B2011205058), the Education Department Foundation of Hebei Province (ZH2012106).

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