first principles calculations of linh 2 bh 3 , linh 3 bh 4 , and nanh 2 bh 3

Phys. Status Solidi B 251, No. 4, 898–906 (2014) / DOI 10.1002/pssb.201350228 p s sbasic solid state physics

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First principles calculations ofLiNH2BH3, LiNH3BH4, and NaNH2BH3

Bheema Lingam Chittari* and Surya P. Tewari

School of Physics and Advanced Centre of Research in High Energy Materials (ACRHEM), University of Hyderabad,Prof. C. R. Rao Road, Gachibowli, Hyderabad 500 046, Andhra Pradesh, India

Received 23 September 2013, revised 11 December 2013, accepted 11 December 2013Published online 14 January 2014

Keywords bonding, charge density, density functional theory, elasticity, hydrogen storage

∗ Corresponding author: e-mail [email protected], Phone: +91 9492011116, Fax: +91 40 23010227

The structural, bonding and elastic properties of alkali amidob-oranes (LiNH2BH3, LiNH3BH4, and NaNH2BH3) have beenstudied. We employ first principles calculations based on vander Waals (vdW) corrected density functional theory. In thepresence of alkali metal the electronic distributions of B–H andN–H bonds are modified and reduce the di-hydrogen bonding.These effects significantly reduce the role of vdW in bindingthese compounds. Further, the band structure and density ofstates are calculated to get basic insights on distribution of elec-

tronic states. These compounds are found to be wide band gapinsulators with the band gap values for LiNH2BH3, LiNH3BH4,and NaNH2BH3 are 4.08, 5.61, and 3.96 eV, respectively. Thecharge density distribution and bond population analysis areused to understand the nature of bonding. It is noted that thesecompounds have a strong covalent bonding between B–H andN–H atoms. The calculated elastic constants reveals that thesecompounds are mechanically stable and LiNH2BH3 is found tobe less plastic compared to the LiNH3BH4 and NaNH2BH3.

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1 Introduction Ammonia borane (NH3BH3) with itshigh hydrogen content and low releasing temperatures ofH2, has been extensively explored for the fuel cell appli-cations [1–6]. Solid NH3BH3 releases one molar equivalentof H2 at temperatures of ∼380 K, and a second equivalent at∼420 K [7–11]. Thus, NH3BH3 based materials have beenfurther developed in combination with metal catalysts, acidcatalysts, ionic liquids and nanoscaffolds [12, 13]. Although,these exhibit some promising properties for hydrogen stor-age, they still have drawbacks such as low H2 density, highH2 release kinetics, irreversibility and impurities [12, 13].As a remedy to this problem, new families of metal ami-doboranes have been developed by replacing one hydrogenin NH3BH3 by an alkali or alkaline earth element [14–16].These metal amidoboranes have high desorption kineticsand suppressed toxic borazine and thus have great potentialfor hydrogen storage applications [14, 15]. These are sta-ble under normal pressures, less exothermic than NH3BH3

and suitable for on-board H2-storage application [14, 15].Recently, LiNH2BH3, NaNH2BH3, and Ca(NH2BH3)2 havebeen highlighted as potential materials [17–19] for hydrogenstorage applications [14, 15]. LiNH2BH3 and Ca(NH2BH3)2

have been reported to show significantly enhanced dehy-drogenation kinetics and suppressed borazine releaseover parent NH3BH3 [14, 15]. Alkali metal amidoboranes

such as sodium or lithium are even considered as efficienthydrogen sources for low temperature proton exchange mem-branes (PEM) fuel cells. Lithium amidoboranes possess ahydrogen content of 13.7% and are excellent hydrogen sourcefor PEM fuel cells since the waste heat generated by thefuel cell can be utilized to free almost all of the mate-rial’s hydrogen content. Although the hydrogen content ofsodium amidoborane is somewhat lower (9.5%), it is stillmuch higher than that of conventional hydrogen sources suchas magnesium hydride (7.7%) or sodium aluminum hydride(7.5%). Even though lithium amidoborane (LiNH2BH3) andsodium amidoborane (NaNH2BH3) were reported earlierin twentieth century [20, 21], no valid structural informa-tion was presented. In early twenty first century [22, 23],the complete crystal structures and solid state synthesis ofLiNH2BH3 and NaNH2BH3 were reported and their dehydro-genation properties were also investigated [14, 16, 24–28].More recently, solid state synthesis of potassium amidob-orane (KNH2BH3) was reported [29]. Metal amidoboranes(MAB) can be synthesized by stoichiometric amounts ofmetal hydrides (or organic hydrides) and ammonia boranethrough the following reaction:

MHn + nNH3BH3 → M(NH2BH3)n + nH2,

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Phys. Status Solidi B 251, No. 4 (2014) 899

where n is the valance state of metal atom M (Li or Na). In thisreaction one equivalent of H2 per NH3BH3 is released. Theabove reaction is an acid-base reaction in which NH3BH3 is acombination of Hδ+ Lewis acid and [NH2BH3]− Lewis base.In metal hydrides Hδ− acts as a Lewis base that competeswith [NH2BH3]− to bind with Hδ+. Therefore, the forma-tion of MAB is strongly dependent on the basicity of metalhydride. Metal hydrides with strong Lewis basicity wouldcombine with Hδ+ in NH3BH3 to form H2 and MAB; whereashydrides of weak Lewis basicity may be difficult to reactwith NH3BH3 [14]. LiNH2BH3 has been synthesized usingseveral methods such as interaction of NH3BH3 with LiH(Metal hydride) or LiNH2 (Amide) or Li2NH (Imide) or Li3N(Nitride). LiNH2BH3 crystallizes in two phases α and β and alithiated subsidiary phase also available. The α and β phaseshave orthorhombic structures with space group Pbca, thelattice parameters for α-LiNH2BH3 are a = 13.94682(7) A,b = 5.14883(3) A, and c = 7.11254(3) A, whereas for β-LiNH2BH3, a = 15.146(6) A, b = 7.721(3) A, and c =9.268(4) A, respectively. The lithiated phase has tetrag-onal structure with a space group of P-42c, the latticeparameters are as a = 4.0288(3) A and c = 16.984(4) A[30, 31]. LiNH2BH3 also reported with another set of latticeparameters a = 7.11274(6) A, b = 13.94877(14) A, and c =5.15018(6) A having orthorhombic structure with the samespace group [24, 31]. This phase has been confirmed byother experiments [14] and supported well by theoreticalcalculations [17, 31]. There is a similar compound namedmonoammoniate borohydride (LiNH3BH4), which can beformed with the interaction of LiH and NH4BH4. LiNH3BH4

crystallizes into orthorhombic structure with the space groupPnma and the lattice parameters are a = 5.96910(3) A, b =4.462632(2) A, and c = 14.34199(8) A, respectively [32–34]. The NaNH2BH3 has a structure similar to LiNH2BH3

and crystallizes in orthorhombic structure with space groupof Pbca and the lattice parameters are a = 7.46931(7) A, b =14.65483(16) A, and c = 5.65280(8) A. Since the molec-ular structure and the crystal geometries of LiNH2BH3,LiNH3BH4 and NaNH2BH3 are entirely different with that ofparent NH3BH3, there would be significant changes in inter-molecular forces and thereby in the physical and chemicalproperties. In this paper, we will discuss about the structural,electronic, bonding and mechanical properties of alkali metalamidoboranes (LiNH2BH3, LiNH3BH4, and NaNH2BH3)and role of van der Waals interactions in binding these molec-ular crystals. The rest of the paper is organized as follows. InSection 2, we discuss computational details, results are pre-sented in Section 3 and Section 4 deals with the conclusions.

2 Computational details The first principles calcu-lations were carried out by using plane wave pseudopotentialmethod based on density functional theory as implemented inthe CAmbridge Series of Total Energy Package (CASTEP)[35, 36]. For LiNH2BH3, LiNH3BH4, and NaNH2BH3, thebasis orbitals used as valence states are Li: 2s1, Na: 2s2 2p6

3s1, H: 1s1, B: 2s2 2p1, and N: 2s2 2p3. We have used ultrasoftpseudopotentials introduced by Vanderbilt [37] together with

local density approximation (LDA) of Ceperley and Alder[38] parameterized by Perdew and Zunger (CA–PZ) [39]and also with generalized gradient approximation (GGA)of Perdew–Burke–Ernzerhof (PBE) [40, 41]. A plane wavebasis set with energy cut-off of 490 eV have been applied. ThevdW forces were taken into account through the semiempir-ical methods proposed by the Grimme (G06) [42] and byTkatchenko and Scheffler (TS) [43] for GGA. For the Bril-louin zone sampling, the 5 × 4 × 6, 5 × 7 × 3, and 4 × 5 × 5Monkhorst–Pack [44] mesh has been used for LiNH2BH3,LiNH3BH4, and NaNH2BH3 respectively, in which the forceson the atoms are converged to less than 0.0005 eV A−1. Themaximum ionic displacement is within 0.005 A and the totalstress tensor is reduced to the order of 0.02 GPa. It is foundthat from structural properties, except GGA all other func-tionals are performing very poorly for these compounds whencomparing to experiment. In particular the approximate vdWfunctionals employed are not good. Which will be discussedin detail in the next section. For this reason we rightfully con-tinue investigating other physical properties such as bondingand mechanical properties by GGA.

3 Results and discussion3.1 Structural properties The crystal structures of

LiNH2BH3, LiNH3BH4, and NaNH2BH3 are optimized usingregular LDA and GGA functionals, in which each formulaunit contains a pair of B and N atoms. In the molecular units ofLiNH2BH3 and NaNH2BH3, B is connected to H1–H3 atoms,N is connected to H3 and H4 atoms and the metal atoms areconnected to N atoms respectively. In the case of LiNH3BH4,each B is surrounded by four H atoms, i.e., to H1, H2 andtwo H3 atoms. Each N is surrounded by three H atoms, i.e.,one H4 and two H5 atoms (the optimized crystal structuresare included in the Supporting Information as Figs. S1–S3).The optimized structural parameters obtained using regu-lar LDA and GGA functionals along with vdW corrected(G06 and TS) calculations are compared along experimentaldata in Table 1 (the optimized atomic positions comparedwith experiments are listed in the Supporting Information asTables S1–S3). It is noted that the unit cell volume obtainedby LDA is underestimated by 17% for both LiNH2BH3 andLiNH3BH4, and 15% for NaNH2BH3, the same is overesti-mated by 1.1% for LiNH2BH3, 0.7% for LiNH3BH4 and 3%for NaNH2BH3 using GGA. In order to study the role of vdWinteractions in LiNH2BH3, LiNH3BH4, and NaNH2BH3 wehave also carried out the calculations including vdW correc-tions using the Grimme (G06) [42] and by Tkatchenko andScheffler (TS) [43] for GGA. Interestingly it is noted that thealkali metal amidoboranes does not show significant effectof vdW interactions on the structural properties. Ammoniaborane (NH3BH3) has a various vdW interactions and theseare playing a major role in binding the crystal, so whenit comes to its derivatives, i.e., alkali metal amidoboranes(LiNH2BH3, LiNH3BH4, and NaNH2BH3) these vdW inter-actions are found to be absent. It is because the charge fromLi/Na have been transferred to N leading to excess charge onN, which modifies the B–N coordination bond to a covalent

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900 C. Bheema Lingam and S. P. Tewari: LiNH2BH3, LiNH3BH4, and NaNH2BH3

Table 1 The optimized structural parameters of LiNH2BH3, LiNH3BH4, and NaNH2BH3 along with experimental data.

property LDA GGA G06 TS other expt.

LiNH2BH3

a (A) 6.624 7.102 6.604 6.719 7.108a 7.1127(6)c

b (A) 12.938 14.037 13.129 13.092 13.945a 13.94877(14)c

c (A) 4.940 5.183 4.936 5.029 5.150a 5.15018(6)c

V (A3) 423.49 516.82 428.08 442.49 510.47a 510.970(15)c

LiNH3BH4

a (A) 5.506 5.918 5.713 5.641 5.926b 5.96910(3)d

b (A) 4.234 4.464 4.259 4.294 4.462b 4.46355(2)d

c (A) 13.491 14.571 14.022 13.688 14.541b 14.34199(8)d

V (A3) 314.58 384.98 341.22 331.65 384.59b 382.119d

NaNH2BH3

a (A) 13.729 14.750 13.881 13.845 − 14.6474(32)e

b (A) 5.415 5.722 5.405 5.518 − 5.6548(09)e

c (A) 7.015 7.540 7.116 6.843 − 7.4680(16)e

V (A3) 521.58 636.44 533.97 522.84 − 618.56e

aRef. [17].bRef. [33].cRef. [24].dRef. [32].eRef. [31].

bonding. These changes in the B–N bond leads to reductionof hydridic and protic nature of N–H and B–H bonds respec-tively. Subsequently the di-hydrogen bonding reduces andleads to absence of vdW interactions over NH3BH3[4].

3.2 Bond dissociation energies The bond dissocia-tion energies (BDEs) of N–H and B–H bonds of LiNH2BH3,LiNH3BH4, and NaNH2BH3 are calculated to understandthe pyrolysis mechanism. The BDE of N/B–H bond forLiNH2BH3 can be calculated as follows:

BDE(N–H) = [�H(LiNHBH3) + �H(H)]

− �H(LiNH2BH3),

BDE(B–H) = [�H(LiNH2BH2) + �H(H)]

− �H(LiNH2BH2)

Then, we removed the H atoms from N/B–H bonds ina given crystal and optimized for total energies. From theabove work reactions the calculated �H values of the par-ent and radical products are combined to estimate the BDEs.The calculated N–H BDEs for LiNH2BH3, LiNH3BH4, andNaNH2BH3 are −22.36, −25.46, and −42.17 eV, respec-tively. Similarly, B–H BDEs for LiNH2BH3, LiNH3BH4, andNaNH2BH3 are −22.46, −19.16, and −42.36 eV, respec-tively. It is noted that the overall N/B–H BDEs for LiNH2BH3

are lower compared to NaNH2BH3, which is consistent withthe recent experiments [14]. B–H bonds dissociation is easierin LiNH3BH4 over LiNH2BH3 and NaNH2BH3.

3.3 Electronic properties Later, the electronic struc-ture of LiNH2BH3, LiNH3BH4, and NaNH2BH3 is studiedthrough band structure and density of states (DOS). Fig-ure 1 shows the band structures, it is found that LiNH2BH3,LiNH3BH4, and NaNH2BH3 are wide band gap insulatorswith the band gaps of 4.08, 5.61, and 3.96 eV, respectively.However these band gaps are found to be lower comparedto NH3BH3 [4] The valence band maximum and the con-duction band minimum of LiNH2BH3 are found to be along�–Z direction and the counter part for NaNH2BH3 are foundalong Y–S direction indicates that these two compounds areindirect band gap insulators. On the other hand LiNH3BH4 isfound to be direct band gap insulator as its valence band max-imum and conduction band minimum are found to be alongthe same direction �. Then, the total and partial density ofstates (PDOS) of LiNH2BH3, LiNH3BH4, and NaNH2BH3

are calculated. The detailed discussion for each compound isas follows:

LiNH2BH3: The total DOS is made up of five well-separated regions in energy (see Figs. 1a and 2): first regioncorresponds to states between −1.5 and 0 eV, i.e., near toFermi level. It is made up of peaks from B-p and N-p states,together with s states of hydrogens connected to B atom. Animportant point is that a small contribution appears from Li-sstates in the PDOS at this same energy. The second regionis between −4 and −1.5 eV, and it corresponds to N-p, B-p,and s states of hydrogens connected to B atom. The statesbetween −5.5 and −4 eV corresponds to third region. It isfrom N-p, B-p states with an admixture of all H-s states. Thefourth region is the states between −6.5 and −5.5 eV and isfrom the peaks of N-p, s states of H’s connected to N togetherwith small contribution from B-p states. Then, from −8 to−6.5 eV states are corresponding to fifth region and it is from

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a) b)

c)

Figure 1 The band structure of alkali metal amidoboranes (a) LiNH2BH3, (b) LiNH3BH4, and (c) NaNH2BH3 calculated within GGA.The zero represents the Fermi level.

N-p and B-s along with the s states all H’s. In the conduc-tion band, it has s states of Li and p states of B, with minorcontribution from all H-s states.

Then for LiNH3BH4: The total DOS is well-separated into three regions in energy (see Figs. 1b and 3): the first regioncorresponds to the states between −2.5 and 0 eV, i.e., nearto Fermi level. It has mainly B-p states together with N-pand Li-s states along with small contribution from s statesfrom H’s connected to B. The second region correspondsto states between −5 and −4 eV and it is dominated by N-pand s states of H’s connected to N. A small contribution fromB-s & p states appears at the same energy. Finally, the thirdregion is from the states between −7 and −5.5 eV. It is madeof peaks from B-s and s states of H’s connected to B, togetherwith N-p states. The conduction band has s states of Li andp states of B, together with smaller contribution from all H-sstates.

In the case of NaNH2BH3: The total DOS has five well-separated regions in energy (see Figs. 1c and 4): the firstregion corresponds to states between −1 and 0 eV, i.e., nearto Fermi level. It is dominated by B-p and N-p states, togetherwith H1-s states. At this energy a small contribution from Na-s & p appears. The second region is between −3 and −1.5 eV,and it corresponds to N-p, B-p, and s states of hydrogensconnected to B atom. The states between −4 and −3 eV cor-respond to third region. It is made up of several peaks fromN-p, B-p states with an admixture of H1-s states. The fourthregion consists of states between −6.5 and −5 eV from thepeaks of N-p, s states of H’s connected to N together with

small contribution from B-p states. Finally the states from−7.5 to −6.5 eV correspond to fifth region, comprised ofN-p and B-s along with the s states H’s connected to B.The conduction band has Na-s & p states. Over all from thePDOS of these compounds is noted that the B-p, N-p, andH-s states are hybridizing in all the energy regions implies asp hybridization between B–H and N–H bonds.

3.4 Mulliken atomic and bond populationanalysis To quantify the charge distribution in LiNH2BH3,LiNH3BH4, and NaNH2BH3, we have calculated Mullikenatomic charges and orbital contributions, which are tabulatedin Table 2. The Mulliken atomic charges for Li and Na arefound to be positive and it is negative for B and N atoms. Thehydrogens connected to B and N atoms are found to havenegative and positive charges, respectively. This scenarioclearly indicates the protic and hydridic nature of B–H andN–H bonds in alkali metal amidoboranes. To understand thebonding nature we have also estimated the Mulliken bondpopulations for each bond (see Table 3). The total overlap(bond) population for any pair of atoms in a molecule is ingeneral made up of positive and negative contributions. If thetotal overlap population between two atoms is positive thenthey are bonded otherwise they are antibonded [45]. A highpositive bond population indicates a high degree of cova-lence. From the calculated bond populations (see Table 3)it is concluded that all the bonds are covalent in nature. TheB–H bonds with high bond population, shows their dom-inating covalent nature relative to N–H bonds in these


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Figure 2 The total, partial, and local density of states of LiNH2BH3

calculated within GGA. The zero represents the Fermi level.

compounds. Besides we have also calculated the populationionicity to know the percentage of covalence of the bonds asdiscussed elsewhere [4]. The lower limit, i.e., Pi = 0 indicatesa pure covalent bond while the upper limit, i.e., Pi = 1indicates a purely ionic bond [45–48]. As expected, B–Hbonds show zero population ionicity and N–H bond showvery low value (0.3) of population ionicity. The B–N bondwith 0.41 population ionicity shows a dominating covalentcharacter. So, B–N bond is no more a dative or coordinativebond in alkali metal amidoboranes. Moreover, the averageionicity value of B–N, N–H, and B–H bonds in LiNH2BH3,LiNH3BH4, and NaNH2BH3 are found to be 0.23, 0.19, and0.18, respectively. From the above discussions, we concludethat alkali metal amidoboranes exhibit high covalent nature.(The charge density iso surfaces and charge density distribu-tions along (100), (010), and (001) at different energy lavelsfor LiNH2BH3, LiNH3BH4, and NaNH2BH3 are plotted inthe Supporting Information as Figs. S4–S7, respectively).

3.5 Dihydrogen bonding Dihydrogen bond is a kindof hydrogen bond, which indicates an interaction betweena metal bond and a OH or NH group or any proton donorgroup. This dihydrogen bond can exist in one moleculeor between two molecules and affects molecular structure,

Figure 3 The total, partial, and local density of states of LiNH3BH4

calculated within GGA. The zero represents the Fermi level.

physical and chemical properties of solids. This also playsan important role in crystal assembly and in super molec-ular systems. So the investigation of dihydrogen bonds isof great importance [49, 50]. To understand the dihydrogenbonding in the alkali metal amidoboranes, we have calculatedthe H–H separation for the inter and intra molecules. Thecalculated shortest distances between inter and intra hydro-gen atoms for LiNH2BH3, LiNH3BH4, and NaNH2BH3 arelisted in Table 4. All the possible shortest distances betweeninter hydrogen atoms are found to be greater than 2.5 A.The intra hydrogen atoms (H4 & H5) of N are havinga shortest distance around 1.63 A and for hydrogen atoms(H1–H3) of B is around 2 A in all LiNH2BH3, LiNH3BH4,and NaNH2BH3. It may be because of the predominant ofshort range interactions over long range interactions in alkalimetal amidoboranes. The inter molecular H–H separationsare beyond the typical dihydrogen bond separation implyingthe absence of the vdW interactions in alkali metal amidob-oranes.

3.6 Mechanical properties The elastic constantsprovide information about the mechanical and dynami-cal behavior, in addition to the stability and stiffness ofsolids. Alkali metal amidoboranes crystallize in primitive


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Figure 4 The total, partial, and local density of states ofNaNH2BH3 calculated within GGA. The zero represents the Fermilevel.

orthorhombic structure similar to NH3BH3. From thecalculated elastic constants, LiNH2BH3, LiNH3BH4, andNaNH2BH3 satisfy the Born’s stability criteria therebyrevealing the mechanical stability of these compounds (seeTable 5). In general C11, C22, and C33 denote the mechanicalstiffness along X, Y and Z directions. The trends of themechanical stiffness along three directions in LiNH2BH3,LiNH3BH4, and NaNH2BH3 are as follows: For LiNH2BH3

we find C33 (62.8 GPa) > C11 (51.3 GPa) > C22 (45.1 GPa),and for LiNH3BH4, C22 (33.1 GPa) > C11 (29.1 GPa) > C33

(19.3 GPa) whereas C11 (38.8 GPa) > C33 (30.4 GPa) > C22

(27.8 GPa) for NaNH2BH3. From this analysis we concludethat LiNH2BH3 is mechanically stiffer along Z directionwhereas LiNH3BH4 and NaNH2BH3 have high mechanicalstiffness along Y and X directions, respectively.

The magnitude of the elastic constants decrease in theorder LiNH2BH3 > NaNH2BH3 > LiNH3BH4, which indi-cates that LiNH2BH3 is mechanical stiffer than NaNH2BH3

and LiNH3BH4. The shear elasticity applied to the two-dimensional rectangular lattice such as in the (100), (010),and (001) planes in LiNH2BH3, LiNH3BH4, and NaNH2BH3

can be estimated from the C44, C55, and C66 elastic constants.The trends in the shear elasticity is as follows: For LiNH2BH3

we find C44 (16.3 GPa) > C66 (13.0 GPa) > C55 (7.1 GPa)

Table 2 The calculated Mulliken atomic charges and atomic pop-ulations of LiNH2BH3, LiNH3BH4, and NaNH2BH3.

atom compound s p total charge

LiNH2BH3 1.16 0.0 1.16 −0.16H1 LiNH3BH4 1.14 0.0 1.14 −0.14

NaNH2BH3 1.23 0.0 1.23 −0.23

LiNH2BH3 1.17 0.0 1.17 −0.17H2 LiNH3BH4 1.17 0.0 1.17 −0.17

NaNH2BH3 1.21 0.0 1.21 −0.21

LiNH2BH3 1.22 0.0 1.22 −0.22H3 LiNH3BH4 1.13 0.0 1.13 −0.13

NaNH2BH3 1.22 0.0 1.22 −0.22

LiNH2BH3 0.66 0.0 0.66 0.34H4 LiNH3BH4 0.62 0.0 0.62 0.38

NaNH2BH3 0.74 0.0 0.74 0.26

LiNH2BH3 0.61 0.0 0.61 0.39H5 LiNH3BH4 0.62 0.0 0.62 0.38

NaNH2BH3 0.74 0.0 0.74 0.26

LiNH2BH3 0.89 2.48 3.37 −0.37B LiNH3BH4 0.99 2.78 3.77 −0.77

NaNH2BH3 0.91 2.52 3.43 −0.43

LiNH2BH3 1.66 4.40 6.05 −1.05N LiNH3BH4 1.71 4.44 6.15 −1.15

NaNH2BH3 1.62 4.31 5.93 −0.93

LiNH2BH3 1.70 0.0 1.70 1.30Li

LiNH3BH4 1.68 0.0 1.68 1.32

Na NaNH2BH3 2.02 5.48 7.49 1.51

and for LiNH3BH4, C66 (9.8 GPa) > C44 (6.8 GPa) >

C55 (2.6 GPa) whereas C66 (7.8 GPa) > C55 (4.1 GPa) >

C44 (1.4 GPa) for NaNH2BH3. From the above, the strongshear elasticity is found along (100) plane for LiNH2BH3

in contrast for LiNH3BH4 and NaNH2BH3 it is along (001)plane. The shear elasticity follows the trend LiNH2BH3 >

LiNH3BH4 > NaNH2BH3 confirming the higher shearelasticity of LiNH2BH3. Further, we have also estimated thepolycrystalline elastic modulii from single-crystal elasticconstants. The calculated bulk (B), shear (G), Young’smodulus (E), and Poisson’s ratio (σ) using the Voigt–Reuss–Hill (VRH) approximation [52–54] are given in Table 5.The bulk modulus (B) for the LiNH2BH3, LiNH3BH4, andNaNH2BH3 are calculated to be 20.6, 16.3, and 17.6 GPa,respectively (see Table 5). The Young’s modulus (E) of theLiNH2BH3, LiNH3BH4, and NaNH2BH3 are calculated to be36.4, 16.1, and 14.8 GPa. The calculated bulk and Young’smodulii values once again confirms stiffness of LiNH2BH3

over other two. The stability of these crystals against shearhas been scaled by calculating the Poisson’s ratio (σ) value.From the σ values we concluded that LiNH2BH3 is softtowards volume change whereas LiNH3BH4 and NaNH2BH3

are soft towards the shape change. The ductile and brittlenature of the materials can be known from the elasticconstants in terms of Cauchy’s pressure (C12–C44) and G/B

ratio. If Cauchy’s pressure is positive, it indicates the ductile


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Table 3 The calculated bond populations (P), population ionicity(Pi) and bond lengths of LiNH2BH3, LiNH3BH4, and NaNH2BH3.

bond compound P Pi bond length (A)

LiNH2BH3 0.90 0.10 1.233B–H1 LiNH3BH4 0.96 0.04 1.229

NaNH2BH3 1.03 −0.02 1.238

LiNH2BH3 0.93 0.07 1.242B–H2 LiNH3BH4 0.99 0.10 1.234

NaNH2BH3 1.03 −0.02 1.241

LiNH2BH3 0.89 0.11 1.246B–H3 LiNH3BH4 0.98 0.02 1.224

NaNH2BH3 1.00 0.0 1.255

LiNH2BH3 0.74 0.29 1.031N–H4 LiNH3BH4 0.71 0.33 1.032

NaNH2BH3 0.80 0.22 1.030

LiNH2BH3 0.74 0.29 1.031N–H5 LiNH3BH4 0.71 0.33 1.033

NaNH2BH3 0.80 0.22 1.031

LiNH2BH3 0.65 0.41 1.547B–N LiNH3BH4 −0.08 − 3.765

NaNH2BH3 0.71 0.33 1.544

LiNH2BH3 0.12 0.99 2.031N–Li

LiNH3BH4 0.11 0.99 2.050

N–Na NaNH2BH3 0.12 0.99 2.391

nature otherwise the material is brittle [55]. The criticalvalue of G/B ratio that separates ductile or brittle nature ofthe materials is 0.57. If G/B > 0.57 indicates brittle natureand G/B < 0.57 indicates ductile nature [56]. The positive

Table 4 The calculated shortest distances between inter and intrahydrogen atom of LiNH2BH3, LiNH3BH4, and NaNH2BH3 withinGGA.

bond LiNH2BH3 LiNH3BH4 NaNH2BH3

H1. . . H2 2.000 2.025 2.005H1. . . H3 1.998 2.005 2.006H1. . . H4 2.633 3.970 2.396H1. . . H5 2.397 2.222 2.673H2. . . H3 1.989 2.009 2.002H2. . . H4 2.572 3.792 3.168H2. . . H5 3.167 3.208 2.588H3. . . H4 2.623 2.392 2.608H3. . . H5 2.621 2.448 2.839H4. . . H5 1.630 1.649 1.636

values of the Cauchy’s pressure of LiNH2BH3, LiNH3BH4,and NaNH2BH3 indicates their ductility behavior, and thishas been confirmed from the calculated G/B ratios. Thevalue of Cauchy’s pressure of LiNH2BH3 found to below compared to the LiNH3BH4 and NaNH2BH3, whichis an indication of the higher ductility of LiNH3BH4 andNaNH2BH3 over LiNH2BH3. The shear anisotropy is ameasure of the degree of anisotropy in bonding betweenthe atoms in different planes. Here, we have calculated theshear anisotropy of LiNH2BH3, LiNH3BH4, and NaNH2BH3

along (100), (010), and (001) shear planes (see Table 5). Thevalues of A1, A2, and A3 are found to be differ from unity,indicating the shear anisotropic behavior of alkali metalamidoboranes. The percentage of the anisotropy in com-pressibility (AB) and shear (AG) are calculated as discussedelsewhere [4]. The percentage bulk modulus anisotropy AB

Table 5 The calculated elastic constants, bulk (B), shear (G), Young’s moduli (E), Cauchy’s pressure (C12–C44) in GPa, G/B ratio,Poisson’s ratio (σ), shear anisotropy factors for (100) plane (A1), for (010) plane (A2), for (001) plane (A3), the percentage of theanisotropy in the compressibility (AB), shear modulii (AG), average wave velocity (vm), longitudinal (vl), and transverse (vt) wavevelocities and the Debye temperature (ΘD) of LiNH2BH3, LiNH3BH4, and NaNH2BH3.

C11 C22 C33 C44 C55 C66 C12 C13 C23

LiNH2BH3 51.3 45.1 62.8 16.3 7.1 13.0 16.8 4.6 15.3LiNH3BH4 29.1 33.1 19.3 6.8 2.6 9.8 15.3 7.6 14.7NaNH2BH3 38.8 27.8 30.4 1.4 4.1 7.8 11.7 13.3 7.4

BV GV BR GR B G G/B E σ C12–C44

LiNH2BH3 25.8 15.4 25.7 2.9 20.6 14.2 0.5 36.4 0.2 0.5LiNH3BH4 17.4 6.8 15.2 5.3 16.3 6.0 0.3 16.1 0.3 8.5NaNH2BH3 18.0 6.9 17.2 3.9 17.6 5.4 0.3 14.8 0.3 10.3

A1 A2 A3 AB AG

LiNH2BH3 0.62 0.36 0.83 0.002 0.068LiNH3BH4 0.82 0.46 1.25 0.218 0.118NaNH2BH3 0.13 0.38 0.72 0.002 0.088

vm (km s−1) vl (km s−1) vt (km s−1) ΘD (K)

LiNH2BH3 4.28 6.47 3.87 636.6LiNH3BH4 3.38 6.04 3.01 473.7NaNH2BH3 2.50 4.75 2.22 347.4


Original

Paper


is found to be low over than the percentage shear modulusanisotropy AG of LiNH2BH3 and NaNH2BH3, implying thatLiNH2BH3 and NaNH2BH3 are highly anisotropic in shearthan in compressibility. In the case of LiNH3BH4, it is moreanisotropic in compressibility over shear. Finally, we havedetermined the Debye temperature ΘD from elastic constantsas discussed elsewhere [4], and are listed in the Table 5. Fromthe calculated ΘD values, we found that ΘD(LiNH2BH3) >

ΘD(LiNH3BH4) > ΘD(NaNH2BH3). Therefore, LiNH2BH3

can possess high thermal conductivity than those ofLiNH3BH4 and NaNH2BH3. This is the first qualitativeprediction of mechanical properties of the alkali metalamidoboranes which still awaits experimental confirmation

4 Conclusions The crystal structures of alkali metalamidoboranes (LiNH2BH3, LiNH3BH4, and NaNH2BH3) arefully optimized, the structural, bonding and elastic proper-ties have been studied by using first principles calculationswith and without van der Waals corrections. Interestingly,alkali metal amidoboranes not showing any effect of vdWinteractions. The optimized structural parameters are in goodagreement with the experimental data using GGA. From theband structure and density of states calculations, it is foundthat alkali metal amidoboranes are wide band gap insula-tors. The band gap values for LiNH2BH3, LiNH3BH4, andNaNH2BH3 are 4.08, 5.61, and 3.96 eV, respectively. Fromthe charge density distribution and bond population analysiswe conclude that there exists a strong covalent bond betweenB–H and N–H atoms. From the calculated elastic constantsthe alkali metal amidoboranes are found to be mechanicallystable and LiNH2BH3 found to be less plastic than LiNH3BH4

and NaNH2BH3. It is noted that the overall N/B–H BDEsfor LiNH2BH3 are lower compared to NaNH2BH3, whichis consistent with the recent experiments [14]. B–H bondsdissociation is easier in LiNH3BH4 over LiNH2BH3, andNaNH2BH3.

Acknowledgements Author thanks DRDO throughACRHEM for RA and CMSD, University of Hyderabad forcomputational facilities.

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first principles calculations of linh 2 bh 3 , linh 3 bh 4 , and nanh 2 bh 3

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