Accurate prediction of hydrogen storage capacity of small boron nitride nanocages by dispersion corrected semi-empirical PM6-DH2 method

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Accurate prediction of hydrogen storage capacity of small boron nitride nanocages by dispersion corrected semi-empirical PM6-DH2 method
an Kinal*, Sinan Sayhan Armag _ Department of Chemistry, Science Faculty, Ege University, 35100 Bornova, Izmir, Turkey

article info

abstract

Article history:

In this study, we have studied endohedral hydrogen storage capability of several selected

Received 13 May 2015

BmNm nanocages (m ¼ 12, 24, 36, 48 and 96) and their durability against hydrogen doping by

Received in revised form

the dispersion corrected semi-empirical PM6-DH2 method. Firstly, we determined perfor-

30 September 2015

mances of the PM6-DH2, PM7, B3LYP methods against the uB97X-D method, which can

Accepted 3 October 2015

make accurate estimations for systems including non-covalent interactions, and found out

Available online xxx

that PM6-DH2 predicted the stabilities of moderate sized hydrogen doped BN nanocages as accurately as uB97X-D with computation times of several thousand times faster. There-

Keywords:

fore, PM6-DH2 was employed to determine endohedral hydrogen storage capability of

Boron nitride nanocages

BmNm nanocages. It predicted that B24N24, B36N36, B48N48, and B96N96 nanocages have rather

Hydrogen storage

significant hydrogen storage percentages of 4.40, 6.67, 8.12 and 12.01%, respectively and

Endohedral doping

B96N96 can endohedrally store up to 142H2 molecules. Analysis of destabilization energies

Semi-empirical methods

of the complexes encapsulating maximum number of H2 molecules indicated that B24N24

PM7 and PM6-DH2

and B48N48 are more durable than B36N36 and B96N96 against hydrogen doping because they

Density functional theory

can both highly inflate and quite compress hydrogen molecules. In addition, the BeN bond breaking energy for B96N96 is much smaller than the passage barrier of a hydrogen molecule through hexagonal holes, so nanocage breaks instead of hydrogen molecules escaping through the hole. According to all these findings, BN nanocages and larger structures built from them might be considered as good candidates for hydrogen storage. Copyright © 2015, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.

Introduction 87% of the global energy consumption in year 2013 is originated from fossil fuels [1]. This huge consumption is the greatest reason of the global warming since large amount of carbon dioxide, the most dangerous greenhouse gas, is being released. Yet, people are using excessive amount of fossil fuels

without considering its environmental impact. Thereby, scientists are trying to find new, clean and reproducible alternative(s) to fossil fuels such as solar energy, wind power, biofuels, geothermal energy, etc. Another very important alternative is the hydrogen energy. In spite of being the most abundant element on Earth, only 1% of hydrogen is found in molecular form as H2 gas since almost all hydrogens are bonded to oxygen in the form of water. H2 gas can be produced

* Corresponding author. Tel.: þ90 232 311 23 95; fax: þ90 232 388 82 64. E-mail address: [email protected] (A. Kinal). http://dx.doi.org/10.1016/j.ijhydene.2015.10.076 0360-3199/Copyright © 2015, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article in press as: Kinal A, Sayhan S, Accurate prediction of hydrogen storage capacity of small boron nitride nanocages by dispersion corrected semi-empirical PM6-DH2 method, International Journal of Hydrogen Energy (2015), http://dx.doi.org/10.1016/ j.ijhydene.2015.10.076

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using a variety of sources e.g. water, biomass, natural gas, etc. The chemical energy stored in a fixed amount of hydrogen is almost three times larger than that stored in the same amount of an ordinary fossil fuel and also if 4 kg of hydrogen gas, which can run a fuel cell electric car up to 400 km, was tried to store conventionally in a tank under 200 bar pressure, the necessary internal volume of the tank would be 225 L, which is obviously inapplicable for the desired purpose [2]. Besides, it is an environmentally friendly energy source since its only discharge is water. In recent years, hydrogen energy has attracted excessive amount of attention of both scientific institutions and industrial companies, because it has a potential to use in hydrogen-powered fuel cell vehicles and/or hydrogen-fueled internal combustion engine vehicles for mobile power applications [3,4]. The use of hydrogen for the above mentioned applications requires an efficient, safe, and stable storage medium [5]. Therefore, many hydrogen storage materials have been investigated both experimentally and computationally such as carbon based materials [6e10], metal hydrides [11,12], metal-organic frameworks [13,14] and organic polymers [15,16]. Among these materials, it is revealed that carbon based materials, such as carbon nanotubes (CNTs), are not very suitable for hydrogen storage because attraction between CNT and hydrogen molecules are rather low [17,18]. To enhance these interactions, two methods have been proposed and both of them are based on introduction of point charges to host materials either by adding light atoms or by creating heteroatoms of host materials. In this way, interaction energy between the hydrogen molecules and host materials would be enhanced due to chargeedipole interactions [19]. Light-atom-added carbon based materials have been attracted the scientific interest and studied as hydrogen storage materials [20e23]. Shortly after their discovery [24e27], boron-nitride nanotubes, BNNTs, were tested as new material for hydrogen storage and it was found out that hydrogen storage capabilities of BNNTs varies from 1.8 to 3 wt% [28e30]. More recent studies performed at moderated conditions indicated that hydrogen uptake of BNNTs cannot exceed 3 wt% [31e33]. Goldberg et al. [34] synthesized BN nanotubes with a collapsed structure and showed that these collapsed BN nanotubes could store up to 4.2 wt% hydrogen at room temperature, leading that their hydrogen storage capability was better than both multi wall BNNTs and carbon nanotubes. On the other hand, Sun and coworkers [35] claimed that BN nanostructures are not suitable for hydrogen storage purposes based on a room temperature molecular dynamic simulation. This simulation showed that B36N36 cannot hold many hydrogen molecules since most of them escape from the cage, although they determined by employing density functional theory (DFT) methods that B36N36 could store up to 4 wt% of hydrogen at very low temperatures. A theoretical study of hydrogen adsorption on CNTs and BNNTs by Schleyer et al. [36] confirmed Sun's findings by claiming that “perfect BN nanotubes are not good candidates for hydrogen storage”. Afterwards, Froudakis and Mpourmpakis [37] are computationally indicated that the ionic character of BeN bonds increases the binding energy between hydrogen molecules and BNNTs. This larger binding energy leads to a better confinement of hydrogen molecules in BNNTs. It was also shown that doping of several metal atoms

(Li, Na, Be, Mg, Ti [38], as well as Pt) inside BN nanocages increases the H2 storage capability of BNNTs due to reaching optimal binding energy range for the storage [39]. Moreover, hydrogen storage of h-BN nanosheets (~2.6 wt%) can be improved by decorating BN nanosheets with Pt or Pd (2.81 and 4.82 wt%, respectively) [40] or by synthesizing porous BN nanosheets whose gravimetric hydrogen storage can reach 5.1 wt% [41]. Recently, it was discovered that a porous BN material called HBBN-1 could store hydrogen up to 5.6 wt% under 3 MPa pressure [42]. Shortly after HBBN-1 study, it was shown that oxygen-doped boron nitride nanosheets have a hydrogen storage capacity of 5.7 wt% under 5 MPa at room temperature, which is the highest hydrogen storage ever experimentally reported for any BN materials [43]. It seems that the gravimetric wt%s reached in these studies slightly exceeds the revised gravimetric density target of DOE for the year 2015. Therefore, these findings can be accepted as an indication of the necessity of further investigation on hydrogen storage capabilities of BN nano-structures. Endohedrally hydrogen-doped BN nanocage systems, in which nanocage atom and hydrogen molecule (B/HeH and N/HeH) are not covalently bonded to each other, include non-covalent (non-bonding) interactions. Reliable computational treatment of these dispersion interactions plays a key role in such systems. Modeling of these types of interactions demands sophisticated first principles methods, such as CCSD(T), that are computationally very expensive [44]. When system size increases, utilization of the expensive methods become impossible. At that point relatively less demanding DFT methods seem to be useful. The DFT-uB97X-D method [45,46] gives reliable thermochemical accuracy for many systems including non-covalent interactions. On the other hand, the DFT methods also require prohibitively long computation time for large systems including non-covalent interactions. Use of semi-empirical methods such as AM1, PM3 and PM6 may be preferable for those systems since they require much less CPU time compared to the first principles and DFT methods. Unfortunately, the older semi-empirical methods cannot properly account for hydrogen bonding and dispersion interactions [47]. Newly developed dispersion-corrected PM6DH2 [48] and PM7 [49] methods were claimed to be fast and powerful methods for dealing with non-bonding interactions and hydrogen bonding [50,51]. In this study we have several objectives: The main aim is to correctly predict the endohedral hydrogen storage capability (gravimetric density as wt%) of several selected BN nanocages (BnNn where n ¼ 12, 24, 36, 48 and 96). The DFT methods that account for dispersion interactions (e.g. uB97X-D) can be employed for B12N12 and B24N24, but they are extremely expensive for the larger BN nanocages, especially for B96N96. Therefore, we first aimed to check the performances of the PM6-DH2 and PM7 methods against the uB97X-D functional for small BN nanocages, namely B12N12 and B24N24, and later by using the data acquired we aimed to decide whether PM6DH2 and PM7 are appropriate for these systems or not, as well as which method is better. Once we determined the most appropriate semi-empirical method, we employed it to predict the hydrogen storage capabilities of the larger BN nanocages. The results obtained by PM6-DH2 for B24N24 is really fascinating in terms of the computation time because the method

Please cite this article in press as: Kinal A, Sayhan S, Accurate prediction of hydrogen storage capacity of small boron nitride nanocages by dispersion corrected semi-empirical PM6-DH2 method, International Journal of Hydrogen Energy (2015), http://dx.doi.org/10.1016/ j.ijhydene.2015.10.076

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almost fully reproduces the uB97X-D results but it is approximately ten thousand times faster.

by means of harmonic vibrational analysis calculations at their levels of optimization. The formation enthalpies of the hydrogen doped complexes of the two nanocage structures at 298 K were calculated from Equation (1);

Computational methodology

DHf

The host molecules used in this study are the BmNm nanocages where m ¼ 12, 24, 36, 48, 96 (Fig. 1). Nanocages having octagonal and higher connections in their geometries are not quite suitable for endohedral hydrogen doping because of high escaping probability of hydrogen molecules from these holes. Therefore, all of the nanocages employed here were chosen to include only tetragonal and hexagonal connections, and hence several of these nanocages are not the thermodynamically most stable isomers. The B12N12, B36N36 and B48N48 nanocages are the lowest energy isomers while the B24N24 nanocage employed in the current study having no octahedral holes, lies 2.4 kcal/mol above the lowest energy isomer with four octahedral holes [52]. The ground state geometries and energies of empty B12N12 and B24N24 nanocages and their hydrogen doped complexes (nH2@BmNm, where m ¼ 12 and 24) have initially been determined by using PM6-DH2, PM7, B3LYP and uB97X-D methods. The cc-pVTZ basis set was employed for all DFT calculations. All of the optimized geometries were characterized as minima

where DHf ðnH2 @hostÞ , DHf ðhostÞ ,DHf ðH2 Þ and are the heats of formation of the complex, host and hydrogen molecules calculated with all of the above mentioned methods, respectively. The accuracy of the PM6-DH2, PM7, B3LYP methods was tested against the results of the uB97X-D functional because it gives reliable thermo-chemical accuracy for the systems with noncovalent interactions. It is revealed that PM6-DH2 gives rather consistent results with those of uB97X-D, especially for the complexes of B24N24 whose non-covalent interactions are more dominant compared to the smallest one. Because of this high consistency, the formation enthalpies of the remaining nanocages (B36N36, B48N48, and B96N96) and their hydrogen doped complexes were calculated with the PM6-DH2 method. The PM7 and PM6-DH2 calculations were performed with MOPAC2012 [53] semiempirical program suite, but all the other calculations were performed with Gaussian09 [54], respectively. In this study “hydrogen storage capacity” is defined as the maximum number of hydrogen molecules endohedrally

complex

B12N12


 ¼ DHf ðnH2 @hostÞ  DHf ðhostÞ þ n DHf ðH2 Þ

B24N24

B48N48

(1)

B36N36

B96N96

Fig. 1 e The PM6-DH2 optimized geometries of all host BmNm nanocages Please cite this article in press as: Kinal A, Sayhan S, Accurate prediction of hydrogen storage capacity of small boron nitride nanocages by dispersion corrected semi-empirical PM6-DH2 method, International Journal of Hydrogen Energy (2015), http://dx.doi.org/10.1016/ j.ijhydene.2015.10.076

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doped into nanocage whose structure is intact. This means that if one more hydrogen molecule enters inside nanocage, its cage-like structure breaks down and some or all hydrogen molecules escape from this torn. Therefore, we systematically placed hydrogen molecules inside nanocages until they break. Additionally, we calculated the energy barrier for H2 molecules to pass through hexagonal holes (DE) for the B96N96 nanocage by using PM6-DH2. To be able to obtain this value, we take the difference between single point energies for both geometries when H2 is in the middle of the hexagonal hole and when it is at outside of the nanocage.

Results and discussion Oku et al. [55] computationally studied hydrogen storage capacities of BN nanocages and they managed to find out that they can store hydrogen molecules up to 4.9 wt%. However, since the method used in these studies was an old version of Parametrized Model namely PM5, these calculations need to be improved by more reliable methods. Hence, our motivations are both improving data on endohedral hydrogen storage capacities of BN nanocages and checking the reliability and performances of the newly developed semi-empirical methods. The formation enthalpies of hydrogen doped B12N12 and B24N24 complexes calculated with the PM6-DH2, PM7, B3LYP and uB97X-D methods at 298 K are given in Table 1, while their hydrogen doped structures are also given in Fig. 2. Performances of the methods for the B12N12 and B24N24 complexes will be discussed separately since dispersive interactions are considerably different for each case. The formation enthalpy of one hydrogen molecule doped complex, H2@B12N12, predicted by uB97X-D is 62.3 kcal/mol (0.099 eV), which is not thermodynamically stable with respect to the infinitely separated nanocage and hydrogen molecule. This is an expected situation because the inner cavity of the cage is rather small. Although encapsulation of the second and third hydrogens enormously increases the instability of the complexes, the cage has the strength to hold them together without rupturing. B3LYP performs better than the semi empirical methods by slightly overestimating the heat of formation values for the B12N12 system, and PM6-DH2 performs considerably well compared to PM7 that fails badly

Table 1 e Formation heats of nH2@B12N12 and nH2@B24N24 complexes. DHf (eV)

Complex

nH2@B12N12

nH2@B24N24

n

uB97X-D

PM6-DH2

B3LYP

PM7

1 2 3 1 2 3 4

0.099 0.392 0.673 0.001 0.051 0.134 0.216

0.139 0.446 0.783 0.007 0.052 0.130 0.217

0.109 0.408 0.697 0.022 0.083 0.175 0.267

0.182 0.663 e 0.017 0.082 0.187 0.302

Bold and italic faces emphasize the closeness of the results to each other.

and cannot even predict a stable structure for the 3H2@B12N12 complex. This failure of the PM7 method may be originated from the large values of coreecore repulsion integrals among the atoms of the non-bonded molecules that are forced to come very close to each other due to the restrictions applied by the cage. Somewhat poor predictions of PM6-DH2 can be related with electroneelectron repulsions being dominant over dispersive interactions in this system. As a result, the hydrogen doped B12N12 system is not very appropriate for plausible determination of the performances of the methods due to severe conditions applied by the nanocage. The B24N24 nanocage has larger inner cavity compared to B12N12, therefore, dispersive interactions are more dominant. It is reasonable when the results are interpreted from this perspective. The uB97X-D method, which estimates the formation enthalpy of H2@B24N24 as 0.5 kcal/mol (0.001 eV), indicates that the inner cavity of B24N24 is large enough that the hydrogen molecule very weakly interacts with nanocage atoms in single hydrogen molecule doping. The closest result to this estimation is that of PM6-DH2 method, which is 4.5 kcal/mol (0.007 eV). Here, PM7 method performs slightly better than B3LYP, but its deviation increases when more hydrogen molecules are added to the system. Even in one hydrogen molecule encapsulation case where weak interactions are dominant, the PM6-DH2 method shows clear performance increase. The formation enthalpy predictions of PM6-DH2 for the 2H2@B24N24, 3H2@B24N24 and 4H2@B24N24 complexes are in almost perfect agreement with those of uB97X-D. In other words, PM6-DH2 can predict the stabilities of hydrogen doped BN nanocages as accurately as the uB97XD method. The best part of the PM6-DH2 method is its very small computational time expense. The largest system calculated with DFT methods is the 4H2@B24N24 complex. The optimization and frequency analysis of this complex at uB97X-D/cc-pVTZ level last approximately 21 days (more than 3  104 min) in a parallel process using 4 CPU. On the other hand, the same calculation takes only a few minutes when the complex is calculated with the PM6-DH2 method. This leads to the fact that PM6-DH2 is approximately ten thousand times faster than the uB97X-D method for a 56-atom system, yet it gives very similar accuracy. It is probable that the difference in computation times will increase for larger systems. We can conclude that the semi-empirical PM6-DH2 method is not only exceptionally reliable and accurate but also the fastest method for large systems including non-covalent interactions, so we can rely on that hydrogen storage capacities of large nanocages can be accurately determined by PM6-DH2. The formation heats of the maximum number of hydrogen doped complexes calculated PM6-DH2 for B24N24, B36N36, B48N48, and B96N96, their formation heats per added hydrogen molecule, i.e. destabilization enthalpy, DHdestability, and the endohedral hydrogen storage weight percentages of these nanocages are given in Table 2. The maximum numbers of hydrogen molecules encapsulated by the B24N24, B36N36, B48N48, and B96N96 cages are 13, 30, 48 and 142, as well as the corresponding hydrogen storage percentages are 4.40, 6.67, 8.12 and 12.01%, respectively. Accordingly, all of the nanocages larger than B24N24 exceed the revised gravimetric density target of DOE for the year 2015. The formation heats of the hydrogen doped nanocages as a function of endohedral H2

Please cite this article in press as: Kinal A, Sayhan S, Accurate prediction of hydrogen storage capacity of small boron nitride nanocages by dispersion corrected semi-empirical PM6-DH2 method, International Journal of Hydrogen Energy (2015), http://dx.doi.org/10.1016/ j.ijhydene.2015.10.076

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13H2@B24N24

5

30H2@B36N36

48H2@B48N48 142H2@B96N96 Fig. 2 e The PM6-DH2 optimized geometries of all nH2@BmNm complexes encapsulating maximum number of H2 molecules.

Table 2 e Formation heats, destabilization enthalpies and maximum H2 storage wt% s of the BN nanocages calculated with PM6-DH2 method. Nanocage Max # of H2 molecules B24N24 B36N36 B48N48 B96N96

13 31 48 142

DHf (eV) 53.635 100.492 126.538 240.742

DHdestability H2 storage wt% (eV) 4.126 3.242 2.636 1.695

4.40 6.99 8.12 12.01

molecule addition are plotted in Fig. 3. Except for B24N24, all other BN nanocages form thermodynamically stable complexes at the initial stages of the doping. As H2 addition continues, the formation heats of all complexes increase and the

nanocages swell up to integrity of their structures being broken down. B96N96 destabilizes much more slowly than other smaller nanocages, so it can store large amount of hydrogen molecules. As previously mentioned, a porous BN material called HBBN-1 was experimentally shown to store hydrogen up to 5.6 wt% under 3 MPa pressure. PM6-DH2 indicates that the B96N96 nanocage can endohedrally store up to 12 wt% which is very large compared to experimentally obtained value. The reason of this difference mainly originates from the fact that 12 wt% is the theoretical maximum storage value at very high pressures, and also, according to TEM images, HBBN-1 mostly formed from boron nitride nanotubes with a thickness of 3.4  A. The destabilization enthalpy, DHdestability, which is the enthalpy gain when one H2 molecule is incorporated in

Please cite this article in press as: Kinal A, Sayhan S, Accurate prediction of hydrogen storage capacity of small boron nitride nanocages by dispersion corrected semi-empirical PM6-DH2 method, International Journal of Hydrogen Energy (2015), http://dx.doi.org/10.1016/ j.ijhydene.2015.10.076

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275

142 H2

250 225 200

B24N24

175

B36N36 B48N48

ΔHf (eV)

150

48 H2

125

B96N96

31 H2

100 75

13 H2

50 25 0 -25 0

10

20

30

40

50

60 70 80 90 100 110 120 130 140 150 Number of H2 molecules

Fig. 3 e Variation of formation heats of the complexes with the hydrogen molecule doping.

nanocage (Equation (2)), can be considered as the sum of three cage factors: a) destabilization due to cage inflation, DHinflation , b) 2 destabilization due to contraction of H2 molecules, DHH contraction , c) interaction energy between cage atoms and H2 molecules cageH2 . The former two enthalpies can be calcudoped, DHinteraction lated from the Equations (3) and (4); cage

cageH

2 2 DHdestability ¼ DHinflation þ DHH contraction þ DHinteraction

cage

empty cage

(2)

empty cage

DHinflation ¼ DHf ; inflated  DHf ; noninflated

(3)

H2 H2 2 DHH contraction ¼ DHf ; contracted  n DHf

(4)

empty cage

empty cage

where DHf ; inflated and DHf ; noninflated terms are formation heats of inflated and non-inflated empty BN nanocages, respec2 tively, DHH f ; contracted is heat of formation of contracted H2 mol2 is heat of formation of H2 ecules without cage and DHH f molecule. All of the formation enthalpies given above were calculated with the PM6-DH2 method at 298 K. The cagecageH2 , can simhydrogen molecule interaction enthalpy DHinteraction ply be found from the difference between destabilization enthalpy and sum of destabilizations due to cage inflation and hydrogen molecule contraction (Equation (2)). All of these enthalpies calculated with PM6-DH2 for the complexes carrying maximum number of H2 molecules, as well as their average BeN and HeH distances are given in Table 3.

The 13H2 molecules inside the B24N24 nanocage push this cage into its inflation limits (average BN distance is 1.67  A) while they are coming very close to each other (average HeH distance is 0.54  A). This severe conditions applied by the cage cause hydrogen molecules making closer contacts with cage atoms. Therefore, the enthalpy of cage-H2 interactions becomes negative (3.066 eV). The similar situation is valid for the B48N48 nanocage, but not as severe as the previous one. These two cages have similar durability since their geometrical conditions in terms of BeN and HeH distances are alike (see Table 3). They can both highly inflate and squeeze hydrogen molecules a lot. On the other hand, B36N36 cageH2 and B96N96 have positive DHinteraction values (1.229 and 0.364 eV, respectively) and they both have rather mild geometrical conditions. These cages cannot inflate as much as B24N24 and B48N48 do and they cannot shorten HeH distances below free HeH bond length. Therefore, we can conclude that these two nanocages are not very durable upon hydrogen doping, leading to the fact that they have weaker BN bonds that can break more easily. On the other hand, durability of the BN nanocages decreases with increasing the cage size when destabilization enthalpies are taken into account. Why do H2 molecules rupture cage structures instead of escaping through hexagonal holes that exist in each nanocage? Koi and Oku [56] reported the energy barrier for a H2

Table 3 e Destabilization, cage inflation, H2 contraction and cage-H2 contraction enthalpies (in eV), average BeN and HeH  for the complexes carrying maximum number of H2 molecules calculated with the PM6-DH2 method. distances (in A) Complex 13H2@B24N24 30H2@B36N36 48H2@B48N48 142H2@B96N96 a b

a

DHdestability 4.126 3.242 2.636 1.695

a

cage

DHinflation 4.636 0.883 2.627 0.488

2 DHH contraction

a

2.556 1.130 1.868 0.844

a

cageH

2 DHinteraction

3.066 1.229 1.859 0.364

Average BeN distanceb

Average HeH distance b

1.67 1.60 1.68 1.56

0.54 0.80 0.57 0.79

in eV. in  A.

Please cite this article in press as: Kinal A, Sayhan S, Accurate prediction of hydrogen storage capacity of small boron nitride nanocages by dispersion corrected semi-empirical PM6-DH2 method, International Journal of Hydrogen Energy (2015), http://dx.doi.org/10.1016/ j.ijhydene.2015.10.076

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H2@B96N96

7

TS structure

Fig. 4 e Optimized geometries of the H2@B96N96 complex and the TS structure.

molecule to pass through hexagonal hole for B24N24 as 15 eV. They used the difference between single point energies for the geometries where a H2 molecule is at the center of hexagonal hole and it is in the middle of the cage in order to calculate this barrier. For our case, we determined the corresponding barrier for the largest nanocage studied, B96N96, with PM6-DH2 as being 10.38 eV in the same way. However, this value is probably higher than its actual value since it does not include any optimized geometry. To be more accurate in the calculation of this barrier, we determined the transition state (TS) structure of a H2 molecule entering B96N96 with the PM6-DH2 method and calculated the correct energy barrier for a H2 molecule to pass through hexagonal hole as being 9.82 eV Fig. 4 depicts the optimized geometries of the TS structure (whose imaginary frequency is found to be 914i cm1) and the H2@B96N96 complex. Since the BeN bond breaking energy for B96N96 must be around its destabilization energy (1.695 eV), which is much smaller than the passage barrier, the nanocage deform before hydrogen molecules escape through hexagonal holes.

6.67, 8.12 and 12.01%, respectively. B96N96 can endohedrally store up to 142H2 molecules. Hence, it can be concluded that the BN nanocages and the larger structures built from them might be good candidate materials for hydrogen storage. The durability of a nanocage upon hydrogen doping can be understood by analyzing its destabilization enthalpy. According to this analysis, B24N24 and B48N48 are found to be more durable than B36N36 and B96N96 since they can both highly inflate and rather squeeze hydrogen molecules. In addition, it is found out that the BeN bond breaking energy for B96N96, which must be around its destabilization energy, is much smaller than the passage barrier. Therefore, instead of hydrogen molecules escaping through hexagonal holes, nanocage breaks, and a much larger hole forms.

Acknowledgments The numerical calculations reported in this paper were partially performed at TUBITAK ULAKBIM, High Performance and Grid Computing Center (TRUBA resources).

Conclusions In this study, endohedral hydrogen storage capability (gravimetric density as wt%) of several selected BN nanocages (BmNm where m ¼ 12, 24, 36, 48 and 96) were computationally investigated by several quantum chemical methods. Initially, we compared performances of the PM6-DH2, PM7, B3LYP methods with the help of the uB97X-D method, known to be accurate for systems including non-covalent interactions. PM6-DH2 predicted the stabilities of hydrogen doped BN nanocages as accurately as uB97X-D with a computation time of ten thousand times faster. Therefore, this method was employed to determine endohedral hydrogen storage capability of the B24N24, B36N36, B48N48, and B96N96 nanocages, whose hydrogen storage percentages are calculated to be 4.40,

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Please cite this article in press as: Kinal A, Sayhan S, Accurate prediction of hydrogen storage capacity of small boron nitride nanocages by dispersion corrected semi-empirical PM6-DH2 method, International Journal of Hydrogen Energy (2015), http://dx.doi.org/10.1016/ j.ijhydene.2015.10.076