A new strategy for hydrogen storage using BNNS: simultaneous effects of doping and charge modulation

Abstract

The adsorption behavior of hydrogen molecule (H₂) on neutral and charged states of C-, Si- and P-doped boron nitride nanosheets (BNNSs), is investigated using density functional theory (DFT) method. The obtained results show that while neutral states and charged states of Si- and P-doped BNNSs adsorb H₂ weakly, the negatively charged states of C_B-BNNS, in which B atom of the nanosheet is replaced by C atom, increase prominently adsorption energy such that four hydrogen molecules per dopant can be effectively trapped (E_ads > 0.2 eV/H₂). This superiority, which supported by the flatness of the surface, more chemical reactivity and thermodynamic stability turn C_B-BNNS into a promising candidate for H₂ adsorption. More importantly, the hydrogen storage/release processes on C_B-BNNS can be simply controlled by switching on/off the charging voltage. This behavior is mainly supported by drastic variation of dipole moment of adsorbent and adsorbate as well as HOMO–LUMO energy gap (E_gap) of C_B-BNNS upon charging. The results also reveal that the induction forces play the main role in the hydrogen adsorption. Finally, the atoms in molecules (AIM) methodology shows that, in uncharged systems, interaction of H₂ with C dopant, due to more the covalent character, is more effective than those of Si and P. Further, the fact that the charge injection leads to a stronger interaction, while the charge removal reflects an inverse trend, agrees with the E_ads variations.

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1. Introduction

Hydrogen, a promising substitute of fossil fuels in the 21st century, has been widely regarded as a nonpolluting, economical and renewable source of energy. Despite immense efforts to find feasible hydrogen storage materials, there are still important challenges addressed by the shortage of suitable media. In this respect, various candidates such as metal hydrides,^1,2 metal–organic frameworks,^3,4 microporous polymers,⁵ metallic cluster-anchored adsorbents⁶ and many more have been investigated. However, considering the current goals of U.S Department of Energy (DOE), a few particular media have been reported to satisfy all the requirements in this respect. To achieve these goals, applied media should have large surface areas and suitable adsorption energies for hydrogen trapping. Accordingly, researchers have mainly focused on sorbents with ultrahigh surface area/weight ratio, such as nanomaterials.^7–10

There are several reports on the adsorption of H₂ on nanomaterial-based medium. A significant portion of these reports is focused on H₂ storage over nanotube, buckyball and nanosheet adsorbents. Among these, two-dimensional materials such as nanosheets are considered as the most appropriate surfaces, since their whole volumes are exposed to the analyte of interest.¹¹ Various kinds of nanosheets have been made and studied during the past two decades. In this context, using DFT calculations,¹² it has been shown that the H₂ can be attached on graphene sheets through physisorption. However, the interaction between this molecule and bare graphite is very weak revealing that the H₂ cannot effectively remain over these layers. To achieve an efficient medium for H₂ trapping, the surface modification of graphene through doping method has been introduced as one of the best alternative techniques. For example, it has been shown that modification of graphene with Al (ref. 13) and B (ref. 14) atoms as dopant can effectively enhance the ability of H₂ adsorption.

Besides graphene, the properties of synthesized monoatomic-layered BNNSs,^15,16 were found to be strongly dependent on the dopants.¹⁷ Currently, these nanosheets are considered as new nanomaterials for various objectives.^18–20 Recently, the DFT results using RPBE functional have indicated that the Al_B-BNNS is a promising material for H₂ storage.²¹

One of the main challenges observed over H₂ storage process in all studied systems was to obtain suitable adsorption energy for H₂. It is difficult to achieve a high capacity of H₂ storage only by physisorption. On the other hand, it has been already stated that chemisorption is also ill-suited for H₂ storage, especially in the case of large adsorption energies. Thus, the great part of researches has focused on intermediate states between physisorption and chemisorption of the H₂ molecule over media, requiring the optimal adsorption energy of 0.2–0.4 eV/H₂.^22–24 This allows both adsorption of molecular H₂ and its release under suitable conditions for practical applications. In this regard, by applying an electric field to polarizable substrates such as B- (or Al-) nitride NS, Zhou et al.²⁵ have suggested a different approach to H₂ storage with good reversibility as well as fast kinetic. However, since the electric-field enhanced H₂ storage on polarizable materials requires large electric fields, the modification of the charge state can be especially considered as alternative approach. Recently, we have shown that modifications of charge states of some doped BNNSs can be used as a good strategy for methane adsorption.²⁶ It is noteworthy to consider that modifications of charge can be experimentally realized by different approaches including electrochemical, electrospray, gate voltage control and electron beam methods.²⁷

On this basis, the present work inquires the ability to understand and make decisions based upon fundamental principles of quantum chemistry for appropriate H₂ storage using C, Si and P-doped BNNSs. More importantly, to enhance the capacity of H₂ adsorption, we investigate the effects of injected or ejected charges to the pristine and, more importantly, doped BN nanosheets. As a result from this strategy, a new path way toward hydrogen storage is purposed in this work.

2. Computational details

All calculations were carried out within the DFT algorithm by using the GAMESS package.²⁸ The geometry optimizations of the structures were performed at the M06-2X functional using the 6-311G (d,p) basis set. The obtained results using M06-2X functional was shown to be in good agreement with experiments. Also, the reliability of the results of this functional for description of non-covalent and long–range interactions has been confirmed.²⁹ Harmonic vibrational frequency calculations at the same level were carried out to confirm that the obtained systems corresponded to real minima. The results are also followed by single point energy calculations and other electronic properties at both M06-2X and the MPW1PW91 (ref. 30 and 31) functionals with the same basis set. The adsorption energies, E_ads, were calculated according to the following expression:

E_ads = E_sheet-H2 − (E_sheet + E_H2) (1)

where E_sheet-H2, E_sheet and E_H2 stand for the energies of the gas-adsorbed sheets, pristine or doped sheets and H₂ molecule, respectively.

Since almost all of the doped BNNSs used in this study have not been synthesized so far, here we investigate some aspects of the thermodynamic stability of these flakes.

The results of the vibrational calculations to estimate the Gibbs free energy for the defection (G_d) of pristine BNNS (by removal of B or N) was obtained as following:

ΔG_d = (G_{defected-BNNS} + G_{removed atom}) − G_{pristine-BNNS} (2)

where G_{defected-BNNS} stands for Gibbs free energy of B or N-defected BNNS, after removing of either B or N atoms. It should be noted that, to create defects on BNNSs, experimentally, ball-milling technique has been used to mechanically break down the structures of hexagonal BNNSs.³² The process of charge transfer is studied using the scheme proposed by Mertz et al.³³ The energy gap variation, ΔE_gap, for any system is defined as ΔE_gap = E_{gap(sheet-H2)} − E_gap(sheet), where E_gap is referred to the difference between the energies of the highest occupied molecular orbital, HOMO, and the lowest unoccupied molecular orbital, LUMO. The density of states (DOS) diagrams of the adsorbent and the gas-adsorbed adsorbent were visualized by the GaussSum program.³⁴ Finally, the AIM analysis³⁵ was applied to analyze the nature and the strength of interactions between H₂ and each of flakes by the AIM2000 program.³⁶

3. Results and discussion

3.1. Pristine and doped BNNSs

Firstly, the structure and electronic properties of the isolated pristine and heteroatom-doped BNNSs were analyzed. Here a BN sheet made by 25 B and 25 N atoms was selected as primer adsorbent, Fig. 1. The selected sites (in the center of flake) for substitution of dopants are denoted by X_N and Y_B, thereby the X and Y letters refer to the C, Si and P atoms. To avoid boundary effects and have the same edges effects, 5H atoms were located on each edge (totally 20H atoms).

Fig. 1 Depiction of h-BNNS by the presentation of X_N and Y_B sites in which X and Y letters refer to the locations for doped atoms.

The structural and electronic properties along the thermodynamic stability of adsorbents were reported in Table 1. Considering the BNNS³⁷ as the base, the thermodynamic stability of adsorbents upon doping was analyzed. It was shown that C_B-BNNS is thermodynamically more stable than any other flake studied in this work. The variation of Gibbs free energy at 298 K for the synthesis of both C_B and C_N states through a vacancy in h-BNNS has been shown in Fig. 2. As seen, the required energy for N-vacancy formation is about 0.56 eV smaller than that of B-vacancy. However, in terms of Gibbs free energy, CB-BNNS is significantly more favorable to form.

Table 1 The structural and electronic properties of the doped BNNSs. The results of the charge injection/removal on BNNSs are reported in the second (for 1e⁻ state) and third (for 1e⁺ state) rows in each cell

System/CS^a	X⋯Y distance (Å)	P^d (Å)	PQCD^e		Dipole moment (D)	Charge on target atoms (|e|)		Egap (eV)
			μ (eV)	η (eV)
	M06^b	M06	MPW^f	MPW	M06	MPW	M06	MPW	M06
a Charge state.b M06-2X.c Data in brackets (used B3PW91 functional), dipole moment of flakes and charge on target atoms are copied from ref. 26.d Protrusion of dopant from the sheet surface, regarding to the entire state.e Pierson's quantum chemical descriptors.f MPW1PW91.g The value in parenthesis refers to the 2e^− charged state.
BNNS	1.44 [1.44]^c	0.00 [0.00]	−3.96	3.01	5.71	−0.483	−0.470	6.019	8.179
1e^−					24.30	−0.357	−0.261	0.537	1.299
1e^+					16.56	−0.513	−0.477	0.728	1.545
CB	1.41 [1.41]	0.00 [0.00]	−2.10	1.15	5.83	0.237	0.235	2.351	4.070
1e^−					11.84 (22.7)^g	0.242	0.218	0.791	1.954
1e^+					3.42	0.541	0.583	3.890	6.015
CN	1.52 [1.52]	0.00 [0.00]	−5.32	1.64	5.81	−0.098	−0.081	3.344	5.476
1e^−					4.76	−0.335	−0.372	2.628	4.449
1e^+					8.00	0.052	0.165	1.145	2.716
PB	1.72 [1.72]	1.39 [1.36]	−3.61	2.64	5.89	0.032	0.058	5.284	7.287
1e^−					25.54	1.390	1.415	0.559	1.378
1e^+					4.16	1.670	1.752	0.782	6.862
PN	1.88 [1.96]	1.75 [1.69]	−3.98	3.00	5.96	−0.373	−0.388	6.034	8.830
1e^−					14.19	−0.504	−0.559	0.517	1.069
1e^+					7.87	−0.178	−0.188	0.721	2.044
SiB	1.71 [1.73]	1.31 [1.36]	−3.28	2.31	5.85	0.298	0.366	4.624	6.489
1e^−					10.05	−1.022	−1.066	1.074	2.618
1e^+					4.37	1.169	1.287	1.393	3.306
SiN	1.95 [1.89]	1.83 [1.87]	−4.90	1.57	5.84	0.225	0.253	3.091	4.750
1e^−					6.91	−0.480	−0.514	2.293	3.911
1e^+					8.18	1.147	1.283	0.910	2.622

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Fig. 2 The profile of Gibbs free energy at 298 K for synthesis of C_B and C_N states of C-doped BNNS through formation of a vacancy in h-BNNS.

For the equilibrium distance around dopants, the results show that Y_B-BNNSs have the smaller bond length than the X_N one.²⁶ Moreover, according to the results, which have not been reported here, the absolute charges on the N and Y atoms are often greater than those of B and X atoms in the same state. These suggest that the ionic nature of the bonds as well as the dispersive and inductive forces in Y_B-BNNSs are more effective than that of X_N ones. Thus, it seems that the Y_B-type systems are more active for gas adsorption, especially when van der Waals forces are in question.

As can be seen, except for C-doped BNNS in which the atomic radius of C atom is closer to that of B and N, the doping pulls the dopants out from the sheet surface. It is important for the growth of a compound on nanosheets that the doped atom does not disturb the surface structure. Thus, from geometry points of view, the C-doped BNNS can be treated as a promising material for the gas storage.

In order to analyze more precisely the thermodynamic stability and chemical reactivity of flakes, the Pierson's quantum chemical descriptors^38–40 were also considered here. As seen from Table 1, the chemical potential (μ) in the Y_B cases is more positive than that of X_N for the same dopant. Consequently, the C_B-BNNS with the most positive amount of μ is more reactive than any other flake studied in this work. Similarly, the values of chemical hardness (η), shown to be a useful global index of reactivity in molecules and clusters,⁴¹ reveal that the C_B-BNNS is more active to interact with foreign species. Interestingly, considering the Gibbs free energies of formation in Fig. 2, production of CB-BNNS is more favorable than the CN one.

In this work in order to find an efficient way to improve the adsorption capacity of H₂, along the surface modification with dopants, the effects of injection and removal of charge on the adsorption properties of BNNSs were specially studied. To gain more understanding of the adsorption behavior of the H₂, the structural and electronic properties including dipole moment, electrostatic charge on dopant and E_gap of flakes, for positively and negatively charged pristine and doped BNNSs, are gathered in Table 1. According to the results, the maximum value of dipole moment is observed in the Y_B-BNNS/1e⁻ state of each system. Thus, it seems that this kind of flakes has the more capacity for the gas adsorption, specially, when van der Waals forces are in question.

The results show that the electrostatic charge in the pristine BNNS is in good agreement with previous reported charge for N atoms (∼0.42 |e|) in BNNSs.⁴² Moreover, after charge injection/removal for this case, no remarkable change of electrostatic charge on targeted atoms was observed. It is evident that the Y_B cases are more positive than those of X_N, agreeing with the more electronegativity of the N atom related to the B one. The results that are presented in Table 1 indicate also that the charge injection/removal increases/decreases the electric charge on dopant. It is expected that, regarding to the reported experimental E_gap of pristine BNNS (∼5–6 eV),⁴³ the E_gap values of BNNSs calculated by the MPW1PW91 functional are more realistic than that of M06-2X. It is interesting to note from Table 1 that the E_gap(η) of C_B-BNNS decreases/increases after charge injection/removal. Thus, according to the Koopman's approach,³⁸ a charge-controlled switchable gas adsorption process upon controlling of electron moving is expected.

3.2. Process of hydrogen adsorption

In this work, different geometries including above the either dopant or the center of hexagon rings including doped atoms (X and Y sites in Fig. 1) were selected as initial configurations of the H₂ molecule on the surface of BNNSs. Further, in each mentioned configuration, the H₂ molecule has been placed on different orientations with respect to the sheet surface. Finally, those positions located on minimum of potential energy surfaces were chosen to discuss.

3.2.1. Geometries and energies. Schematically, Fig. 3 shows the adsorbent/H₂ systems for pristine (A) and doped (B–D) sheets. The obtained results for the stabilization energies and charge transfers, between moieties, upon H₂ adsorption on the pristine and doped BNNSs are reported in Table 2.

Fig. 3 The most stable configurations and some structural properties during adsorption of the H₂ on the surface of BNNS; (A) pristine, (B) B(B1) and N(B2) atoms of sheet replaced by C atom, (C) B(C1) and N(C2) atoms of sheet replaced by Si atom, (D) B(D1) and N(D2) atoms of sheet replaced by P atom. The dash lines represent the minimum distances between dopant and H₂.

Table 2 Adsorption energy, E (eV/H₂), and charge transfer, CT (|e|), of the adsorption on BNNSs using the M06-2X method

System	Injected charges
	0		−1		+1
	E	CT^a	E	CT	E	CT
a The negative sign indicates charge transfer from the sheets to the H2.b The values given in parenthesis refer to the +2 and −2 charged states.
BN/H2	−0.049	−0.006	−0.052	−0.007	−0.049	−0.002
CB/H2	−0.127	−0.069	−0.378 (−0.641)^b	−0.085 (−0.078)	0.453 (0.446)	−0.054 (0.051)
CB/cis 2H2	−0.095	−0.056A	−0.258 (−0.370)	−0.032 (−0.063)	0.210 (0.208)	−0.043 (−0.040)A
		−0.066B		−0.072 (−0.101)		−0.035 (−0.041)B
CB/trans 2H2	−0.097	−0.068	−0.241 (−0.362)	−0.090 (−0.081)	0.203 (0.194)	−0.048 (−0.050)A
		−0.055		−0.090 (−0.068)		−0.041 (−0.037)B
CB/3H2	−0.088	−0.063	−0.207 (−0.274)	−0.090 (−0.095)	0.121 (0.086)	−0.051 (−0.046)
		−0.050		−0.074 (−0.082)		−0.034 (−0.030)
		−0.058C		−0.087 (−0.090)		−0.054 (−0.051)
CB/4H2	−0.082	−0.076	−0.176 (−0.235)	−0.102 (−0.0108)	0.076 (0.070)	−0.057 (−0.050)
		−0.056		−0.054 (−0.061)		−0.051 (−0.050)
		−0.099		−0.120 (−0.122)		−0.092 (−0.087)
		−0.019D		−0.039 (−0.047)		−0.009 (−0.005)
CN/H2	−0.046	−0.003	−0.017	0.000	−0.054	0.008
SiB/H2	−0.042	−0.090	−0.083	−0.181	−0.040	−0.057
SiN/H2	−0.055	−0.011	−0.078	−0.123	−0.054	−0.102
PB/H2	−0.056	0.011	−0.059	0.011	−0.053	−0.015
PN/H2	−0.023	−0.041	−0.027	−0.041	−0.025	0.002

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A closer look at the pristine system shows that the H₂ molecule is oriented perpendicularly to the pristine BNNS from the center of hexagonal ring. The interaction distance between the nearer H atom of H₂ and each of B and two nearer N atoms of the sheet was estimated to be 3.01 Å. It is obtained from the results that the H₂ molecule cannot bind effectively (E_ads ∼ 0.04 eV/H₂) to the surface of the pristine BNNS. This is in good agreement with previous reports which the E_ads has been estimated about 0.03 eV/H₂, when one layer of these molecules is adsorbed on a BN sheet.^25,44

As mentioned above, in order to increase the adsorption energies of H₂ molecule on the BNNS, the C, Si and P atoms were separately doped on sheet surface. The equilibrium distance between doped atoms and the nearer H atom from H₂ molecule is shown in Fig. 3. As can be seen the minimum distance of 2.64 Å is observed in the H₂ adsorption on C_B-BNNS. Regarding to the values of E_ads, the smallest distance observed for the H₂ adsorption on C_B-BNNS fits well with the maximum E_ads seen in this work (Table 2). Thus, compared with the other neutral cases, this state has the most potential for H₂ adsorption. This is in good agreement with the more reactivity seen for the C_B-BNNS, Table 1. Importantly, it is favorable that H₂ adsorption on C-doped BNNS does not break (Table 2) the structure of the sheets showing the suitability of C atom as dopant on BNNS for H₂ storage (in this situation H₂ can bind to the sheet from both sides).

Next, to understand the maximum H₂ storage capacity per doped carbon, the adsorption effects of the more H₂ molecules, C_B-BNNS/nH₂, have been studied, Fig. 4 and Table 2. Further, in order to know the more favorable position for the adsorption of the second H₂, two possible positions (cis and trans) have been considered. It is obvious from the Table 2 that there is no prominent difference in the adsorption energies of H₂ in these positions. As a result of smoothness of the flake, this indicates that both sides of the C_B-BNNS are active. Our results show also that the third H₂ molecule would attach to the dopant, with the average E_ads of 0.08 eV/H₂. The configurations of the second and third hydrogen adsorptions are similar to the first one. This situation is in agreement with the H₂ adsorption positions on 1Na-decorated single side BN nanomaterial.⁴⁵ Further investigation reveals that the fourth H₂ molecule placed in the near of the sheet has no tendency for staying near the surface and it is moved away from the doped atom and adsorbed weakly on neighbor N atom, with a long distance of 4.07 Å (from C atom).

Fig. 4 The most stable configurations and some structural properties of adsorption of the two (in cis and trans states), three and four H₂ on the surface of C_B-BNNS.

3.2.2. The charging effects of BNNSs on H₂ adsorption. In this work, the effects of the charge injection/removal on the H₂ adsorption using the pristine and doped BNNSs were persisted. Therefore, firstly we applied theoretically the injection and removal of one extra electron to realize its effect on adsorption process. Then, the effect of the injection and removal of two electrons was applied on those systems in which the charge-controlled switchable process has been observed for one-electron adding/release process one. Our results show that there is an excellent charge-controlled switchable H₂ adsorption on the C_B-BNNS. When the first extra electron introduces to this sheet, the adsorption energy is increased three times larger than the natural one (0.37 eV/H₂). It is interesting that by reversing the circuit and ejection of two electrons (1e⁺ state), the H₂ molecule spontaneously desorbs from the surface of the C_B-BNNS. This is very important that the adsorption/desorption process could be controlled through charge injection/removal. In this regard, Tan et al.⁴⁶ have recently found that the charge modulation in graphitic carbon nitride (g-C₄N₃ and g-C₃N₄) can be used as a switchable approach to high-capacity H₂ storage. Our results show also that the amount of charge transferred from 1e⁻ state of C_B-BNNS to the absorbed H₂ molecule is increased from −0.069 to −0.085 |e| and the nearer H atom is negatively charged (−0.125 |e|), whereas the charge on the farther one is positive (+0.040 |e|). This indicates that the adsorbed H₂ molecule on the 1e⁻ state is polarized. The amplitude of charge-controlled switchable process on C_B-BNNS, desirably, is continued by the injection and removal of two extra electrons, data in parentheses (Table 2). It is noteworthy to mention here that the maximum value of E_ads for the single H₂ adsorption on C_B-BNNS, with two injected extra electrons (0.6 eV/H₂), is greater than the commonly accepted range for appropriate H₂ storage (0.2–0.4 eV/H₂). Therefore, the idea of “charge-controlled switchable H₂ adsorption on C_B-BNNSs” is technically important and can be considered as an efficient way for the H₂ storage. This is similar with the recently reported results supporting H₂ adsorption through the charge modulation of g-C₄N₃ and g-C₃N₄.⁴⁶ The results show interestingly that, related to g-C₄N₃ and g-C₃N_4, there is more E_ads for special charge injected into C_B-BNNS. This can be related to the more ionic nature of B–N bond (from C_B-BNNS), compared with C–N counterpart (from g-C₄N₃ and g-C₃N₄) which can improve the induction forces on C_B-BNNS. Thus it seems that the situation of charge-controlled switchable hydrogen storage using C_B-BNNS is more sensitive to the charge modulation than that of g-C₄N₃ and g-C₃N₄. Also, as shown in Fig. 1 and mentioned in the above, assuming that atom removal is not the determining step, the production of C_B-BNNS is thermodynamically more favorable than that of C_N-BNNS. Therefore, from H₂ storage point of view, C_B-BNNS is preferable to C_N-BNNS. The results also reveal that there is no acceptable trend for H₂ adsorption on the other studied flakes, regarding to the lower values of E_ads. Similar to the pristine one, these adsorbents are not appropriate for the H₂ adsorption neither in the neutral nor in the positively or negatively charged states.

To insight into the capacity of hydrogen storage per doped C atom on negatively charged C_B-BNNS, we studied also the effects of injection and removal of charge on two up to more H₂ molecules adsorption, Table 2. It is worthy to note that the same pattern, similar to the single H₂ molecule adsorption, was observed in the adsorption energies of the more molecules, showing the charge-controlled switchable hydrogen adsorption for these states, Fig. 5. According to the results from Table 2, reaching the maximum storage capacity on the centrally selected region on 2e⁻-injected C_B-BNNS (Fig. 5) as a main pattern for the hydrogen adsorption, 4H₂ per dopant can be effectively adsorbed by E_ads ∼ 0.22 eV/H₂. This shows the corresponding gravimetric density of stored hydrogen ∼5% which is close to the target of 6 wt% set by DOE for 2010. Considering that more than one C atom can be experimentally doped in the selected pattern, this gravimetric density would probably exceed 5%, closing to the energy (DOE) target of ∼10 wt% for H₂ storage by 2015.

Fig. 5 The absolutely average adsorption energy of H₂ molecule on neutral, 1e⁻ and 2e⁻ injected C_B-BNNS at different hydrogen coverages. The ideal range of E_ads is highlighted using the gray color.

Charge transfer analysis demonstrates that, for the C_B-BNNS, while the first charge injection/removal increases/decreases the CT values from the nanosheets to the H₂ molecules, there is no similar trend in the injection and removal of the second one.

Regarding to the values of the dipole moment of bare and H₂-adsorbed C_B-BNNS as a function of charge states, Fig. 6, the strength of the H₂ adsorption versus injected charges can be described using the dipole moment quantity induced in the systems of under investigation. Thus, the induction forces can be considered as an important factor in the process of hydrogen adsorption.

Fig. 6 The dipole moment as a function of the charge states of bare sheet and sheet/H₂ systems.

The similar trend has been shown for the H₂ adsorption on g-C₄N₃ and g-C₃N₄.⁴⁶ Considering E_ads of all the states, the effects of van der Waals forces are more important than the other energy terms like as electrostatic one. This is specially confirmed when no obvious trend is observed for the values of electrostatic charge on dopants (Table 3) and H atom from H₂ versus E_ads.

Table 3 Structural and electronic properties of the H₂ adsorption on the doped BNNSs

Systems	P^a (Å)	Charge on doped atoms (|e|)	Egap variation^d (eV), [M06-2X], [MPW1PW91]
			Charging state
		M062X	0	1e^−	1e^+
a The protrusion of the dopant (related to the bare sheet) after H2 adsorption.b The B and two nearer N atoms of pristine sheet are the target of H2.c The values given in parenthesis refer states of +2 and −2 electrical charging.d The Egap,after − Egap,before for H2 adsorption.e The percentage of Egap variation, relative to the uncharged case, was gathered in bracket.
BN/H2	0.01	−1.1 N^b	0.003	0.001	0.001
		+1.1 B
CB/H2	0.03	0.553
1e^−		0.201 (0.473)^c	0.559	0.146 [−75%]^e	0.547
1e^+		0.922 (0.938)	0.510	0.148 [−70%]	0.531
CB/cis 2H2	0.05	1.008
1e^−		1.096 (1.206)	0.574	0.197 [−66%]	0.592
1e^+		1.228 (1.216)	0.471	0.191 [−60%]	0.564
CB/trans 2H2	0.01	0.242
1e^−		−0.305 (0.115)	0.554	0.183 [−67%]	0.562
1e^+		0.649 (0.701)	0.501	0.179 [−65%]	0.552
CB/3H2	0.04	0.545
1e^−		0.252 (0.338)	0.583	0.228 [−61%]	0.590
1e^+		0.768 (0.773)	0.523	0.224 [−58%]	0.656
CB/4H2	0.02	0.186
1e^−		−0.380 (−0.293)	0.585	0.238 [−60%]	0.591
1e^+		0.559 (0.570)	0.534	0.229 [−58%]	0.515
CN/H2	0.01	−0.655	0.029	0.013	0.017
SiB/H2	1.66	0.755	0.009	0.041	0.033
SiN/H2	1.98	0.282	0.012	0.029	0.020
PB/H2	1.29	−0.013	0.010	0.001	0.010
PN/H2	1.69	−0.225	0.005	0.001	0.004

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3.2.3. Structural and electronic properties of hydrogen adsorption on the nanosheets. The adsorptive properties of the hydrogen adsorption on BNNSs are shown in Table 3. As illustrated, the initial structures of C_N and C_B-BNNS have been almost kept after H₂ adsorption. Thus, as mentioned above, the C_B-BNNS showing the more potential for the H₂ adsorption can be considered as an appropriate adsorbent for the H₂ storage. The next column in this table gives the charge on dopants. It is evident from the results that the first charge injection leads to more negative value of charge on dopant in the C_B-BNNS/nH₂. However the second one shows inverse trend, suggesting that the electrostatic forces does not play the main role for the H₂ adsorption on this flake. Similarly, this situation has been recently observed for the methane adsorption on Al-doped BNNS.²⁶ The E_gap of all the systems were also listed in Table 3. Regarding to the more consistency with the experimental data, the E_gap values for the C-doped BNNSs predicted by MPW1PW91 functional were also reported. Our results reveal that the charge injection decreases/increases dramatically the E_gap(∼η)/E_ads for the C_B-BNNS/H₂ system, Fig. 7. Also, this charge injection decreases the E_gap variation (E_gap,after − E_gap,before for H₂ adsorption),by around 60–75% related to its uncharged counterpart, which is much more than the positive one. Besides the large amount of E_ads for C_B-BNNS, which is suitable for the H₂ storage, the largest E_gap variation shows that this system can be also considered as a good candidate for H₂ detection.

Fig. 7 The representation of E_gap of the C_B-BNNS/H₂ system as a function of the charge states.

3.2.4. DOS analysis. In order to investigate the effects of the H₂ adsorption on density of electronic states, the PDOS analysis was performed and the spectrum, for the situation in which the H₂ adsorption shows a suitable value of E_ads (C_B-BNNS), is extracted in Fig. 8. According to what was mentioned above, to get a more realistic data, the PDOS schemes were calculated at MPW1PW91 level. As shown in Table 1, pristine BNNS is a typical semiconductor with a wide band gap. When the B atom on the pristine sheet is replaced by the C atom (C_B), a prominent decrease (∼4.0 eV) in the energy gap (increase in conductivity) between occupied and virtual orbitals is appeared. Thus, compared to the other studied BNNSs, it is expected that the conductivity of C_B case would be more impressed by gases attacking like as H_2. Moreover increasing in the E_gap after H₂ adsorption, amplification for the peak located around the Fermi level on the C_B-BNNS was observed, Fig. 8. Considering the more E_ads, this amplification of peaks suggests that the C_B-BNNS can be used as an appropriate flake for the H₂ detection. However, according to the results of E_ads, other flakes studied here are not suggested for the H₂ detection.

Fig. 8 The PDOS diagram of the C_B-BNNS (above spectrum) and C_B-BNNS/H₂ (below spectrum).

3.2.5. AIM analysis. The topological analysis of the electron density can show the presence of intermolecular bond critical points (BCPs) and corresponding bond paths connecting the bonded dopant and H_(H2) atoms. Electron densities at BCPs (ρ_BCP) can be seen to increase as intermolecular distances decrease, in agreement with previously noted tendencies for intermolecular interactions.⁴⁷ The values of the Laplacian of the electron density at the BCP (∇²ρ_BCP) have been also used to assess the degree of covalency of the interactions. According to the Virial theorem at critical points (CP),⁴⁸ ∇²ρ(r) is associated to energetic topological parameters of G_C and V_C (respectively, the kinetic and potential energy density at CP) by a local expression:

1/4∇²ρ(r) = V(r) + 2G(r) (3)

Further, the −G_C/V_C ratio has been used to measure of the covalency in non-covalent interactions in which values greater than 1 generally state a non-covalent interaction without covalent character, while ratios smaller than 1 are referring the more covalent nature of the interactions.⁴⁹ Notice that, while negative values of ∇²ρ(r) show addition potential energy at BCP which is the specialty of shared interactions (for example covalent bonds), positive values of this quantity indicate the spread of electric charge along the bond path, presenting the closed-shell interactions (such as hydrogen bonds).

Fig. 9 and Table 4 show interaction path and also data obtained by the AIM analysis. As seen, except for P_B-BNNS/H₂, the interactions of H_(H2) atom with the dopant from BNNSs (three N atoms from pristine BNNS) are dominant in the systems under study. Further, there is additionally important interaction in the Si_N-BNNS/H₂ in which the neighbor N atom of dopant interacts directly with the H_(H2) atom. The values of ρ_BCP for the all hydrogen bond intermolecular interactions at the present work are in the range of 0.002–0.011 au. These values lie in the commonly accepted range of a hydrogen bond (0.002–0.035 a.u.),⁵⁰ Considering the mentioned reference, the hydrogen bond seen in the P_N-BNNS/H₂ is the weakest interaction seen in the present study.

Fig. 9 The representation of molecular graph of all considered systems by AIM analysis. The red and yellow dots represent the position of the bond and ring critical points, respectively.

Table 4 Interatomic distances (Å) and bond critical point data (a.u) calculated for all the systems at the M06-2X method

System	Interaction	Distance	ρ	∇^2ρ	−G/V
BN/H2	N1⋯H	3.00	0.0046	0.0144	1.3043
	N2⋯H	3.05	0.0044	0.0144	1.3102
	N3⋯H	3.15	0.0044	0.0152	1.3255
CB/H2	C⋯H	2.64	0.0086	0.0215	1.1344
−1	C⋯H	2.64	0.0112	0.0213	1.0405
−2	C⋯H	2.64	0.0094	0.0212	1.1162
+1	C⋯H	2.64	0.0069	0.0211	1.2571
+2	C⋯H	2.64	0.0069	0.0211	1.2571
CN/H2	C⋯H	3.06	0.0054	0.0168	1.3435
SiB/H2	Si⋯H	3.25	0.0050	0.0096	1.1764
SiN/H2	Si⋯H	3.12	0.0050	0.0112	1.3636
	N⋯H	3.02	0.0051	0.0152	1.2854
PB/H2	N⋯H	2.83	0.0062	0.0176	1.1875
PN/H2	P⋯H	3.61	0.0021	0.0056	1.5701

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Further, among all interactions seen in the single H₂ adsorption, the maximum values of the ρ(r) and ∇²ρ(r) from one hand and also the minimum values of the interaction distance and the −G(r)/V(r) ratio on the other hand, are belonged to the interaction seen in the most stable system, C_B-BNNS/H₂.

It is extracted from the results that there is reverse result considering the values of ρ(r) and ∇²ρ(r) versus interatomic distances, Fig. 10. Previous reports have shown that this correlation should be exponential.⁵¹

Fig. 10 The obtained exponential relationships between the interatomic distances (Å) and the ρ_BCP or ∇²ρ_BCP (a.u). All interactions between doped atoms and the nearer H atom from H₂ are considered here.

Next, the effects of charge states on the strength of C⋯H interaction for the C_B-BNNS/H₂ were pursued, Table 4. As indicated for the single H₂ adsorption, generally, the charge injection leads to a more value of ρ(r), while the charge removal has an inverse trend. It should be noted that the first charge injection in this case shows the most value of ρ(r). Further, regarding to the adsorption of two H₂ molecules, the maximum average value of ρ(r) in cis and trans states is calculated to be 0.0113 and 0.0145 a.u for the cis/-2 and trans/-1 systems, respectively. In consistent with the single and double H₂ adsorption, the triple adsorption is accrued through only C⋯H interactions. Thus, in the C_B-BNNS/1,2 or 3H₂ system, the interaction between dopant and the H atom from H₂(C⋯H) plays the more significant role. However, reaching the maximum storage capacity per dopant, the fourth (D) H₂ moves away from the dopant and interacts directly with the N atoms of the neighbor ring.

4. Conclusion

We have studied the H₂ adsorption process on pristine, C, Si and P-doped BNNSs via DFT calculation. It was found that, while the pristine, Si and P-doped BNNSs are not appropriate candidates for H₂ storage, C-doped BNNSs can be useful in this regard. This is mainly supported by the fact that the adsorption energy for H₂ molecule increases up to 0.64 eV/H₂ on 2e⁻-charged C_B-BNNS. More importantly, there is a prominent charge-controlled switchable H₂ adsorption on this adsorbent such that the H₂ storage/release processes can be simply controlled and reversed by switching on/off the charged states. This is confirmed by drastic decrease of E_gap in the negatively charged C_B-BNNS, related to the uncharged case one. Regarding to the DOS analysis, among all the nanosheets studied in this work, only the C_B-BNNS can effectively detect H₂ molecule. The AIM analysis shows that the charge injection/removal increases/decreases ρ_BCP at the bond paths connecting the dopant and H_H2 atom. Thus it is concluded that charge modification of C-doped BNNSs can be used as an efficient strategy for the H₂ adsorption.

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