Introduction

Ammonia N–H bond cleavage is a first rung, not only in the transformation of abundant ammonia into a valuable amino compound, but also in the start of numerous catalytic reactions [1, 2]. Conventional N–H bond cleavage methods depend mainly on the different transition metal centers [2]. But toxicity problems, high cost and simple Lewis acid–base adducts formation with transition metals impose great limitations on the possible applications as an NH3 splitter [3]. Therefore, researchers have attempted to find metal-free ammonia splitters. Recently, nanostructured materials have invoked extensive interest as substrates due to their unique properties, such as high surface to volume ratio, and exclusive electronic properties [4–10]. Using density functional theory (DFT) calculations, Ding et al. [3] demonstrated that pristine SiC nanotubes can break the ammonia N–H bond by molecular chemisorption, releasing energy of ~1.370 eV. The latter authors used the Perdew Burke Ernzerhof (PBE) exchange correlation density functional with double numerical basis sets plus polarization functional (DNP) [3]. Using the B3LYP/6-31G (d) method, it has been revealed that open-ended BN nanotubes can cleave the N–H bond of ammonia via a two-step mechanism [11].

Numerous studies to date have focused on graphene-like boron nanosheets because they are of similar interest as graphene [12–14]. It has been shown that the B atoms cannot form a honeycomb hexagonal nanosheet because of electron deficiency [15]. In 2004, Piazza et al. [15] reported the synthesis of a quasiplanar whole boron sheet with a central hexagonal hole. They found that this neutral B36 sheet is a highly stable sheet with C6v symmetry, extension of which would afford larger planar boron nanosheets with hexagonal vacancies. Following this report, B36 borophene has attracted considerable attention from the scientific community [16–18]. For example, based on the DFT calculations, Liu et al. [17] have shown that metallized B36 borophene can serve as reversible hydrogen storage. At the B3LYP level, the adsorption of CO, N2, H2O, O2, H2 and NO molecules on B36 borophene has been explored [18]. In this work, by performing DFT calculations at different levels and with different basis sets, we examine the potential application of B36 borophene as a metal free NH3 splitter

Computational details

Energy predictions, transition state calculations and geometry optimizations on a B36 and different NH2–B36–H complexes were performed using B97D level [19] of theory with 6-31G (d) basis set as implemented in the GAMESS suite of program [20]. Vibrational frequency analysis was performed at the same level of theory to confirm that all structures were in true local minimum, and also to obtain thermodynamic data. Molecular electrostatic potential (MEP) [21, 22], nuclear magnetic resonance (NMR), and natural bond orbital (NBO) analyses were done at B97D level with the 6-311++G (d, p) basis set. Also, the effect of different exchange correlation density functionals and basis sets were explored.

We defined adsorption energy as:

$$ {\mathrm{E}}_{\mathrm{ad}} = \mathrm{E}\ \left({\mathrm{NH}}_2\hbox{-} {\mathrm{B}}_{36}\hbox{-} \mathrm{H}\right)\ \hbox{--}\ \mathrm{E}\ \left({\mathrm{B}}_{36}\right)\ \hbox{--}\ \mathrm{E}\ \left({\mathrm{NH}}_3\right) $$
(1)

where E (NH2–B36–H) corresponds to the electronic energy of the NH2–B36–H complex, E (B36) is the energy of the isolated fullerene, and E (NH3) is the energy of a single NH3. The HOMO–LUMO energy gap is defined as

$$ {\mathrm{E}}_{\mathrm{g}} = {\mathrm{E}}_{\mathrm{LUMO}}\hbox{-} {\mathrm{E}}_{\mathrm{HOMO}} $$
(2)

where E LUMO and E HOMO are the energy of the lowest unoccupied molecular orbital (LUMO and highest occupied molecular orbital (HOMO), respectively. The change in the HOMO–LUMO gap, as an index of the electronic sensitivity of the B36 toward the dissociative adsorption of ammonia, is obtained by:

$$ {\Delta \mathrm{E}}_{\mathrm{g}} = \left[\left({\mathrm{E}}_{\mathrm{g}2}\hbox{-}\ {\mathrm{E}}_{\mathrm{g}1}\right)/{\mathrm{E}}_{\mathrm{g}1}\right]\ *\ 100 $$
(3)

where E g1 and E g2 are, respectively, the value of E g in the initial and the final state.

Results and discussion

In Fig. 1, the optimized geometry of the B36 sheet indicates that it is not completely planar and has a curvature that was first synthesized and reported by Piazza and co-workers [15]. Five kinds of boron atoms can be detected on a trapezoid shape (Fig. 1) based on B-11 NMR analysis. The calculated NMR chemical shifts for B1, B2, B3, B4, and B5 atoms (Fig. 1) are about 121.5, 120.9, 57.8, 91.4, and 86.1 ppm, respectively. The structure includes a central hexagon with C6v symmetry. This symmetry degenerates the energy levels so that the HOMO and LUMO are two-fold degenerated levels (Fig. 2), which lie at −5.12 and −4.01 eV, respectively. Thus, the calculated HOMO–LUMO gap is about 1.11 eV at B97D level of theory. The MEP maps (Fig. 1) show that inner side of the sheet is much more negatively charged in comparison to the outer side, hence the outer site will be more appropriate for a nucleophilic NH3 molecule attack. Different bonds in the range of 1.59 to 1.75 Å exist, with B3–B4 and B4–B3 (Fig. 1) being the largest and shortest bonds, respectively. Using PBE0/6-31G(d) level of theory, Piazza et al. [15] showed that neutral B36 has perfect hexagonal symmetry ©6v), and is overwhelmingly stable relative to the closest-lying isomers. They indicated that the shortest bond length occurs between the six apex B atoms and their neighbors (1.58 Å), while the remaining six peripheral B–B bonds are slightly longer (1.67 Å). Based on our results, the vibrational frequency modes are in the range of 108–1282 cm−1, indicating that B36 is in a true local minimum on the potential energy surface.

Fig. 1
figure 1

Optimized structure of B36 borophene and its inner and outer molecular electrostatic potential maps. The surface is defined by the 0.0004 electrons b−3 contour of the electronic density. Color ranges (in a.u.): blue more positive than 0.010, green between 0.010 and 0, yellow between 0 and −0.010, red more negative than −0.010

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Fig. 2
figure 2

The two-fold degenerated highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) profiles of B36 borophene

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To explore N–H bond cleavage on the surface of borophene, we investigated the feasibility of different cleavage from the standpoint of thermodynamics and kinetics. Towards this aim, we first assumed that an NH3 molecule dissociates into two fragments, –H and –NH2, attacking different B–B bonds. Figure 3 illustrates the four most stable predicted complexes with positive frequencies. Among these complexes, the most stable complex (A) is that in which the ammonia molecule attacks the B3–B4 bond, and hydrogenates the B4 atom, retaining the –NH2 group on the B3 atom. The adsorption energy for this process is about −42.7 kcal mol−1, demonstrating a favorable reaction. In the second most stable complex (B), in contrast to complex A, the B3 atom is hydrogenated and the NH2 group is attached to the B4 atom with adsorption energy of −24.5 kcal mol−1. The higher stability of complex A compared to B shows that the nucleophilic –NH2 group tends to attach to the B3 atom because it is three-fold coordinated while the B4 atom is four-fold coordinated. In the next most stable structure (C), the B1 atom is hydrogenated and the –NH2 group shifts on the B2–B3 bond and forms a bridge with adsorption energy of about −17.38 kcal mol−1. Upon the adsorption process, a strong structure deformation occurs and the B1–B2–B3 fragment is projected out. For complex (D) the adsorption energy is positive (+13.91 kcal mol−1), indicating that the complex formation is energetically unfavorable. In this complex, the ammonia dissociates on the B atoms of central hexagon so that –NH2 attaches to a B atom and –H shifts to the adjacent B–B bond. Generally, complexes (C and D) in which the central hexagon participates in the reaction are less favorable.

Fig. 3
figure 3

Optimized structures of different H–B36–NH2 complexes

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Here, we will focus on the energetically most stable complex (A). In this complex, two new bonds including B–H and B–NH2, are formed with bond lengths of 1.21 and 1.40 Å, and Wiberg bonds index (WBI) [23] of 0.878 and 1.193, respectively, showing a covalent nature of the bonds formed. After the dissociative adsorption of ammonia, the B3–B4 bond was broken, so the bond length increased from 1.59 to 1.94 and the WBI from 1.137 to 0.534. The reaction yielding this complex was accompanied by a decrease in entropy, so the ∆S is about −0.034 kcal mol−1 K at room temperature and 1 Atm. Under these conditions, the change in Gibbs free energy (∆G) is about −31.9 kcal mol−1, indicating a thermodynamically favorable reaction. The vibrational frequency modes were calculated to be in the range of 46–3589 cm−1. The B–H and B–N stretching modes appeared at 2579 and 1391 cm−1, respectively, and the maximum vibrational mode belongs to the asymmetric stretch of H–N–H. The dissociative adsorption of ammonia significantly influences the electronic properties of the B36 borophene, especially the HOMO level. After the adsorption process, the LUMO does not change significantly but the HOMO jumps sharply to higher energies by about 0.35 eV. This narrows the HOMO–LUMO gap by about 37 %, reducing from 1.11 to 0.69 eV. The HOMO–LUMO gap is an important index in determining the electrical conductivity and kinetic stability of semiconductors [24–30].

It is well known that several properties depend on the density functional used, and there is no universal exchange-correlation density functional for all properties. Therefore, we inspected the effect of different density functionals on the energetic and electronic properties of B36 and complex A. For this purpose, the calculations were repeated with four Minnesota 06 functionals, including M06-L [31], M06 [32], M06-2X [32], and M06-HF [33], with 0, 27, 54, and 100 % Hartree Fock (HF) exchange, respectively. The results in Table 1 show that the HOMO, LUMO, and HOMO–LUMO gap depend strongly on the type of density functional used. In all systems, the HOMO and LUMO stabilized and destabilized, respectively, upon increasing the %HF exchange, thereby increasing the HOMO–LUMO gap. For instance, the HOMO, and LUMO of B36 against the %HF exchange of the functionals was plotted in Fig. 4, illustrating a linear relationship.

Table 1 The results of different density functionals with 6-31G (d) basis set for dissociation of NH3 on B36 borophene. Activation (E act) and adsorption (E ad) are in  kcal mol−1, and the unit of electronic properties is eV. The E g is HOMO–LUMO gap and ΔE g is its change after the adsorption of NH3
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Fig. 4
figure 4

The HOMO, and LUMO of B36 against the %HF exchange of the different functionals

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Also, by growing the %HF exchange, the ∆E g value decreases (Table 1, Fig. 4). The ∆E g is a key value in the calculation of sensitivity of an adsorbent toward a chemical and in estimating the semiconductor electrical transport [34–37]. Non-hybrid functionals (B97D and M06-L) predicts higher HOMO and lower LUMO, thereby giving a smaller HOMO–LUMO gap. The %HF exchange has quite a large effect on the adsorption energy, so that by increasing the %HF the adsorption energy becomes more negative. The different results are due to the charge delocalization error and many self-interaction errors of approximate density functionals [38]. Based on the adsorption energy dependency on the %HF, it seems that the charge delocalization and self-interaction errors are more stabilized than two separate NH3, and B36 borophene more than the complex.

We also probed the effect of different basis sets, including split-valence 6-31 + G(d), and 6-311++G(d,p), and correlation-consistent cc-pVDZ, and cc-pVTZ at the same B97D level of theory. The results in Table 2 show that enlarging the basis set by adding polarization or diffuse functions on hydrogen or heavy atoms slightly influences the adsorption energies, HOMO and LUMO levels, but it has no significant effect on the HOMO–LUMO gap and its change upon the adsorption process. The results of the correlation-consistent basis sets are in good agreement with those of split-valence. Generally, the results depend much more on the exchange correlation functional than on the basis set.

Table 2 Results of different basis sets at B97D level for dissociation of NH3 on the B36 borophene. Adsorption energy (E ad) is in kcal mol−1, and the unit of electronic properties are eV. The E g is HOMO–LUMO gap and ΔE g is its change after the adsorption of NH3
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In the next step, we have explored the kinetic possibility of NH3 dissociation on the B36 borophene. With this aim, we calculated the transition state structure using the synchronous transit-guided quasi-Newton (STQN) method [39]. Our calculations show that the NH3 molecule moving toward the tube has to overcome an energy barrier of 17.4 kcal mol−1 before entirely breaking the N–H bond at the B36 edge. When the reaction reaches the TS structure (Fig. 5), the H–NH2 bond is lengthened from 1.028 Å (in single NH3) to 1.381 Å, and the corresponding WBI decreased to 0.352, representing a tendency for bond breaking. We predicted a strong negative vibrational mode at −1598 cm−1, which corresponds to the coordination of detaching the –H atom from the NH3 and attaching to the B atom of B36. An animation of this mode is provided in the Supplementary material, which can be viewed with internet browser software.

Fig. 5
figure 5

The optimized structure of transition state of dissociation of ammonia molecule on the B36 borophene. Distances in Å

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The activation energy was calculated once again at the M06-L, M06, M06-2X, and M06-HF levels. Figure 6 shows a scheme of the reaction pathway for the dissociative adsorption of NH3 on the B36 borophene at these levels. The zero energy level relates to the two reactants (NH3 and B36) being infinitely far from each other. The results indicate that, similar to the adsorption energy, the activation energy is lowered as the %HF increases. This is attributed to a reduction in the charge delocalization error in the separated species. It can be expected that the dissociative adsorption of NH3 may be carried out even at room temperature, according to the small energy barrier and large adsorption energy.

Fig. 6
figure 6

A scheme of the reaction pathway for the dissociative adsorption of NH3 on the B36 borophene at different levels

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Conclusions

Using DFT calculations at B97D, M06-L, M06, M06-2X, and M06-HF levels of theory, the dissociative adsorption of NH3 on the surface of a B36 borophene was investigated. It was shown that this reaction may be carried out at room temperature, considering the small energy barrier of 14.1 kcal mol−1 and ∆G of −31.9 at B97D level of theory. The results reveal that the adsorption and activation energies are decreased and the HOMO–LUMO gap sharply increased by increasing the %HF exchange. Also, we predicted a linear relationship between the HOMO or LUMO of B36 borophene and the % HF exchange of functionals.