1 Introduction

The 2D boron nitride (BN) with hexagonal symmetry and heteronuclear boron-nitrogen bonds was reported for the first time in 2005 [1] with electronic behavior of insulator (5.9–6.1 eV) [2]. The hexagonal BN nanosheets have similar structure to graphene with sp2 hybridization, as well as B–N bond length of 1.44 Å, which is comparable to the C–C bond length of 1.42 Å in graphene. This nanosheet has gained great interest due to, first, its intrinsic properties [3] and, second, to its various technological applications recently reported [4,5,6,7].

However, in the search for new and/or better properties of this 2D BN system, it is essential to propose nanosheets rich of boron and nitrogen atoms (homonuclear bonds) with the chemical composition B30N24H18 and B24N30H18, respectively, such as it was reported in 2017 [8]. These are stabilized in anionic charge (Q = − 1|e|) and doublet state (M = 2) due to the position of boron atoms forming a linear chain of homonuclear boron bonds. So far, only a few theoretical reports are available on 0D [9, 10], 1D [11, 12] and 2D [13] nanostructures considering these homonuclear bonds and inferring changes in their electronic properties as well as a possible synthesis routes in the case of 0D systems [10].

In this sense, this short investigation reports an electronic structure analysis of two novel boron nitride nanosheets containing homonuclear boron bonds in a specific geometry and the chemical compositions B30N24H18 and B33N21H18 using de density functional theory (DFT) for the quantum simulations. This study or quantum analysis allows us to propose this nanosheet as adsorber and possible vehicle for drug delivery, and that perhaps it can give us indications of its possible synthesis since it was reported for fullerene-like structures [10].

This work is divided as follows: Sect. 2—Methodology addresses information on the level of DFT theory used to perform quantum simulations, as well as the characteristics of the analyzed systems. In Sect. 3, the analysis was carried out through quantum descriptors typical of DFT theory, to visualize their possible applications, and finally the conclusions are reported.

2 Quantum simulations: computational details

Quantum simulations using density-functional were developed to propose two novel armchair modified boron nitride nanosheets (BNNs) constructed from hexagonal BN patterns. The chemical compositions were: B30N24H18 and B33N21H18 for a BN nanosheets generating homonuclear boron bonds (see Fig. 1). These systems are generated through the re-emplacement of a central hexagon and periphery by boron atoms. The size of these systems was determined in such manner that the calculated cohesion energy and the |HOMO–LUMO| gap energy are in concordance with the reported experimental and theoretical results [2, 14]. Neutral (Q = 0), anionic (Q =  − 1|e|) and cationic (Q =  + 1|e|)) systems were considered in this study (see Supplementary material). Furthermore, two spin-states, defined by multiplicity values (M = 2ST + 1; ST = total spin) of 1 and 2, they were addressed for the hexagonal BN nanosheet/rich in boron atoms. The full geometry optimization for the BN nanostructures were performed with the HSEh1PBE hybrid functional, coupled with 6–311 +  + g(d,p) orbital basis sets, as it is implemented in the quantum chemistry Gaussian-09 software [15]. The HSEh1PBE functional, being derived from the Perdew- Burke-Ernzerhof exchange–correlation method (PBE), can describe the non-covalent interactions reasonably well. This functional includes 25% of the exact Hartree–Fock exchange energy [16, 17]. The electronic gap using DFT descriptors [18] was approached as the energetic difference between the frontier orbitals: HOMO (Highest Occupied Molecular orbital) and LUMO (Lowest Unoccupied Molecular Orbital) for case spin no-polarized, and GapHL spin up ↑ = |(εHOMO ↑—εLUMO ↑)/2| ≈ |εHOMO ↑–εLUMO ↑| and GapHL spin down ↓ = |(εHOMO ↓—εLUMO ↓)/2| ≈ |εHOMO ↓—εLUMO ↓| [19] for open-shell systems. The cohesion energy of these structures was determined as follows: ECoh = ET(BN nanosheets/Rich in Boron)–kET (Boron)–pET(Nitrogen)–mET (Hydrogen)/(k + p + m), where ET represents the total energy for the most stable structures of neutral (Q = 0, multiplicity = 1 or 3) or charged (Q =  − 1|e|), multiplicity = 2) nanosheets. While ET (Boron or nitrogen) represents the total energy for the ground state of the boron or nitrogen atoms. The labels k, p and m represent the number of boron, nitrogen and hydrogen atoms in the structures.

Fig. 1
figure 1

Boron nitride nanosheets in the chemical composition a, b B30N24H18 (neutral and cation charge); c, d B33N21H18 (neutral charge)

Full size image

3 Results and discussion

For the new proposals of BN nanosheets, these are stabilized in neutral, anionic (− 1|e|) and cationic (+ 1|e|) charge, due to the introduction of a greater amount of boron atoms (55.56% more than chemical composition B30N24 and 61.11% for B33N21, respectively) than pristine BN structure (50/50% of boron/nitrogen). The geometry presented by this nanosheet is influenced by global charge, that is, for chemical composition B30N24H18 exhibits pentagonal and triangular geometry at the central zone, as result of the geometric optimization, see Fig. 1a-top view, versus the hexagonal geometry in the rest of the nanosheet. It is noteworthy that the energetic difference between this nanosheet and that reported in reference 8 (but different arrangement, that is a linear chain of boron atoms) at the same level of theory used in this work is ∆E = 1.60 eV, indicating that we have found it to be more stable the composition and ordering reported in this work. See Table S1—Supporting Information.

The range of values for B–B bond length is larger (1.56–1.79 Å) than those of reported for the other nanosheets rich in boron atoms of the same chemical composition [8]. Here a convexity is also observed in the central zone, see Fig. 1b-top side. Similar situation of increasing occurs for the B–N heteronuclear bond, this range is from 1.40 to 1.47 Å. Therefore, a lot of flexibility is observed in these types of bonds, which may provoke improvements in their mechanical properties. For this same chemical composition with cationic charge (Fig. 1a), a completely triangular geometry is observed at the central hexagon analogous to the boron nanostructures [20], and also this structural change is attributed to the effect of the global charge and multiplicity or spin magnetic moment, as it has been already reported in the literature in the case of a cluster of B6 being adsorbed on a fullerene-like structure [21].

For the second nanosheet, B33N21H18 (see Fig. 1c—top view) chemical composition, the bond distance of B–B is 1.52 to 1.70 Å and 1.44 to 1.48 Å for B–N. Similarly, this nanosheet has a concavity at the central area, see Fig. 1d—top side. Here, around the central zone, a geometry combination of hexagons, pentagons and triangles is observed, this is in the second ring (coronene-like structure).

According to these latter structural features, the new nanosheets improve considerably their stability, as can be seen in Table 1 according to the cohesion energy with a value of − 10.94 eV/atom for B30N24H18 in neutral charge and of − 10.10 eV/atom for B33N21H18 also in neutral charge compared to the value reported for BCN nanosheet (− 7.4 eV [22]) and graphene − 7.8 eV/atom [23], so its structural and chemical stability is guaranteed. Furthermore, to guarantee the determination of local minima, vibrational calculations also as a criterion of structural stability, within the harmonic approximation, were carried out for the lowest energy structures, obtaining positive values, see Fig. 2.

Table 1 Bond length (Å), HOMO−LUMO gap (eV), Dipole moment (Debye), Chemical potential (eV), Moment magnetic (µB) and cohesion energy (eV/atom) for pristine hBNNs, hBNNs/Rich in Boron
Full size table
Fig. 2
figure 2

Vibrational spectrum for nanosheets with neutral, cation and anion charge, a, b, c B30N24H18; d, e, f B33N21H18

Full size image

In the same way, this small variation or introduction of a greater number of boron atoms makes it more stable than the previously reported BN nanosheet, which contains a linear chain of homonuclear boron bonds, whose value was found to be − 5.48 eV/atom [8].

On the other hand, analyzing their electronic properties such as the value of |HOMO–LUMO| energy gap as a qualitative measure of its electrical conductivity indicates two important transitions: (i) insulator (pristine BN nanosheet) → semiconductor (B30N24H18 nanosheet) and (ii) insulator (pristine BN nanosheet) → conductor (B33N21H18) transition. This information is corroborated by means of the density of state plot (Fig. 3) obtained from periodic calculations, the conductor-like electronic behavior is clearly observed since it does not present an energy gap. This same electronic transition (insulator-conductor) is also observed in fullerenes with large chemical composition B47N53 [23] and B116N124 [24] due to the combination of heteronuclear and homonuclear bonds causing its stability.

Fig. 3
figure 3

Total DOS of boron nitride nanosheet (B33N21H18-in neutral charge and multiplicity 3)

Full size image

The value of their polarity (1.55 to 1.88 D) indicates their affinity with solvents such as water (1.85 D). This effect leads to propose them as sensors or vehicles for drug delivery. In addition, this parameter as a vector (for these cases they point out to the central hexagon with the largest number of boron atoms) tells us how the electric charge distribution is, causing reactive sites, unlike to the pristine structure which it has a null dipole moment.

Also, it is highlighted the fact that the nanosheet in B33N21H18 chemical composition is stabilized in global neutral charge and multiplicity 3 (see Table S1—Supporting Information) it is inferred possible magnetism, that is, a magnetic moment of 2.0 µB coming from the atoms of boron hybridized to the nitrogen atoms in the middle of the nanosheet as it is observed in the total spin density, see Fig. 4. This magnetic moment is compared with previous reports for the BN nanoribbons with values of 0.90 (for boron) and 0.83 (for nitrogen) µB [25]. Therefore, under these characteristics, it is feasible that we can propose these nanosheets as sensors and/or vehicles for drug delivery due to their richness in the number of boron atoms. As an example of this situation, it is presented in the BN nanosheets that when the pristine is compared versus those containing homonuclear boron bonds, these improve the adsorption of DNA nucleobases on their surface [26] or the possible degradation and activation of contaminants by considering in B12N12 fullerenes these types of bonds [9, 27] due to a re-distribution of charge, that is, considering areas with negative and positive charge on boron atoms (Fig. 5) that become attracting sites for various molecules, also the high polarity, low chemical reactivity and magnetic behavior. This magnetism could favorably influence the adsorption process of various molecules.

Fig. 4
figure 4

Total spin density for chemical composition B33N21H18 nanosheet in neutral charge

Full size image
Fig. 5
figure 5

Atomic charges of a BN nanosheet pristine, b B30N24H18 nanosheet, and c B33N21H18 nanosheet. In red and deep red: negative; green: positive

Full size image

Finally, the low value of their electronic affinity/ionization potential (1.71/5.82 eV) indicates that it is feasible for the nanosheet to behave as a charge acceptor/electrodonating, consistent with their nature as a semiconductor/conductor according to their gap energy, respectively.

4 Conclusions

DFT calculations were developed to propose two novel armchair boron nitride nanosheets with heteronuclear and homonuclear boron bonds which were stabilized with neutral, anionic and cationic charge and semiconductor and conductor-like behavior. These were more stable than the pristine B27N27 nanosheet (50/50% in boron/nitrogen atoms or heteronuclear bonds) according to their cohesion energy, the dependence is observed in the position where it is doped with boron atoms. They also present high polarity and possible magnetic behavior for the composition B30N24H18 (55.56% in boron atoms) and B33N21H18 (61.11% in boron atoms) in global neutral charge. According to these electronic properties, these nanosheets are proposed to improve applications for drug sensing and/or transport processes due to higher negative charge (concentrated in boron atoms) that causes areas of attraction for various molecules.