Introduction

Since the tubular diameter and chirality have meaningful effects on the electronic properties of carbon nanotubes (CNTs), extensive studies have been performed on analogous tubular nanomaterials that their electronic properties are independent of these features [1–3]. BNNTs are the structural analog of CNTs in which alternating B and N atoms fully substitute for C atoms [4]. However, CNTs and BNNTs have similar structures, but their properties are thoroughly different. BNNTs are known as semiconductors with a wide band gap (~5.5 eV) nearly independent of tube structure [5, 6], while CNTs can show metallic or semiconductor behaviors [7–9]. In addition, BNNTs have high oxidation resistance, unique mechanical properties, high thermal conductivity, and structural stability [10, 11]. These beneficial properties make BNNTs promising materials for various potential applications.

The large band gap and chemical inertness impose great restriction on the wider applications of BNNTs. Therefore, functionalization of BNNTs either by covalent or noncovalent methods expands their potential applicability. Covalent functionalizations of BNNTs using atoms, organic molecules, and functional groups can effectively change the electronic structures [12, 13], magnetic properties [14, 15], and solubilities [16, 17] of BNNTs [18]. Thus, many experimental and theoretical studies have been reported on covalent [13, 17, 19–25] and noncovalent [18, 26–28] functionalization of BNNTs. Saikia et al. [29] utilized DFT calculation to investigate the effect of noncovalent functionalization on the structural and electronic properties of (5,5) and (10,0) BNNTs. They found that functionalization of BNNTs with isoniazid displays the presence of new impurity states within the HOMO–LUMO energy gap of pristine BNNT. The functionalization of (5,5) BNNT by C10H7CO, CH3(CH2)2CO, and CH3(CH2)16CO molecules has been investigated by Zhi et al. [13]. They showed that the covalently functionalized BNNTs can be either n- or p-doped depending on the electronegativity of molecules attached. Anota et al. have investigated the properties of the chemical functionalization of (5,5) BNNTs with levothyroxine [30], thiol, and hydroxyl groups [31] on the basis of density functional theory calculations.

In our previous works [25], we investigated the effect of CH3CO functional group on electronic and structural properties of zigzag-type single-walled BNNTs. Functionalization of CNTs via the 1,3-dipolar cycloaddition reaction of azomethine ylides has been investigated extensively for their unique properties and many potential applications [32–35]. So far, 1,3-dipolar cycloaddition reaction of azomethine ylides with BNNT to form a functionalized BNNT has not been investigated. In this work, we have investigated structural and electronic properties of (6,0) BNNT functionalized with 2-methoxy-N,N-dimethylethanamine (MDE) using the M05-2X method. The changes in geometrical parameters, reaction energy, bond gaps, isodensity surfaces of highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), electrophilicity index, chemical potential, chemical hardness and softness, dipole moment, atomic charge, and the maximum amount of electronic charge are calculated. Furthermore, we have investigated atomic charge distribution in nanotubes by NBO [36] analysis.

Computational details

ONIOM approach [37, 38] has clear advantages for modeling nanoscale systems. Using this technique, it is possible to model a large system by applying a high-level quantum mechanical theory to the immediate region of interest and a lower level of theory, such as semiempirical or molecular mechanics, to the rest of the system. It can avoid the computationally prohibitive step of applying high-level theory to a system with many atoms while still yielding accurate results. In fact, ONIOM calculations have been shown to successfully model both reactions and noncovalent interactions involving nanotubes [22, 39–50]. In ONIOM approach, the full system is divided into a reactive part, which is treated at an appropriately high level of theory computationally, while the remainder of the system is included at a less-expensive lower level of theory. This ensures an appropriately high level of accuracy for the reactive part of the system while reducing the computational cost by only calculating this smaller part with the expensive method [50].

In this work, ONIOM methodology is used to study the effect of functionalization on the electronic and structural properties of BNNT. We selected a (6,0) zigzag single-walled BNNT consisting of 36 B and 36 N atoms, that the end atoms were saturated by hydrogen atoms to avoid the boundary effects. The length and diameter of optimized pure tube are computed about 11.46 and 4.92 Å, respectively. The structure of the functionalized BNNT was calculated using M05-2X functional [51] at the ONIOM(M05-2X/6-31+G(d,p):M05-2X/STO-6G) level of theory. In addition, single-point energy calculation at the M05-2X/6-31+G(d,p) level is carried out to obtain more reliable energies. All calculations have been performed using the GAUSSIAN-09 program package [52]. NBO analysis was carried out for all complexes at the M05-2X/6-31+G(d,p) level of theory.

From the optimized structures, global molecular descriptors [53–57] such as HOMO–LUMO energy gap, electronegativity (χ), chemical potential (µ), chemical hardness (η), chemical softness (S), the maximum amount of electronic charge (ΔN max) that the system may accept, and electrophilicity index (ω) [58] are calculated as follows:

$${\text{Energy}}\;{\text{gap}}\, = \,E_{\text{LUMO}} - E_{\text{HOMO}}$$
(1)
$$\mu = - \chi = - (I + A)/2$$
(2)
$$\eta = (I - A)/2$$
(3)
$${\text{S}} = 1/2\eta$$
(4)
$$\Delta N_{\hbox{max} } = - \mu /\eta$$
(5)
$$\omega = \mu^{2} /2\eta ,$$
(6)

where I and A are the first ionization energy and electron affinity, respectively. According to Molecular Orbital (MO) theory, the ionization potential of a molecule is simply the orbital energy of the HOMO, and the electron affinity is the orbital energy of the LUMO, with changes in sign. These are consequences of Koopmans’ theorem [59, 60]. The electrophilicity index is a measure of the capacity of an electrophile to accept the maximal number of electrons in a neighboring reservoir of electron sea.

Results and discussion

Energies and geometries

The optimized geometrical parameters for monomers and functionalized BNNT (f-BNNT) are shown in Fig. 1. In whole of this work, CB and CN denote C atoms of MDE functional group connected to B and N atoms of BNNT, respectively. The circumferences of the BNNT consist of one kind of atoms, either N or B atoms; if one of the ends is formed by N atoms, the other end is formed by B atoms. Diameters of the N-terminated, B-terminated, and middle rings of pure BNNT are 5.090, 4.820, and 4.910 Å, respectively. The tube diameter at the end of N-terminated is greater than that of B-terminated. This study examines the reaction between MDE functional group and nanotube surface.

Fig. 1
figure 1figure 1

Optimized structural parameters for monomers and D1–A5 complexes

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There are two different B–N bonds in BNNTs. The B–N bonds around the tube axis (L1) and the B–N bonds along the tube axis (L2). Since BNNTs are obtained by rolling the BN graphene-like sheet, the slanted B–N bonds have a larger local curvature in zigzag BNNTs and are more reactive than the B–N bonds parallel to the tube axis. As shown in Fig. 1, due to the greater curvature, the L1 bond lengths in the pristine NT are longer than L2 ones, indicating that the slanted L1 bonds are more reactive than the L2 bonds paralleled to the tube axis.

All L1 and L2 bonds on the sidewall of BNNT were considered for attachment of an individual MDE functional group. We found the eleven minima energy structures on the potential energy surface (Fig. 1). For axial (A) and diagonal (D) structures, MDE is bonded to the L2 and L1 bonds of BNNT, respectively.

Because of the iconicity of B–N bonds, results show that in the addition of MDE to the B–N bonds of zigzag BNNTs, the formation of open structures is preferable for mentioned tube. As can be seen, diagonal B–N bonds increase from an average value of 1.458 Å in pristine BNNT to 3.325, 1.895, 1.896, 1.810, 1.794, and 1.810 Å, in D1-D6 complexes, respectively. In configuration D1, the MDE functional group interacting with the end of N-terminated BNNT leads to the opening B–N bond. Thus, the longest diagonal B–N bond attached to MDE is observed in D1 complex. The increase in diagonal B–N bonds of B-terminated BNNT is shorter than that in the middle bonds. For the D structures, the newly B–C and N–C chemical bonds formed between MDE and BNNT make a nine-membered ring, thus inducing a local structural deformation in BNNT.

The optimized geometries of the D group of f-BNNT exhibit the B–C and N–C bond lengths of 1.593 and 1.423 Å in D1, 1.613 and 1.498 Å in D2, 1.610 and 1.500 Å in D3, 1.638 and 1.496 Å in D4, 1.637 and 1.497 Å in D5, and 1.604 and 1.499 Å in D6, respectively. These results reveal that the N–C bonds are shorter than B–C bonds. The average values of B–C and N–C bond lengths are 1.508, 1.556, 1.555, 1.567, 1.567, and 1.552 Å, respectively. These results indicate that the reactions between MDE and B–N bonds at the end of N-terminated and B-terminated BNNT are stronger than other bonds. Thus, these sites in BNNT are favored for functionalization by MDE.

The length of N–C bond in the A1–A5 complexes is 1.510, 1.567, 1.510, 1.513, and 1.501 Å and that of B–C bond is 1.631, 1.635, 1.620, 1.620, and 1.622 Å, respectively. As can be seen, similar to D group of complexes, the B–C bonds in A group of complexes are longer than N–C bonds. The average value of B–C and N–C bond lengths are 1.571, 1.601, 1.565, 1.567, and 1.562 Å, respectively, showing that the bonds formed in A5 complex are stronger than those in A1–A4 ones. Thus, L2 bond in the end of B-terminated BNNT is favored for reaction with MDE functional group. In addition, comparison of the bonds formed between MDE and BNNT in A and D complexes shows that the bonds in D complexes are stronger than those in A ones.

As shown in Fig. 1, the axial (L2) B–N bond lengths increase from an average value of 1.448 Å in pristine BNNT to 1.693, 1.679, 1.693, 1.687, and 1.682 Å in the A1–A5 complexes, respectively. Comparison of B–N bonds in two types of complexes shows that the change in B–N bond length upon functionalization of BNNT in D complexes is bigger than that in the A ones.

The complex formation also leads to structural changes in MDE molecule. The C atoms of the MDE bonded to N and B atoms of NT are symbolized as CN–N and CB–N, respectively. For the free MDE functional group, the optimized CN–N and CB–N bond lengths are 1.336 and 1.329 Å, respectively. The CB–N (CN–N) bond lengths of D1-D6 complexes are 1.476 (1.454), 1.465 (1.444), 1.465 (1.444), 1.471 (1.438), 1.473 (1.440), and 1.464 (1.442) Å, respectively, showing that both the CN–N and CB–N bond lengths increase upon complex formation, so that this increase in D1 complex is greater than that in the other ones. For A1–A5 complexes, the optimized CB–N and CN–N bond lengths are (1.467 and 1.431), (1.486 and 1.414), (1.471 and 1.435), (1.466 and 1.429), and (1.471 and 1.438), respectively.

Total energy, relative energy, reaction energy (RE), and dipole moment of the D and A compounds are summarized in Table 1. Relative energy of f-BNNTs in D1–D6 is 0.0, 14.4, 16.2, 15.9, 16.1, and 11.1 kcal/mol and that of A1–A5 is 19.4, 15.2, 16.4, 17.5, and 12.1 kcal/mol, respectively. Thus, D1 in the D group complexes and A5 in the A ones are more stable than other complexes in each group of compounds, in good agreement with the predicted structural parameters involved in the reaction.

Table 1 Total energy, relative energy, reaction energies (RE), and dipole moment for BNNT-MDE system at M05-2X/6-31+G(d,p) level of theory
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The calculated reaction energies for A and D complexes at M05-2X/6-31+G(d,p) level of theory are presented in Table 1. The RE is defined as RE = E complex − (E BNNT + E MDE), where E complex is the total energy of the BNNT-MDE system. As can be seen in Table 1, RE values for D1, D2, D3, D4, D5, and D6 complexes are −37.0, −22.1, −20.3, −20.7, −20.5, and −25.7 kcal mol−1 and for A1, A2, A3, A4, and A5 complexes are −17.2, −21.4, −20.0, −19.1, and −24.5 kcal mol−1, respectively. The negative RE means exothermic addition reaction on BNNT sidewalls. Comparison of REs reveals that the stability of complexes decreases in the order of D1 > D6 > D2 > D4 > D5 > D3 for D complexes and A5 > A2 > A3 > A4 > A1 for A complexes. It is evident from the RE values that the D complexes are more stable than A complexes. According to these results, it is energetically favorable for the MDE functional group to interact with the slanted B–N bonds at the end of the N-terminated (D1), due to the rather large local curvature of this kind of B–N bonds, and B-terminated (D6) BNNT and axial B–N bonds at the end of the B-terminated (A5) BNNT. The reaction energies obtained for attachment of the MDE to BNNT are comparable with that of reported [33] for attachment to (5,5) CNT at PBE/6-31G* level (20.3 kcal mol−1).

Frontier molecular orbitals

The influences of functional group on electron density distributions of HOMOs and LUMOs have also been investigated. Figure 2 presents the isodensity surfaces of the HOMOs and LUMOs of pristine and functionalized BNNT. It can be seen that the HOMO in MDE is quite localized on the CH2 groups, indicating a tendency of molecule to react through the CH2 groups. The HOMO in pristine BNNT is quite localized on the N atoms at the end of N-terminated, whereas LUMO is distributed on axial B–N bonds and mainly on the end of B-terminated. For the f-BNNTs, the HOMO states are basically localized on the MDE functional group and in the vicinity of the covalently attached functional group, whereas electron density of LUMO is distributed on the B–N pairs along the tube axis and mainly on the end of B–terminated. The analysis of the electron density distributions of HOMOs and LUMOs reveal that the upon electronic excitation from HOMO to LUMO, electron density on the MDE decreases.

Fig. 2
figure 2

The isodensity surface of HOMO and LUMO for MDE, pristine BNNT, and D1–A5 complexes at the isovalue of 0.02. N and B atoms are represented by blue and pink spheres

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Global reactivity descriptors

To better understand the effect of functional group on the electronic properties of BNNT, the electronic structures of pristine and functionalized BNNT were investigated. The frontier molecular orbitals, HOMO–LUMO energy gap, μ, η, S, ω, and ΔN max are tabulated in Table 2.

Table 2 HOMO energy (E HOMO), LUMO energy (E LUMO), HOMO–LUMO energy gap (E L–H), electronic chemical potential (µ), chemical hardness (η), chemical softness (S), electrophilicity index (ω), and the maximum amount of electronic charge (ΔN max) for MDE, pristine BNNT, and functionalized BNNT
Full size table

The energy gap between HOMO and LUMO usually defines the lowest electronic energy absorption band [55]. A high HOMO–LUMO energy gap indicates greater stability and low reactivity of the chemical system. Hard molecules have a large energy gap, and soft molecules have a small energy gap. A soft molecule with a small gap will be more polarizable than hard molecules.

As can be seen in Table 2, the bond gap of pure nanotube is calculated as 7.17 eV. After attachment of MDE, the bond gap between HOMO and LUMO decreases, implying an increase in reactivity of the f-BNNT systems. Decrease in bond gaps upon complex formation of A complexes is greater than those of the corresponding D complexes. Although stability of D complexes is greater than that of the A ones, the conductivity of A complexes is predicted to be greater than that of the D ones. The conductivity of complexes increases in the order of A2 > A1 > A3 ~ A4 > A5 > D1 > D2 > D6 > D4 > D5 > D3. Comparison of values in Table 2 indicates that chemical potential, hardness, and electrophilicity index (with the exception of A3) decrease and the chemical softness increases upon functionalization. On the other hand, functionalization of BNNT by MDE functional group is accompanied with the increase of ΔN max in A complexes and decrease in D ones.

The DOS (shown in Fig. 3) of pure and f-BNNTs was plotted to illustrate how the functional group affects the electronic structure of the BNNTs. As can be seen in this figure, the DOS of BNNT/MDE complexes is significantly changed when the MDE is localized on the BNNT surface. Figure 2 also shows that the presence of MDE on the BNNTs decreases the band gap of the pure BNNT and increases its electrical conductance.

Fig. 3
figure 3

Density of states (DOS) for MDE, pristine BNNT, and D1–A5 complexes

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NBO analysis

Among theoretical methods, NBO analysis is a unique approach to the evaluation of the atomic charges and charge transfer energies. The NBO analysis reveals interesting details on the electron density transfer in donor → acceptor interactions [36]. The results of NBO analysis at the M05-2X/6-31+G(d,p) level of theory are given in Table 3. It is clear that the charges of N and B atoms in these structures are negative and positive, respectively. According to NBO analysis, the strongest effect of the functional group on the net charges takes place on B and N atoms connected to the functional group. It can be seen from Table 3 that the positive charge of B atoms and negative charge of N atoms connected to MDE functional group in all complexes decrease upon complexation. In all complexes, the negative charge of CB atom of f-BNNT increases upon complex formation and that of CN atom of f-BNNT decreases. The negative charges of CB atoms are larger than those of the corresponding CN atoms. Also the negative charge of N atom of MDE functional group connected to C atoms increases upon functionalization.

Table 3 NBO results calculated at the M05-2X/6-31+G(d,p) level of theory
Full size table

Table 3 also shows that the charge transfer (CT) occurs from nanotube to MDE group (with the exception of A2). In the A2 complex, the charge is transferred from MDE group to the nanotube. The CT values for D1–D6 complexes are 0.0502, 0.0277, 0.0172, 0.0150, 0.0006, and 0.0189 au and in A1, A2, A3, A4, and A5 complexes are 0.0348, 0.0429, 0.0193, 0.0115, and 0.0137, respectively. The amount of charge transfer has been defined as the sum of electronic charge of atoms in MDE functional group.

Conclusions

In this paper, we have studied the structural and electronic properties of the covalent functionalization of (6,0) BNNT surface with MDE functional group based on density functional calculations. There are two different B–N bonds in BNNTs. The B–N bonds around the tube axis are designed as L1 and the B–N bonds along the tube axis are labeled as L2. All B–N bonds on the sidewall of BNNT were considered for adsorption of an individual MDE group. For axial (A) and diagonal (D) structures, MDE is located on the L2 and L1 bonds of BNNT, respectively. Due to the greater curvature, the L1 bonds are more reactive than the B–N bonds parallel to the tube axis. The results show that the reaction of MDE with (6,0) BNNT is exothermic. It is evident from reaction energies that the D complexes are more stable than the A ones. The configuration of the lowest minimum energy corresponds to geometry D1, in which the functional group interacts with N-terminated of the BNNT.

Functionalization of BNNT by MDE functional group is accompanied by a decrease in the band gap of the pure BNNT and an increase in the electrical conductance. Decrease in band gap of nanotubes for A complexes is greater than that for corresponding D complexes. Also, the chemical potential, hardness, and electrophilicity index decrease and the chemical softness increases upon functionalization. In addition, we have considered the isodensity surfaces of the HOMOs and LUMOs for pure and f-BNNTs. Also, the results obtained by NBO analysis showed that the charge transfer occurs from nanotube to MDE group (with the exception of A2).