Nuclear Magnetic Resonance Parameters of Pure and Diborinin-Doped (6,0) Single-Walled Zigzag BNNT: DFT Study

Arshadi, Sattar; Abedini, Saboora; Asghari, Ameneh; Alipour Zaghmarzi, Fatemeh

doi:https://doi.org/10.1155/2013/421091

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Molecular Modeling: Advancements and Applications

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Volume 2013 | Article ID 421091 | https://doi.org/10.1155/2013/421091

Nuclear Magnetic Resonance Parameters of Pure and Diborinin-Doped (6,0) Single-Walled Zigzag BNNT: DFT Study

Sattar Arshadi,¹Saboora Abedini,¹Ameneh Asghari,¹and Fatemeh Alipour Zaghmarzi¹

Academic Editor: Sebastian O. Danielache

Received24 Jun 2012

Revised14 Sept 2012

Accepted04 Oct 2012

Published20 Nov 2012

Abstract

A computational study on the basis of density functional theory (DFT) calculations has been performed to investigate the properties of the electronic structure of (6,0) zigzag boron nitride nanotubes and two models ((a) and (b)) of diborinin-doped boron nitride nanotubes (DBD-BNNTs). The calculated structural energies yield similar values for two models of DBD-BNNTs. Isotropic () and anisotropic () chemical shielding parameters of the optimized BNNT and DBD-BNNTs are calculated. The results illustrate that the changes in chemical shielding tensors of ¹¹B and ¹⁵N nuclei are more significant in the nearest neighborhood of the diborinin ring due to doping process. The changes of the electronic sites of the N atoms are also more significant than those of the B atoms. The dipole moments of the diborinin-doped BNNT structures show changes with respect to the pristine model. It is clear that the doping of diborinin ring decreases the energy gaps of the pure BNNT. For the pure model, the HOMO is located on the nitrogen atoms, and the LUMO is uniformly distributed throughout the B–N bonds. In contrast, for the diborinin-doped models, the majority of the HOMO and LUMO are located at the diborinin-doped regions.

1. Introduction

Nanostructures such as nanotube are currently the subject of intense research because of the potential applications in nanoscale electronic and optoelectronic fields [1–4]. After the exploration of carbon nanotubes (CNT) by Iijima in 1991 [1], nanotubes of other chemical compositions such as boron nitride have also been investigated [5]. Boron nitride nanotubes (BNNTs) have been the focus of several experimental and theoretical studies on account of their potential applications in high speed electronics [6]. BNNTs were successfully synthesized [7] shortly after prediction in theory [8].

BNNTs are a typical member of III-V, compound with morphology similar to that of carbon nanotubes (CNTs) but with their own distinct properties. However, the electrical properties of BNNTs are very different from those of CNTs. While CNTs come in three basic forms (metallic, small-gap semiconductor, and modest-gap semiconductor) rely on diameter and chirality, first approximation of BNNTs are electrically uniform with an energy gap of about 4-5 eV [9]. This energy gap is independent of wall number, diameter, or chirality. For low applied electric fields, BNNTs are thus essentially insulating.

A tubular structure of BN can be formed by rolling up a sheet of hexagonal rings with boron and nitrogen in equal proportions possessing peculiar electrical [10], optical [11], and thermal [12] properties, which drastically differ from those of CNTs. BNNTs have high surface area, unique physical properties and morphology. On top of that, BNNTs possess high chemical stability. These properties make BNNTs one of most promising materials for nanotechnology applications, especially under oxidative, hazardous and high-temperature environments. But there have been quite a few attempts to control the properties by incorporating extrinsic foreign atom doping. These substitutions in BNNT significantly modify the chemical binding configuration, physical, chemical, and optical properties in comparison to pure BNNT [13].

Carbon-, Si-, Ti- and Pt-doped [14–18] BNNTs have been studied, and their results reveal that the electronic properties of BNNTs might be exploited for various applications. Generally, doping of BNNTs with other elements is a promising approach to control their electronic structures. On the other hand, the BNNTs are produced through heating of C templates with B₂O₃ in a flowing N₂ atmosphere at 1503–1773 K. Due to this process, carbon atoms replace with B and N atoms but somewhere, diborinin ring formation as a defection in BNNT structure come into view.

Exploitation of the chemical and physical properties of nanotubes requires understanding and control of their structure during synthesis. While several techniques are used to probe nanotube structure, full characterization is not possible. ¹¹B and ¹⁵N NMR spectroscopy have the potential to provide a more detailed structural characterization.

In this direction, we have studied the structure of electronic properties and nuclear magnetic resonance (NMR) parameters of ¹¹B and ¹⁵N nuclei for pure (6,0) single-walled zigzag BNNT ((a) model) and DBD-BNNT ((b) and (c) models) via density functional theory method (DFT). The zigzag (6,0) BNNT is chosen here because the zigzag orientation is a preferred growth one and the (6,0) BNNT has a moderate diameter. In addition, we have investigated atomic charge of distribution in nanotubes by natural bond orbital (NBO).

2. Models and Computational Details

DFT calculations were carried out using the Gaussian 98 program [19] on the structure of pure and DBD-BNNT BNNTs. DFT has become extremely popular for molecular applications because it accounts for the correlation energy in computationally efficient manner and offers a substantially improved accuracy over conventional approaches. Subsequently, frequency calculations (keyword: FREQ = NORAMAN) were carried out by standard techniques on the optimized structures. For minimum state species, only real frequency values (with a positive sign) are accepted.

As was pointed out in the previous section, calculations have been performed on (a), (b), and (c) models (Figure 1). Two structural isomers of DBD-BNNTs ((b) and (c) models) were considered in the calculations within four sp²-hybridized carbon and two borons atoms (diborinin ring) were substituted instead of three boron and three nitrogen atoms in the middle of the nanotube.

(a)

(b)

(c)

(d)

At the first step of this study, each of the considered pure and diborinin-doped representative models of BNNTs was allowed to fully relax during the geometrical optimization and frequency calculation. The geometries were optimized at the B3LYP/6-311G** level of theory. Subsequently, the NBO analysis was carried out on the B3LYP/6-311G** wave functions. From the NBO calculations, highest-occupied molecular orbital (HOMO) and lowest-unoccupied molecular orbital (LUMO) energies, the band gap energies, dipole moments and electronegativity () for (a), (b), and (c) models of BNNTs were obtained.

Also, we investigated electronegativity () in the optimized structures. Within the conceptual framework of DFT, the electronegativity of a system of particles, with total energy and subject to the external potential , is defined as In (1), is the electronegativity [20–25]. Pauling introduced the concept of electronegativity as the power of an atom in a molecule to attract electrons [20]. Using the method of finite difference, an operational and approaching definition of is: where IP is the ionization potential and EA is the electron affinity of the system. Within the validity of Koopman’s theorem for closed-shell species, the frontier orbital energies are given by Therefore, on the basis of orbitals, we can write and are the energies of the lowest unoccupied and the highest occupied molecular orbitals LUMO and HOMO, respectively.

Finally nuclear magnetic resonance (NMR) parameters at ¹¹B and ¹⁵N nuclei of the optimized structures have been calculated. As noted, we have carried out these calculations at the GIAO/B3LYP/6-311++G** level, one of the best compromises between accuracy and computer time [26].

Mathematically, the anisotropic and isotropic chemical shifts are described by a 3 by 3 matrix. In this principal axis system, the chemical shift tensor is fully described by the three diagonal elements—the principal components (σ₃₃> σ₂₂> σ₁₁)—and the three eigenvectors or Euler angles describe the orientation of the principal axes with respect to an arbitrary frame. Therefore, (5) and (6) are used to convert the calculated chemical shielding (CS) tensors to the isotropic () and anisotropic () parameters. The isotropic value (the centre of gravity) is the average value of the principal components, and the anisotropy describe the largest separation from the centre of gravity. The evaluated NMR parameters for (b) and (c) models of DBD-BNNTs are listed in Tables 2 and 3, respectively. For the ease of comparison, the NMR parameters for (a) model of pure BNNT are listed in these tables. The following are equations (5) and (6):

3. Result and Discussion

3.1. Geometries

As shown in Figure 1, by substituting three B and three N atoms of pure BNNT ((a) model) with four sp²-hybridized carbons and two boron atoms, in the middle of the nanotube, (b) and (c) models of DBD-BNNTs are produced.

At the first step, geometrical optimizations and frequency calculations have been successfully carried out for the pure and doped models (a, b, and c) of single-wall (6,0) BNNT at the level of B3LYP/6-311G** basis set. The optimized geometries of pure and doped models of the BNNTs are listed in Figures 2 and 3. These figures present the optimized parameters including the bond lengths and bond angles for three models that investigated (6,0) BNNT. In the pure BNNT (Figure 2(a)), the average B–N bond length is 1.46 Å, consistent with previously reported DFT calculations [27, 28]. This value was also changed by the diborinin-doping in the DBD-BNNT due to existence of B–C, N–C, B–B, and C=C bonds, in addition to, B–N one.

(a)

(b)

(c)

(a)

(b)

(c)

However, the effects of this deformation are consequential, just at the geometrical properties of the nearest atoms to the diborinin-doped ring, whereas those of other atoms are almost remained unchanged. As shown in Figures 2(b) and 2(c), the average C=C and B–C bond lengths (1.36 Å and 1.56 Å, resp.) are different from B–N bond length (1.46 Å). Moreover, the changes of the bond angles are more than those of the bond lengths in the (6,0) zigzag DBD-BNNT (Figures 2 and 3).

The calculated structural energies, LUMO-HOMO gaps, electronegativity (), and dipole moments for three models of the investigated BNNTs have been listed in Table 1.

The calculated structural energies of two structural isomers ((b) and (c) models) of DBD-BNNT are equal to −51.2 keV and indicate no difference between them.

For better understanding of the nature of interaction in the diborinin-doped models, we studied the electronic properties of the models. The energies of both the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) are negative in all of model systems under study. The calculated energy gap for the pure BNNT is 4.87 eV (Table 1). In comparison to the pure systems, the energy gaps between HOMO and LUMO, (), have small values in (b) and (c) models of DBD-BNNT. The electronic densities of states (DOSs) of pure and diborinin-doped BNNT are plotted in Figure 4 for better understanding, the effect of diborinin ring doping to the electronic structure of BNNT. The electronic structures observed near Fermi level of the pure BNNT (Figure 4(a)) also show significant changes due to the diborinin ring doping (see Figures 4(b)-4(c)). So, the band gaps near Fermi level become sharply narrower. It is clear that the doping of diborinin ring decreases the energy gaps of the pure BNNT.

(a)

(b)

(c)

The HOMO and LUMO, the pure and diborinin-doped models are plotted in Figure 5. For the pure model, the HOMO is located on the nitrogen atoms of the (6,0) zigzag BNNT model and corresponds to the lone pair of electron on nitrogen atoms. In contrast, the LUMO is uniformly distributed throughout the B–N bonds. For the diborinin-doped models, the majority of the HOMO and LUMO are located at the diborinin-doped regions.

(a)

(b)

(c)

The edges of the armchair BNNTs include N and B atoms in both ends. In contrast to armchair models, edges of the zigzag BNNTs consist of one type atoms, either N or B atoms; if one of the ends is formed by N atoms, the other end is formed by B atoms. The B atoms are slightly positive and the N atoms are slightly negative. Therefore, the zigzag BNNT is a polar material (has a nonzero dipole moment) and this entry could be better seen by the value of its dipole moment. Comparing the values of the dipole moments for the two diborinin-doped models indicate, that the value for the (b) model is significantly increased (D = 9.28 Debye) whereas for (c) model is significantly reduced (D = 6.98 Debye), compared with the pure model (D = 7.47 Debye), which means that the orientations of diborinin ring in two diborinin-doped models foundation diverse dipole moment for these models (Figure 1 and Table 1).

3.2. NMR Parameter

NMR spectroscopy has proven to be an exceptionally powerful technique in characterizing molecular systems and structures. So, we have performed theoretical calculations of ¹¹B and ¹⁵N NMR data for (a), (b), and (c) models to study the influence of diborinin ring doping on the electronic structure properties of the (6,0) BNNT.

3.2.1. Pure Model

Tables 2 and 3 present the calculated NMR parameters for various ¹¹B and ¹⁵N nuclei in the pure (a) model of BNNT. This model includes 24 B and 24 N atoms, where the edges are saturated by 12 H atoms (Figure 1). The edge of this model consists of one type atom, either N or B atoms; if one of the end is formed by N atoms (N-tip), the other ends is formed by B atoms (B-tip).

According to the previous studies, to compare CS tensors between pure and doped models, ¹¹B and ¹⁵N nuclei in the pure (a) model are divided into four different layers which sense similar electrostatic properties in each layer, yielding the same values of the and parameters [29]. Almost no significant difference is observed in the calculated NMR parameters for the atoms of each layer; hence, just the average values in each layer for ¹⁵N and ¹¹B nuclei are reported in Tables 2 and 3.

The first layer consists of N1–N6 atoms and the last layer contains B19–B24 atoms, which forms the N-tip and B-tip of the considered models of BNNT, respectively. The values of NMR properties for the ¹¹B and ¹⁵N nuclei of the pure (a) model indicate that the B-tip has the smallest value of for both ¹¹B (64 ppm) and ¹⁵N (75 ppm) nuclei. Similarly N-tip has the smallest value of for both ¹¹B (44 ppm) and ¹⁵N (95 ppm) nuclei, among the other layers of nuclei.

The nature of the valence shells of the N atoms, which have lone pair of electrons, and the B atoms, which have a lack of electrons, is different. Therefore, different behaviors of the CS properties are expected and are also observed for these atoms. For these reasons, the average values of are greater than in ¹¹B nuclei whereas the opposite order have been seen for ¹⁵N nuclei.

3.2.2. Diborinin-Doped Models

We characterize ¹¹B and ¹⁵N NMR parameters of BNNT and illustrate how the diborinin-doping modifies the NMR parameter of the pure BNNT. According to Gauge-Independent Atomic Orbital (GIAO) calculations performed later, doping of diborinin ring in (6,0) BNNT, in both cases of doped models induces significant deformation of the B and N layers. These impurities lead to a significant change of the NMR parameter.

Compared to the pure model, in (b) model of the diborinin-doped (Figure 1(b)), N8, N14, N15, B8, B14 and B9 atoms are, respectively, doped by the b1, C3, C5, C2, b4 and C6 atoms. In contrast of (b) model, in (c) model of the diborinin-doped (Figure 1(c)), N8, N14, N15, B8, B14 and B9 atoms, respectively, are doped by the C6, C2, B4, B1, C3 and C5 atoms.

Among the B atoms of the (b) and (c) models, B2, B13 and B15 are significantly influenced by diborinin-doping due to the (b) model B2, B13 and B15 are directly bonded to the b1, C3 and C5 atoms, respectively while in the (c) model, B2, B13 and B15 are directly bonded to the C6, C2 and b4 atoms respectively, hence, their CS parameters detect some changes due to the diborinin doping. This observation was more significant for N7, N9, and N20 atoms which were directly bonded to the diborinin ring. This is because, in the DBD-BNNT, the CS parameters are proportional to the electronic density at the atomic sites and could detect any perturbation to these sites.

The results of Tables 2 and 3 reveal the significant effect of diborinin-doping at the sites of those ¹¹B and ¹⁵N nuclei located in the nearest neighborhood (closer distance) of the DBD-BNNTs ((b) and (c) models), but negligible influence at the sites of those nuclei farther from the diborinin-doped rings. Also, in (b) and (c) models, the parameters are changed by diborinin-doping, the magnitude of the change for ¹⁵N being more significant rather than that for the ¹¹B nuclei.

The parameters of B20 and B21 which were located in the B-tip of the (c) model are influenced indirectly by the diborinin-doping, whereas those of B20 and B21 in the (b) model remained unchanged.

Meanwhile, the magnitude of changes of the CS tensors at the sites of ¹⁵N nuclei was placed in the nearest neighborhood of diborinin ring is larger for the form (b) than the form (c), whereas the magnitude of changes of the CS tensors at the sites of ¹⁵N nuclei was placed in the first neighborhood of diborinin ring is larger for the form (c) than the form (b).

In the diborinin-doped models, when compared to the pure model, changes are greater in the values of CS parameters of those N atoms (N7, N9 and N20) which are directly bonded to diborinin ring in the (b) model borininthan in the (c) model whereas, the magnitude of changes of CS parameters of those B atoms (B2, B13, and B15) which are directly bonded to diborinin ring are more in (c) model borininthan in (b) model.

Table 4 shows the average deviations of (b) model (and (c) model in bracket) for and of ¹¹B and ¹⁵N in all layers of DBD-BNNT. The positive average deviations show increasing the values of and in DBD-BNNT models relative to pure model. The changes of CS parameters of B atoms in the diborinin-doped (c) model are generally greater than (b) model. These orders are reverse for N atoms.

As a result, Table 4 shows changes in the average deviations of N atoms are greater than those of B atoms. Also changes of and of ¹¹B and ¹⁵N in layer 2 and 3 (directly bonded) are more than N-tip and B-tip of DBD-BNNT.

4. Conclusion

In this study, we have used DFT calculations to investigate the properties of the electronic structure of pure and DBD-BNNTs through to simulate the ¹¹B and ¹⁵N spectra. The calculated structural energies yield similar values for the (b) and (c) models of DBD-BNNTs. However, the band gap differences between the forms (b) and the pure models are more than the differences between the forms (c) and the pure models of the BNNTs. Also, the B–N bond lengths and bond angles detect changes of diborinin-doped models. When diborinin is doped on the BNNT, dipole moment of the pure system is significantly changed. CS parameters detect the effects of diborinin-doping on the properties of nanotubes in comparison with the pure model. For the (b) and (c) models, both of the and parameters were significantly changed due to the diborinin-doped ring. The changes in the NMR () parameters due to the diborinin doping are more significant for the N atoms than the B atoms regarding to the pure model.

Results show the Average deviations of (b) model [and (c) model in bracket] for and of ¹¹B and ¹⁵N in all layers of DBD-BNNT. The positive average deviations show increasing the values of and in DBD-BNNT models relative to pure model. In the diborinin-doped (c) model, when compared to the (b) model, changes generally are greater in the values of CS parameters of those B atoms. These orders are reverse for N atoms.

Our results show that changes in the average deviations of N atoms are greater than those of B atoms. Also, changes of and of ¹¹B and ¹⁵N in layer 2, and 3 (directly bonded) are more than N-tip and B-tip of DBD-BNNT.

In DOS, the electronic structures observed near Fermi level of the pure BNNT show significant change due to the diborinin ring doping. So the band gaps near Fermi level become sharply narrower. It is clear that the doping of diborinin ring decreases the energy gaps of the pure BNNT.

For the pure model, the HOMO is located on the nitrogen atoms and the LUMO is uniformly distributed throughout the B–N bonds. In contrast, for the diborinin-doped models, the majority of the HOMO and LUMO are located at the diborinin-doped regions.

Acknowledgment

This paper is dedicated to the beloved colleague Mr. Ali Karimian, who rests in peace at this time; but without his sincere assistance, this work would not be materialized.

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Copyright © 2013 Sattar Arshadi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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