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

Authors: Sattar Arshadi; Saboora Abedini; Ameneh Asghari; Fatemeh Alipour Zaghmarzi
Journal: Journal of Chemistry
 (2013)

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## 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 (CSI) and anisotropic (CSA) 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.


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## Body

## 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 of11B 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 (Figure1). 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.Typical geometric structures pure and diborinin-doped (6,0) single-walled zigzag BNNT; (a) front side of pure model, (b) and (c) front side of DBD-BNNTs, and (d) back side of pure and DBD-BNNTs models.
(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 (χ) for (a), (b), and (c) models of BNNTs were obtained.Also, we investigated electronegativity (χ) in the optimized structures. Within the conceptual framework of DFT, the electronegativity of a system of N particles, with total energy E and subject to the external potential v(r), is defined as
(1)χ=-(∂E∂N)v(r),T.
In (1), χ 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 χ is:
(2)χ=12(IP+EA),
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
(3)-ELUMO=IP;-EHOMO=EA.
Therefore, on the basis of orbitals, we can write
(4)χ=-12(ELUMO+EHOMO).ELUMO and EHOMO are the energies of the lowest unoccupied and the highest occupied molecular orbitals LUMO and HOMO, respectively.Finally nuclear magnetic resonance (NMR) parameters at11B 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 (CSI) and anisotropic (CSA) 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):
(5)CSI(ppm)=(σ11+σ22+σ33)3,(6)CSA(ppm)=σ33-(σ11+σ22)2.


## 3. Result and Discussion

### 3.1. Geometries

As shown in Figure1, 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 Figures2 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.Optimized bond lengths (Å) at B3LYP/6-311G** level; (a) pure model, (b) and (c) diborinin-doped models.
(a)
(b)
(c)Optimized bond angles (°) at B3LYP/6-311G** level; (a) pure model, (b) and (c) diborinin-doped models.
(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 Figures2(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 (χ), and dipole moments for three models of the investigated BNNTs have been listed in Table 1.Table 1
B3LYP/6-311G** calculated properties of pure and diborinin-doped ((b) and (c) models) of BNNT.
Systems
HOMO (eV)
LUMO (eV)
Δ
E
(
LUMO-HOMO
) (eV)
χ (eV)
Dipole moment (Debye)
Energy (keV)
Pure (a)
−6.86
−1.99
4.87
4.42
7.47
−52.2
DBD-BNNT (b)
−5.93
−3.28
2.64
4.61
9.28
−51.2
DBD-BNNT (c)
−5.99
−3.15
2.83
4.57
6.98
−51.2Table 2
TheCSI and CSA parameters of the (b) model of DBD-BNNT.
C
S
I (ppm)
CS
A (ppm)
11B
Pure
DBD-BNNT
15N
Pure
DBD-BNNT
11B
Pure
DBD-BNNT
15N
Pure
DBD-BNNT
layer 1
layer 1
B1
70.5
72.5
N1
147.5
144.1
B1
44.5
43.2
N1
95
90.8
B2
67.2
N2
127.3
B2
80.4
N2
124.7
B3
72.6
N3
128.1
B3
42.9
N3
123.3
B4
70.8
N4
144.1
B4
44.4
N4
91.4
B5
69.8
N5
147.6
B5
44.7
N5
95.3
B6
70.9
N6
146.9
B6
44.2
N6
96.6
layer 2
layer 2
B7
69
67.3
N7
114
80.3
B7
40.5
43.0
N7
187
213.0
B8
—
N8
—
B8
—
N8
—
B9
—
N9
80.0
B9
—
N9
213.2
B10
67.4
N10
116.4
B10
43.7
N10
187.0
B11
68.7
N11
113.8
B11
39.0
N11
187.9
B12
68.3
N12
115.8
B12
40.7
N12
187.5
layer 3
layer 3
B13
69.5
67.2
N13
111
94.4
B13
43
59.5
N13
195.5
232.0
B14
—
N14
—
B14
—
N14
—
B15
66.9
N15
—
B15
60.3
N15
—
B16
69.4
N16
94.0
B16
42.5
N16
232.6
B17
68.9
N17
109.7
B17
43.6
N17
197.4
B18
69.3
N18
110.5
B18
42.8
N18
197.0
layer 4
layer 4
B19
64
64.9
N19
75
67.9
B19
60
60.8
N19
241.5
257.2
B20
63.1
N20
49.1
B20
59.8
N20
267.0
B21
63.6
N21
67.5
B21
58.5
N21
258.0
B22
65.0
N22
73.9
B22
60.5
N22
243.3
B23
63.8
N23
75.5
B23
59.5
N23
242.2
B24
63.9
N24
73.5
B24
58.9
N24
243.2Table 3
TheCSI and CSA parameters of the (c) model of DBD-BNNT.
C
S
I (ppm)
CS
A (ppm)
11B
Pure
DBD-BNNT
15N
Pure
DBD-BNNT
11B
Pure
DBD-BNNT
15N
Pure
DBD-BNNT
layer 1
layer 1
B1
70.5
68.6
N1
147.5
143.3
B1
44.5
46.2
N1
95
93.2
B2
65.1
N2
137.6
B2
63.0
N2
102.9
B3
68.6
N3
130.3
B3
48.8
N3
129.6
B4
69.5
N4
148.0
B4
46.4
N4
92.8
B5
70.1
N5
148.4
B5
45.8
N5
92.5
B6
69.1
N6
147.8
B6
47.5
N6
92.4
layer 2
layer 2
B7
69
68.5
N7
114
98.2
B7
40.5
39.7
N7
187
211.8
B8
—
N8
—
B8
—
N8
—
B9
—
N9
86.3
B9
—
N9
184.3
B10
67.9
N10
110.6
B10
39.0
N10
184.0
B11
67.9
N11
111.7
B11
41.1
N11
190.3
B12
67.9
N12
113.6
B12
42.1
N12
185.5
layer 3
layer 3
B13
69.5
66.3
N13
111
108.0
B13
43
64.1
N13
195.5
205.6
B14
—
N14
—
B14
—
N14
—
B15
56.6
N15
—
B15
89.9
N15
—
B16
70.3
N16
84.8
B16
43.8
N16
243.9
B17
68.8
N17
112.3
B17
43.8
N17
196.5
B18
69.2
N18
111.4
B18
43.0
N18
195.9
layer 4
layer 4
B19
64
65.0
N19
75
67.9
B19
60
58.3
N19
241.5
276.7
B20
69.8
N20
45.9
B20
60.0
N20
256.6
B21
66.0
N21
65.8
B21
55.4
N21
273.4
B22
66.0
N22
70.7
B22
59.5
N22
247.9
B23
64.5
N23
73.8
B23
58.1
N23
244.5
B24
64.9
N24
70.4
B24
58.1
N24
247.4The 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 (Table1). In comparison to the pure systems, the energy gaps between HOMO and LUMO, (ΔE(LUMO-HOMO)), 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.The density of states (DOS) of (a) pure model, (b) and (c) diborinin-doped models.
(a)
(b)
(c)The HOMO and LUMO, the pure and diborinin-doped models are plotted in Figure5. 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.HOMO and LUMO orbitals for different models of the BNNTs; (a) pure model, (b) and (c) diborinin-doped models.
(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 (Figure1 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 of11B 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

Tables2 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 CSI and CSA 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 the11B and 15N nuclei of the pure (a) model indicate that the B-tip has the smallest value of CSI for both 11B (64 ppm) and 15N (75 ppm) nuclei. Similarly N-tip has the smallest value of CSA 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 ofCSI are greater than CSA in 11B nuclei whereas the opposite order have been seen for 15N nuclei.


#### 3.2.2. Diborinin-Doped Models

We characterize11B 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 (Figure1(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 Tables2 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 CSI parameters are changed by diborinin-doping, the magnitude of the change for 15N being more significant rather than that for the 11B nuclei.TheCSI 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 of15N 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.Table4 shows the average deviations of (b) model (and (c) model in bracket) for CSI and CSA of 11B and 15N in all layers of DBD-BNNT. The positive average deviations show increasing the values of CSI and CSA 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.Table 4
The average deviations of (b) model (and (c) model in brackets) forCSI and CSA of 11B and 15N in N-tip and B-tip of DBD-BNNT.
C
S
I
CS
A
11B
15N
11B
15N
Layer 1 (N-Tip)
0.13[-2.00]
−7.82[-4.93]
5.47[5.12]
8.68[5.56]
Layer 2
−1.075[-0.95]
−13.24[-10.42]
1.1[-0.025]
10.72[4.18]
Layer 3
−1.16[-3.26]
−8.85[-6.87]
6.74[13.92]
19.25[14.97]
Layer 4 (B-Tip)
0.05[2.03]
−7.1[-9.25]
−0.33[-1.77]
10.32[16.25]As a result, Table4 shows changes in the average deviations of N atoms are greater than those of B atoms. Also changes of CSI and CSA of 11B and 15N in layer 2 and 3 (directly bonded) are more than N-tip and B-tip of DBD-BNNT.


## 3.1. Geometries

As shown in Figure1, 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 Figures2 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.Optimized bond lengths (Å) at B3LYP/6-311G** level; (a) pure model, (b) and (c) diborinin-doped models.
(a)
(b)
(c)Optimized bond angles (°) at B3LYP/6-311G** level; (a) pure model, (b) and (c) diborinin-doped models.
(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 Figures2(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 (χ), and dipole moments for three models of the investigated BNNTs have been listed in Table 1.Table 1
B3LYP/6-311G** calculated properties of pure and diborinin-doped ((b) and (c) models) of BNNT.
Systems
HOMO (eV)
LUMO (eV)
Δ
E
(
LUMO-HOMO
) (eV)
χ (eV)
Dipole moment (Debye)
Energy (keV)
Pure (a)
−6.86
−1.99
4.87
4.42
7.47
−52.2
DBD-BNNT (b)
−5.93
−3.28
2.64
4.61
9.28
−51.2
DBD-BNNT (c)
−5.99
−3.15
2.83
4.57
6.98
−51.2Table 2
TheCSI and CSA parameters of the (b) model of DBD-BNNT.
C
S
I (ppm)
CS
A (ppm)
11B
Pure
DBD-BNNT
15N
Pure
DBD-BNNT
11B
Pure
DBD-BNNT
15N
Pure
DBD-BNNT
layer 1
layer 1
B1
70.5
72.5
N1
147.5
144.1
B1
44.5
43.2
N1
95
90.8
B2
67.2
N2
127.3
B2
80.4
N2
124.7
B3
72.6
N3
128.1
B3
42.9
N3
123.3
B4
70.8
N4
144.1
B4
44.4
N4
91.4
B5
69.8
N5
147.6
B5
44.7
N5
95.3
B6
70.9
N6
146.9
B6
44.2
N6
96.6
layer 2
layer 2
B7
69
67.3
N7
114
80.3
B7
40.5
43.0
N7
187
213.0
B8
—
N8
—
B8
—
N8
—
B9
—
N9
80.0
B9
—
N9
213.2
B10
67.4
N10
116.4
B10
43.7
N10
187.0
B11
68.7
N11
113.8
B11
39.0
N11
187.9
B12
68.3
N12
115.8
B12
40.7
N12
187.5
layer 3
layer 3
B13
69.5
67.2
N13
111
94.4
B13
43
59.5
N13
195.5
232.0
B14
—
N14
—
B14
—
N14
—
B15
66.9
N15
—
B15
60.3
N15
—
B16
69.4
N16
94.0
B16
42.5
N16
232.6
B17
68.9
N17
109.7
B17
43.6
N17
197.4
B18
69.3
N18
110.5
B18
42.8
N18
197.0
layer 4
layer 4
B19
64
64.9
N19
75
67.9
B19
60
60.8
N19
241.5
257.2
B20
63.1
N20
49.1
B20
59.8
N20
267.0
B21
63.6
N21
67.5
B21
58.5
N21
258.0
B22
65.0
N22
73.9
B22
60.5
N22
243.3
B23
63.8
N23
75.5
B23
59.5
N23
242.2
B24
63.9
N24
73.5
B24
58.9
N24
243.2Table 3
TheCSI and CSA parameters of the (c) model of DBD-BNNT.
C
S
I (ppm)
CS
A (ppm)
11B
Pure
DBD-BNNT
15N
Pure
DBD-BNNT
11B
Pure
DBD-BNNT
15N
Pure
DBD-BNNT
layer 1
layer 1
B1
70.5
68.6
N1
147.5
143.3
B1
44.5
46.2
N1
95
93.2
B2
65.1
N2
137.6
B2
63.0
N2
102.9
B3
68.6
N3
130.3
B3
48.8
N3
129.6
B4
69.5
N4
148.0
B4
46.4
N4
92.8
B5
70.1
N5
148.4
B5
45.8
N5
92.5
B6
69.1
N6
147.8
B6
47.5
N6
92.4
layer 2
layer 2
B7
69
68.5
N7
114
98.2
B7
40.5
39.7
N7
187
211.8
B8
—
N8
—
B8
—
N8
—
B9
—
N9
86.3
B9
—
N9
184.3
B10
67.9
N10
110.6
B10
39.0
N10
184.0
B11
67.9
N11
111.7
B11
41.1
N11
190.3
B12
67.9
N12
113.6
B12
42.1
N12
185.5
layer 3
layer 3
B13
69.5
66.3
N13
111
108.0
B13
43
64.1
N13
195.5
205.6
B14
—
N14
—
B14
—
N14
—
B15
56.6
N15
—
B15
89.9
N15
—
B16
70.3
N16
84.8
B16
43.8
N16
243.9
B17
68.8
N17
112.3
B17
43.8
N17
196.5
B18
69.2
N18
111.4
B18
43.0
N18
195.9
layer 4
layer 4
B19
64
65.0
N19
75
67.9
B19
60
58.3
N19
241.5
276.7
B20
69.8
N20
45.9
B20
60.0
N20
256.6
B21
66.0
N21
65.8
B21
55.4
N21
273.4
B22
66.0
N22
70.7
B22
59.5
N22
247.9
B23
64.5
N23
73.8
B23
58.1
N23
244.5
B24
64.9
N24
70.4
B24
58.1
N24
247.4The 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 (Table1). In comparison to the pure systems, the energy gaps between HOMO and LUMO, (ΔE(LUMO-HOMO)), 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.The density of states (DOS) of (a) pure model, (b) and (c) diborinin-doped models.
(a)
(b)
(c)The HOMO and LUMO, the pure and diborinin-doped models are plotted in Figure5. 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.HOMO and LUMO orbitals for different models of the BNNTs; (a) pure model, (b) and (c) diborinin-doped models.
(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 (Figure1 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 of11B 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

Tables2 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 CSI and CSA 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 the11B and 15N nuclei of the pure (a) model indicate that the B-tip has the smallest value of CSI for both 11B (64 ppm) and 15N (75 ppm) nuclei. Similarly N-tip has the smallest value of CSA 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 ofCSI are greater than CSA in 11B nuclei whereas the opposite order have been seen for 15N nuclei.


### 3.2.2. Diborinin-Doped Models

We characterize11B 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 (Figure1(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 Tables2 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 CSI parameters are changed by diborinin-doping, the magnitude of the change for 15N being more significant rather than that for the 11B nuclei.TheCSI 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 of15N 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.Table4 shows the average deviations of (b) model (and (c) model in bracket) for CSI and CSA of 11B and 15N in all layers of DBD-BNNT. The positive average deviations show increasing the values of CSI and CSA 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.Table 4
The average deviations of (b) model (and (c) model in brackets) forCSI and CSA of 11B and 15N in N-tip and B-tip of DBD-BNNT.
C
S
I
CS
A
11B
15N
11B
15N
Layer 1 (N-Tip)
0.13[-2.00]
−7.82[-4.93]
5.47[5.12]
8.68[5.56]
Layer 2
−1.075[-0.95]
−13.24[-10.42]
1.1[-0.025]
10.72[4.18]
Layer 3
−1.16[-3.26]
−8.85[-6.87]
6.74[13.92]
19.25[14.97]
Layer 4 (B-Tip)
0.05[2.03]
−7.1[-9.25]
−0.33[-1.77]
10.32[16.25]As a result, Table4 shows changes in the average deviations of N atoms are greater than those of B atoms. Also changes of CSI and CSA of 11B and 15N in layer 2 and 3 (directly bonded) are more than N-tip and B-tip of DBD-BNNT.


## 3.2.1. Pure Model

Tables2 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 CSI and CSA 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 the11B and 15N nuclei of the pure (a) model indicate that the B-tip has the smallest value of CSI for both 11B (64 ppm) and 15N (75 ppm) nuclei. Similarly N-tip has the smallest value of CSA 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 ofCSI are greater than CSA in 11B nuclei whereas the opposite order have been seen for 15N nuclei.


## 3.2.2. Diborinin-Doped Models

We characterize11B 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 (Figure1(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 Tables2 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 CSI parameters are changed by diborinin-doping, the magnitude of the change for 15N being more significant rather than that for the 11B nuclei.TheCSI 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 of15N 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.Table4 shows the average deviations of (b) model (and (c) model in bracket) for CSI and CSA of 11B and 15N in all layers of DBD-BNNT. The positive average deviations show increasing the values of CSI and CSA 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.Table 4
The average deviations of (b) model (and (c) model in brackets) forCSI and CSA of 11B and 15N in N-tip and B-tip of DBD-BNNT.
C
S
I
CS
A
11B
15N
11B
15N
Layer 1 (N-Tip)
0.13[-2.00]
−7.82[-4.93]
5.47[5.12]
8.68[5.56]
Layer 2
−1.075[-0.95]
−13.24[-10.42]
1.1[-0.025]
10.72[4.18]
Layer 3
−1.16[-3.26]
−8.85[-6.87]
6.74[13.92]
19.25[14.97]
Layer 4 (B-Tip)
0.05[2.03]
−7.1[-9.25]
−0.33[-1.77]
10.32[16.25]As a result, Table4 shows changes in the average deviations of N atoms are greater than those of B atoms. Also changes of CSI and CSA 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 the11B 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 CSI and CSA parameters were significantly changed due to the diborinin-doped ring. The changes in the NMR (CSI) 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] forCSI and CSA of 11B and 15N in all layers of DBD-BNNT. The positive average deviations show increasing the values of CSI and CSA 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 ofCSI and CSA 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.



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*Source: 421091-2012-11-20.xml*