Journal of Chemistry

Volume 2013 (2013), Article ID 948010, 10 pages

http://dx.doi.org/10.1155/2013/948010

Research Article

Influence of Pyrazine Ring Doping on the ¹⁵N and ¹¹B NMR and Electronic Structure Parameters in Zigzag Boron Nitride Nanotube: A DFT Study

Sattar Arshadi, Ameneh Asghari, Hojatollah Raheimi, and Saboora Abedini

Department of Chemistry, Payame Noor University, P.O. Box 19395-4697, Iran

Received 24 June 2012; Accepted 18 November 2012

Academic Editor: André Silva Pimentel

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.

Abstract.

Density functional theory (DFT) calculations have been performed to investigate the properties of the electronic structures of pyrazine-doped boron nitride nanotubes (PD-BNNTs). The structural forms were firstly optimized and then nuclear magnetic resonance (NMR) parameters have been calculated on the optimized structures. The chemical shielding isotropic () and chemical shielding anisotropic () parameters were calculated at the sites of ¹¹B and ¹⁵N nuclei in structural forms of BNNT including the perfect (a) model and PD-BNNTs (b), (c), and (d) models. The results indicated that the changes are most significant for those nuclei placed in the nearest neighborhood of the pyrazine-doped ring. The changes of the electronic sites of the N atoms are also more significant than those of the B atoms. The difference of LUMO-HOMO gap for the perfect model was larger than the PD-BNNTs models. Also the atomic charge distribution of N and B atoms has been determined in nanotubes by natural bond orbital (NBO) analysis. All calculations were performed by the B3LYP method and 6-311G** basis set using Gaussian 98 package of program.

1. Introduction

The existence of tubular forms of matter with nanoscale diameters has opened an exciting field of research in science. Since the discovery of carbon fullerene C₆₀ by Smalley et al. in 1985 and carbon nanotubes by Iijima in 1991, electronic and mechanical properties of carbon and noncarbon nanotubes have been investigated by various groups [1–4].

Boron nitride (BN) is the first candidate to replace carbon, because hexagonal-BN structure is quite similar to that of graphite. Boron nitride nanotubes (BNNTs) have attracted an enormous amount of attention [5–13] as a typical representative of III–V compound tubes, partially because they have the morphology of honeycomb analogous to carbon nanotubes (CNTs). It has been shown that BNNTs exhibit many interesting properties such as significant resistance to oxidation at high temperatures when compared to the carbon nanotubes [14–19].

Unlike CNTs, all BN nanotubes exhibit semiconducting behavior with a wide band gap which is almost independent of tubular diameter, chirality, and number of walls [6, 20]. Furthermore, in contrast to the nonpolar CNTs, slight positive charge of boron atom (B) and slight negative charge of nitrogen atom (N) increase the polarity and the ionicity of the BNNTs. Therefore, the BNNTs have been proposed as more proper materials than the CNTs for applications in the specific electronic and mechanical devices.

The structure of BNNTs was firstly predicted by theoretical calculations [7, 21]. In 1995, Chopra et al. [5] reported the production of multiwalled BNNTs using arc-discharge techniques. The other synthesis methods are laser-assisted technique [22, 23] using pyrolytically grown CNTs as templates to prepare BNNTs, using chemical vapor deposition (CVD) by Lourie et al. [24]. In 2001, Bengu and Marks proposed a new method to synthesize the single-walled BN nanotubes [25]. This new synthesis technique has made it possible to bring BN nanotubes into the nanotechnology applications.

Previous studies have indicated that the properties of the electronic structure of the BNNTs are influenced by the doping atoms and impurities. Thus, uniformly doped BNNTs obtained through chemical modification could be very effective for tailoring the electronic properties, and the related mechanism and behavior are valuable to be explored in theory [26, 27].

Within present research, we have investigated the electronic structures and NMR parameters at the sites of ¹¹B and ¹⁵N nuclei of perfect and pyrazine-doped models of BNNTs by density functional theory (DFT) calculations. Furthermore, we have investigated atomic charge distribution in nanotubes by natural bond orbital (NBO) [28] analysis.

2. Models and Computational Methods

Conveniently, BN nanotube could be presented by a (, ) pair of numbers, where the (, 0) and (, ) BN nanotubes designate the zigzag and armchair types, respectively. For the zigzag type BN nanotube, n denotes the number of triazines in the circumference of the tube and the translation axis is the tubular length.

We have considered four models: a perfect and three pyrazine-doped models in Figures 1(a)–1(d) of the representative (6,0) zigzag single-walled BNNTs in present study. Figure 1(a) shows the perfect model, which consists of 24 boron (B) atoms and 24 nitrogen (N) atoms where the two tips of the nanotube are saturated by 12 hydrogen (H) atoms. In the perfect zigzag BNNTs, three B and three N atoms in the center of nanotube have been replaced by four carbon atoms (sp²-hybridized) and two N atoms to create the pyrazine-doped BNNTs (pyrazine-BNNTs). Figures 1(b)–1(d) show three doped models which have different position for pyrazine ring in corresponding models.

(a)

(b)

(c)

(d)

Figure 1: The front side view of perfect BNNTs model (a) and pyrazine-doped BNNTs models ((b)–(d)).

In the first step, the structures have been allowed to relax by all atomic geometrical optimization at the DFT level with B3LYP exchange-functional method and 6-311G** basis set. Furthermore NBO analysis was carried out on the B3LYP/6-311G** wave functions using version 3.1 of NBO package [29] included in Gaussian 98 program package [30].

Also we investigated electronegativity () in the optimized structures. As we already know, electronegativities may be considered as the power of an atom in a given molecule to attract electrons to itself [31]. For an N-electron system with potential acting on an electron at due to the nuclear attraction plus such other external forces as may be present (external potential) and total energy , electronegativity () [32] is defined as the following:

The electronegativity is defined as the half part of the difference between the HOMO and the LUMO energies as follows:

The CS tensors are calculated for optimized nanotubes at the DFT level employing the B3LYP method and 6-311G** basis set based on the gauge independent atomic orbital (GIAO) approach [33]. The calculated CS tensors at the sites of ¹¹B and ¹⁵N are yielded in the principal axes system (PAS) [34]. Thereafter, they are converted to isotropic chemical shielding () and anisotropic chemical shielding () parameters using (3) [35] and are showed in Tables 5, 6, and 7:

The DFT calculations have been performed by the Gaussian 98 package.

3. Results and Discussion

3.1. The Optimized Parameters

At the first step of this task, structural optimization was successfully carried out for the perfect ((a) model) and doped models ((b), (c), and (d) models) of the single-wall (6, 0) BNNT at the level of B3LYP, DFT method and 6-311G** basis set.

Subsequently, frequency calculations (keyword: ) were carried out by standard techniques on the optimized structures. For minimum state species, only real frequency values (with a positive sign) are accepted.

Table 1 presents the results for structural energies, the highest occupied molecular orbital (HOMO), the lowest unoccupied molecular orbital (LUMO), LUMO-HOMO gaps, dipole moments, and electronegativity obtained by the DFT calculations.

Table 1: Structural energies, , , LUMO-HOMO gap, dipole moments and electronegativity for the perfect model (a) and PD-BNNT models ((b), (c), and (d)) at B3LYP/6-311G** level.

Models
Energy (keV)
(eV)
(eV)
Δ(LUMO-HOMO) (eV)
Dipole moment (Debye)
Electronegativity ()

Perfect (a)
−52.22
−1.99
−6.85
4.86
7.47
4.42

(b)
−52.85
−1.86
−4.89
3.03
8.27
3.37

(c)
−52.85
−2.13
−4.70
2.57
6.93
3.41

(d)
−52.85
−2.13
−4.70
2.57
6.93
3.41

Our results indicated that the values of LUMO-HOMO gaps of the PD-BNNTs models are smaller than the perfect model. Also among the values of the LUMO-HOMO gaps of the pyrazine-doped models, the most significant changes were observed for the c and d models.

As we know, the band gap for the BN nanotube is higher in energy than the CNTs [6]. On the other hand, pyrazine-doped BN nanotube has similarities to CNTs in view of the prescience of carbons in the nanotube wall. Therefore the band gap in pyrazine-doped BN nanotube is similar to CNTs to some extent. This is proved by the calculated energies which are shown in Table 1.

The LUMO-HOMO gap is 4.86 eV for perfect model, 3.03 eV for (b) model, and 2.57 eV for (c) and (d) models, respectively (Table 1).

Also the densities of states (DOSs) of perfect and pyrazine-doped BNNT are shown in Figure 2 for better understanding the effect of pyrazine ring doping on the electronic structure of BNNT. It is clear that, after doping of pyrazine ring, the HOMO-LUMO energy gap of tube has significant change. On the other hand, the doping of pyrazine ring decreases the HOMO-LUMO energy gaps of the perfect BNNT.

Figure 2: The density of states (DOS) of (a) the perfect model and (b), (c), and (d) pyrazine-doped models.

The HOMO and LUMO in the perfect and pyrazine-doped models are plotted in Figure 3. For the perfect 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 pyrazine-doped models, the majority of the HOMO and LUMO are located at the pyrazine-doped regions.

(a)  

(b)

(c)

(d)

Figure 3: HOMO and LUMO orbitals for different models of the BNNTs: (a) perfect model, (b), (c), and (d) pyrazine-doped models.

The circumferences of the armchair BNNTs include both N and B atoms in both ends. In contrast to armchair models, circumferences 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 that could be better seen by the value of dipole moment. Comparing the values of the dipole moments for the four models indicates that the value for the (b) model is significantly increased ( Debye) whereas those for the (c) and (d) models are significantly reduced ( Debye) compared with the perfect (a) model ( Debye), which means that the strengths of the charge points are balanced in the two latter models (Table 1).

The calculated structural energies in Table 1 also indicate no difference between the three models of the PD-BNNTs ( keV). On the other hand, the (c) and (d) models are structural isomers of the (b) model.

Tables 2, 3, and 4 present the optimized parameters including the bond lengths and bond angle for four models of the investigated (6, 0) BNNT (Figures 1(a)–1(d)).

Table 2: Optimized bond lengths (Å) and bond angles (°) for the perfect (in bracket) and PD-BNNT models (b) at B3LYP/6-311G** level.

Bonds
Length ()
Bonds
Length ()
Bonds
Length ()
Bonds
Angle (°)
Bonds
Angle (°)

B41–N44
1.45 1.45
B42–n4
1.44 1.45
B43–N41
1.45 1.45
c2–n1–c6
113 118
B23–c6–c5
119 118

B41–N33
1.45 1.45
B42–N42
1.45 1.45
c5–N31
1.42 1.46
c3–c2–n1
117 118
c5–N31–B43
119 118

B41–N43
1.45 1.45
c3–n4
1.43 1.46
B34–N31
1.46 1.46
c2–c3–n4
120 120
c3–n4–B42
119 118

B31–N33
1.46 1.46
c5–n4
1.43 1.46
c5–c6
1.35 1.45
c3–n4–c5
109 111
c5–n4–B42
119 118

c3–N33
1.42 1.46
c2–c3
1.35 1.45
c6–B23
1.54 1.46
n4–c5–c6
120 120
B41–N33–c3
119 118

B31–N24
1.44 1.46
c2–n1
1.44 1.46
B23–N11
1.43 1.45
c5–c6–n1
117 118
c3–N33–B31
115 111

B21–N24
1.45 1.45
n1–N12
1.42 1.45
B23–N21
1.45 1.45
B23–c6–n1
116 110
c5–N31–B34
115 111

B21–N13
1.43 1.45
C6–n1
1.44 1.46
B13–N11
1.46 1.46
B21–c2–n1
116 110
N24–B21–c2
117 118

c2–B21
1.54 1.45
B12–N12
1.46 1.46
B14–N11
1.46 1.46
B21–c2–c3
119 118
c6–B23–N21
117 118

B11–N13
1.46 1.46
B13–N12
1.46 1.46
B34–N21
1.44 1.46
n4–c5–N31
116 118
c6–B23–N11
119 120

B12–N13
1.46 1.46
B43–N42
1.45 1.45
B14–N16
1.46 1.46
N33–c3–n4
116 118
c2–B21–N13
119 120

B42–N43
1.45 1.45
B43–N31
1.45 1.45
B15–N16
1.46 1.46
c6–c5–N31
121 120
c2–c3–N33
121 120

Table 3: Optimized bond lengths (Å) and bond angles (°) for the perfect (in bracket) and PD-BNNT models (c) at B3LYP/6-311G** level.

Bonds
Length ()
Bonds
Length ()
Bonds
Length ()
Bonds
Angle (°)
Bonds
Angle (°)

B41–N44
1.46 1.45
c2–B42
1.52 1.45
B43–N41
1.46 1.45
c6–c5–n4
121 118
B23–n4–c3
119 118

B41–N33
1.44 1.45
B42–N42
1.45 1.45
c3–N31
1.42 1.46
n1–c6–c5
121 118
c3–N31–B43
118 118

B41–N43
1.46 1.45
n1–c2
1.47 1.46
B34–N31
1.48 1.46
c6–n1–c2
115 120
n1–c2–B42
117 118

B31–N33
1.46 1.46
c2–c3
1.36 1.46
c3–n4
1.40 1.45
n1–c2–c3
120 111
c3–c2–B42
121 118

n1–N33
1.49 1.46
c6–n1
1.40 1.45
n4–B23
1.46 1.46
c2–c3–n4
122 120
B41–N33–n1
115 118

B31–N24
1.44 1.46
c5–c6
1.38 1.46
B23–N11
1.43 1.45
c3–n4–c5
115 118
n1–N33–B31
117 111

B21–N24
1.46 1.45
c5–N12
1.41 1.45
B23–N21
1.44 1.45
B23–n4–c5
114 110
c3–N31–B34
110 111

B21–N13
1.45 1.45
c5–n4
1.44 1.46
B13–N11
1.45 1.46
B21–c6–c5
107 110
N24–B21–c6
115 118

c6–B21
1.53 1.45
B12–N12
1.47 1.46
B14–N11
1.46 1.46
B21–c6–n1
123 118
n4–B23–N21
108 118

B11–N13
1.46 1.46
B13–N12
1.45 1.46
B34–N21
1.44 1.46
c2–c3–N31
120 118
n4–B23–N11
119 120

B12–N13
1.44 1.46
B43–N42
1.44 1.45
B14–N16
1.45 1.46
N33–n1–c2
106 118
c6–B21–N13
120 120

B42–N43
1.45 1.45
B43–N31
1.47 1.45
B15–N16
1.46 1.46
n4–c3–N31
118 120
c6–n1–N33
114 120

Table 4: Optimized bond lengths (Å) and bond angles (°) for the perfect (in bracket) and PD-BNNT models (d) at B3LYP/6-311G** level.

Bonds
Length ()
Bonds
Length ()
Bonds
Length ()
Bonds
Angle (°)
Bonds
Angle (°)

B41–N44
1.46 1.45
c6–B42
1.52 1.45
B43–N41
1.46 1.45
n4–c3–c2
121 118
B23–c2–n1
123 118

B41–N33
1.47 1.45
B42–N42
1.45 1.45
n1–N31
1.49 1.46
c5–n4–c3
115 118
n1–N31–B43
115 118

B41–N43
1.44 1.45
c5–C6
1.36 1.46
B34–N31
1.46 1.46
n4–c5–c6
122 120
c5–c6–B42
121 118

B31–N33
1.48 1.46
c6–N1
1.47 1.46
n1–c6
1.47 1.45
c5–c6–n1
120 111
n1–c6–B42
117 118

c5–N33
1.42 1.46
c5–n4
1.40 1.45
c2–B23
1.53 1.46
c6–n1–c2
115 120
B41–N33–c5
117 118

B31–N24
1.44 1.46
c3–n4
1.44 1.46
B23–N11
1.45 1.45
n1–c2–c3
121 118
c5–N33–B31
110 111

B21–N24
1.44 1.45
c3–N12
1.41 1.45
B23–N21
1.46 1.45
B23–c2–c3
107 110
n1–N31–B34
117 111

B21–N13
1.43 1.45
c2–c3
1.38 1.46
B13–N11
1.44 1.46
B21–n4–c3
114 110
N24–B21–n4
118 118

n4–B21
1.46 1.45
B12–N12
1.45 1.46
B14–N11
1.46 1.46
B21–n4–c5
119 118
c2–B23–N21
115 118

B11–N13
1.46 1.46
B13–N12
1.47 1.46
B34–N21
1.44 1.46
c6–n1–N31
106 118
c2–B23–N11
120 120

B12–N13
1.45 1.46
B43–N42
1.46 1.45
B14–N16
1.46 1.46
N33–c5–c6
120 118
n4–B21–N13
119 120

B42–N43
1.45 1.45
B43–N31
1.44 1.45
B15–N16
1.45 1.46
c2–n1–N31
114 120
n4–c5–N33
118 120

Table 5: The B3LYP/6-311G** calculated NMR parameters of the perfect model and model (b) of PD-BNNT.

CSI (ppm)
CSA (ppm)

CSI (ppm)
CSA (ppm)

Nuclei

Nuclei

Perfect
Doped
Perfect
Doped

Perfect
Doped
Perfect
Doped

Layer 1

Layer 1

    B1
64
—
60
—
N1
75
—
242
—

    B11
—
65
—
59
N11
—
89
—
257

    B12
—
74
—
54
N12
—
28
—
194

    B13
—
74
—
54
N13
—
89
—
257

    B14
—
65
—
59
N14
—
73
—
244

    B15
—
64
—
60
N15
—
73
—
238

    B16
—
64
—
60
N16
—
73
—
244

Layer 2

Layer 2

    B2
69
—
43
—
N2
111
—
195
—

    B21
—
69
—
55
N21
—
105
—
209

    B22
—
—
—
—
N22
—
—
—
—

    B23
—
69
—
55
N23
—
—
—
—

    B24
—
70
—
44
N24
—
105
—
209

    B25
—
69
—
44
N25
—
110
—
195

    B26
—
70
—
44
N26
—
110
—
195

Layer 3

Layer 3

    B3
69
—
39
—
N3
115
—
187
—

    B31
—
68
—
40
N31
—
115
—
124

    B32
—
—
—
—
N32
—
101
—
92

    B33
—
—
—
—
N33
—
115
—
124

    B34
—
68
—
40
N34
—
115
—
188

    B35
—
70
—
38
N35
—
113
—
187

    B36
—
70
—
38
N36
—
115
—
188

Layer 4

Layer 4

    B4
70
—
46
—
N4
148
—
94
—

    B41
—
74
—
39
N41
—
153
—
86

    B42
—
77
—
44
N42
—
163
—
74

    B43
—
74
—
39
N43
—
163
—
74

    B44
—
71
—
44
N44
—
153
—
86

    B45
—
69
—
46
N45
—
147
—
98

    B46
—
71
—
44
N46
—
147
—
98

Table 6: The B3LYP/6-311G** calculated NMR parameters of the perfect model and model (c) of PD-BNNT.

CSI (ppm)
CSA (ppm)

CSI (ppm)
CSA (ppm)

Nuclei

Nuclei

Perfect
Doped
Perfect
Doped

Perfect
Doped
Perfect
Doped

Layer 1

Layer 1

    B1
64
—
60
—
N1
75
—
242
—

    B11
—
66
—
57
N11
—
88
—
241

    B12
—
73
—
54
N12
—
59
—
224

    B13
—
70
—
54
N13
—
76
—
263

    B14
—
65
—
58
N14
—
75
—
245

    B15
—
64
—
59
N15
—
74
—
243

    B16
—
64
—
58
N16
—
74
—
242

Layer 2

Layer 2

    B2
69
—
43
—
N2
111
—
195
—

    B21
—
75
—
49
N21
—
115
—
195

    B22
—
—
—
—
N22
—
112
—
137

    B23
—
74
—
42
N23
—
—
—
—

    B24
—
68
—
45
N24
—
119
—
199

    B25
—
69
—
43
N25
—
110
—
198

    B26
—
70
—
44
N26
—
110
—
194

Layer 3

Layer 3

    B3
69
—
39
—
N3
115
—
187
—

    B31
—
70
—
42
N31
—
114
—
136

    B32
—
—
—
—
N32
—
—
—
—

    B33
—
—
—
—
N33
—
64
—
97

    B34
—
68
—
42
N34
—
113
—
182

    B35
—
68
—
41
N35
—
115
—
188

    B36
—
69
—
41
N36
—
113
—
184

Layer 4

Layer 4

    B4
70
—
46
—
N4
148
—
94
—

    B41
—
74
—
44
N41
—
151
—
92

    B42
—
70
—
57
N42
—
141
—
119

    B43
—
70
—
47
N43
—
152
—
94

    B44
—
70
—
45
N44
—
155
—
77

    B45
—
70
—
45
N45
—
149
—
94

    B46
—
70
—
45
N46
—
148
—
95

Table 7: The B3LYP/6-311G** calculated NMR parameters of the perfect model and model (d) of PD-BNNT.

CSI (ppm)
CSA (ppm)

CSI (ppm)
CSA (ppm)

Nuclei

Nuclei

Perfect
Doped
Perfect
Doped

Perfect
Doped
Perfect
Doped

Layer 1

Layer 1

    B1
64
—
60
—
N1
75
—
242
—

    B11
—
65
—
58
N11
—
76
—
263

    B12
—
70
—
54
N12
—
59
—
224

    B13
—
73
—
54
N13
—
88
—
241

    B14
—
66
—
57
N14
—
74
—
242

    B15
—
64
—
58
N15
—
74
—
243

    B16
—
64
—
59
N16
—
75
—
245

Layer 2

Layer 2

    B2
69
—
43
—
N2
111
—
195
—

    B21
—
74
—
42
N21
—
119
—
199

    B22
—
—
—
—
N22
—
—
—
—

    B23
—
75
—
49
N23
—
112
—
137

    B24
—
70
—
44
N24
—
115
—
195

    B25
—
69
—
43
N25
—
110
—
194

    B26
—
68
—
45
N26
—
110
—
198

Layer 3

Layer 3

    B3
69
—
39
—
N3
115
—
187
—

    B31
—
68
—
42
N31
—
64
—
97

    B32
—
—
—
—
N32
—
—
—
—

    B33
—
—
—
—
N33
—
114
—
136

    B34
—
70
—
42
N34
—
113
—
184

    B35
—
69
—
41
N35
—
115
—
188

    B36
—
68
—
41
N36
—
113
—
182

Layer 4

Layer 4

    B4
70
—
46
—
N4
148
—
94
—

    B41
—
70
—
47
N41
—
155
—
77

    B42
—
70
—
57
N42
—
152
—
94

    B43
—
74
—
44
N43
—
141
—
119

    B44
—
70
—
45
N44
—
151
—
92

    B45
—
70
—
45
N45
—
148
—
95

    B46
—
70
—
45
N46
—
149
—
94

In the perfect BNNT (Figure 1(a)), the average B–N bond length was 1.45-1.46 Å, but this value also was changed by the pyrazine-doping in the PD-BNNT due to existence of B–C, C–N, N–N, and C=C bonds in addition to B–N one.

However, the effects of this deformation were significant just at the geometrical properties of the nearest atoms to the pyrazine-doped ring whereas those of other atoms almost remained unchanged. Furthermore, the changes of the bond angles were more than those of the bond lengths in the zigzag PD-BNNT.

Among theoretical methods, natural bond orbital (NBO) analysis is a unique approach to the evaluation of the atomic charges. It is clear that the charges of N and B atoms in these structures are negative and positive, respectively. The charges of N and B atoms at the end of tubes are smaller than those of other ones. Moreover, the results of NBO analysis indicated that the atomic charge distribution in the pyrazine-doped models is different from the perfect model.

3.2. NMR Parameters

In this computational work, the CS tensors ( and ) for various ¹¹B and ¹⁵N atoms are calculated to study the influence of pyrazine ring doping on the electronic structure properties of the (6, 0) BNNT.

In the following text, the calculated ¹¹B and ¹⁵N NMR parameters for the perfect and the pyrazine-doped models of BNNT are discussed, respectively.

3.2.1. The Perfect Model

Tables 5, 6, and 7 present the calculated NMR parameters for various ¹¹B and ¹⁵N nuclei in the perfect model of BNNT. This model includes 24 B and 24 N atoms, where the edges are saturated by 12 H atoms (Figure 1(a)).

A quick look at the results reveals that various ¹¹B and ¹⁵N nuclei are divided into four layers along the nanotube length. The layers have equivalent calculated and parameters, which means that the nuclei in each layer have equivalent electrostatic properties around similar 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 behavior of the CS properties is expected and is also observed for these atoms.

The values of NMR properties for the ¹¹B and ¹⁵N nuclei of the perfect model indicate that the B-mouth (B1) has the smallest value of (¹¹B), 64 ppm, and the N-mouth (N4) has the largest value of (¹⁵N), 148 ppm, among the other layers of nuclei.

In contrast, the opposite behavior is observed for the values of : the B-mouth has the largest value of (¹¹B), 60 ppm, whereas the N-mouth has the smallest value of (¹⁵N), 94 ppm, among the other layers of nuclei.

3.2.2. The PD-BNNT Models

In the doped models, three B and three N atoms are doped by four carbon atoms (sp²-hybridized) and two N atoms to construct PD- BNNTs ((b), (c) and (d)) models of Figure 1.

Due to this doping, the CS tensors at the sites of ¹¹B and ¹⁵N nuclei which are directly bonded to the pyrazine ring undergo significant changes among the other nuclei in comparison with the perfect model. Furthermore, the magnitude of changes of the CS tensors is more significant at the sites of ¹⁵N nuclei than at those of ¹¹B nuclei.

Although the other not directly bonded B and N layers are influenced by the pyrazine-doped ring, due to the sensitivity of the CS tensors, they also undergo some minor changes in the doped model. Moreover, the CS tensors at the sites of those nuclei shown in Figures 1(b)–1(d) (front side) change while those at the other side (back side) do not undergo any significant changes and their NMR parameters remain unchanged as those of the perfect model.

For example, in the (b) model (Figure 1(b)), NMR parameters of B42 (directly bonded) and B41, B43 (indirectly) were influenced by the pyrazine-doping whereas those of B44, B45, and B46 undergo some minor changes.

The evaluated NMR parameters at the sites of ¹¹B and ¹⁵N nuclei in the perfect and doped models are presented in Tables 5, 6, and 7. In the (b) model of the zigzag PD-BNNT (Figure 1(b)), B32, B33, N22, and N23 atoms are doped by the C atoms and B22 and N32 atoms are doped by the N atoms which yield B–C, C–N, N–N, and C=C bonds. The results indicated that the changes are most significant for those nuclei placed in the nearest neighborhood of the pyrazine-doped ring.

In the first layer, N12 has the smallest and values (28 and 194 ppm, resp.) among the remaining N atoms in this layer. Also the calculated results show that those N atoms (N41, N42, N43, and N44) have the largest values (153, 163, 163, and 153 ppm) but the smallest values (86, 74, 74, and 86 ppm) among all N atoms.

The changes in the values of the CS parameters for B12, B13, B41, B42, and B43 atoms are also notable (Table 5).

The doping of B22, B33, N23, and N32 atoms by the C atoms and the doping of B32 and N22 atoms by the N atoms take place in the (c) model of the zigzag PD-BNNT (Figure 1(c)) which yield B–C, C–N, N–N, and C=C bonds.

Among the B atoms of the (c) model, B21, B23, and B42 are directly bonded to the pyrazine ring; hence, their NMR parameters ( or ) detect some changes due to the pyrazine-doping. Moreover, the NMR parameters of atoms further away show minor changes.

The and values for the N nuclei in the (c) model are different from those values in the (b) model. However notable changes in the CS tensors are observed for all of the N atoms due to the direct and indirect effect of the pyrazine-doped ring (Table 6).

In the (d) model (Figure 1(d)), B22, B32, N22, and N32 atoms are doped by the C atoms and B33 and N23 atoms are doped by the N atoms.

The NMR parameters at the sites of ¹¹B, ¹⁵N nuclei in (d) model are quite similar with the (c) model (Tables 6 and 7).

4. Conclusion

We have investigated the properties of the electronic structure of the pyrazine-doping in the BNNTs by performing the DFT calculations. The geometries were optimized at the B3LYP/6-311G** level of theory. The structural energies, LUMO-HOMO gaps, dipole moments, and electronegativity () for perfect model and doped models have been calculated. The results of the perfect and doped models reveal some remarkable trends.

First, the optimization process reveals that BN nanotube surface is not smooth like CNTs but the N nuclei were relaxed outward and the B nuclei were relaxed inward of the nanotubes surface. Second, the values of dipole moments and band gaps are changed in the pyrazine-doped models. Third, the average B–N bond length in the (6,0) perfect BNNT was 1.45-1.46 Å, but this value was changed in the PD-BNNTs. Fourth, in the perfect model, the NMR parameters can divide BNNT structure into equivalent layers in which the B-mouth (B1) has the smallest but the N-mouth (N4) has the largest among the B and N layers, respectively.

Fifth, the results indicated the changes of NMR parameters are significant just for those atoms placed in the nearest neighboring of the pyrazine-doped ring. Clearly, pyrazine ring doping effect is totally different from Carbon impurity effect on electrostatic properties of BNNTs [36].

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