Theoretical Study of Boron Nitride Nanotubes with Armchair Forms

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Theoretical Study of Boron Nitride Nanotubes with Armchair Forms a

b

M. Monajjemi , M. Seyed Hosseini & F. Molaamin

c

a

Department of Chemistry, Science and Research Branch, Islamic Azad University, Tehran, Iran b

Ph.D Student, Science and Research Branch, Islamic Azad University, Tehran, Iran c

Department of Chemistry, Qom Branch, Islamic Azad University, Qom, Iran

To cite this article: M. Monajjemi, M. Seyed Hosseini & F. Molaamin (2013): Theoretical Study of Boron Nitride Nanotubes with Armchair Forms, Fullerenes, Nanotubes and Carbon Nanostructures, 21:5, 381-393 To link to this article: http://dx.doi.org/10.1080/1536383X.2011.629752

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Fullerenes, Nanotubes, and Carbon Nanostructures, 21: 381–393, 2013 Copyright © Taylor & Francis Group, LLC ISSN: 1536-383X print / 1536-4046 online DOI: 10.1080/1536383X.2011.629752

Theoretical Study of Boron Nitride Nanotubes with Armchair Forms M. MONAJJEMI1 , M. SEYED HOSSEINI2 AND F. MOLAAMIN3

Downloaded by [M. Monajjemi] at 07:57 25 October 2012

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Department of Chemistry, Science and Research Branch, Islamic Azad University, Tehran, Iran 2 Ph.D Student, Science and Research Branch, Islamic Azad University, Tehran, Iran 3 Department of Chemistry, Qom Branch, Islamic Azad University, Qom, Iran To investigate the electromagnetic interaction of molecules inside the nanotubes, we studied the nuclear magnetic resonance properties(NMR) and shielding parameters between nanotubes, after optimizing the structure of nanotubes with a formula BxNx (x = 2,3,4,5) with hybrid density functional theory (B3LYP) using the EPR-II basis set. We also performed natural bond orbital (NBO) analysis, which revealed some important atomic and structural features. Besides structural characteristics, the lowest unoccupied molecular orbital and the highest occupied molecular orbital for the lowest energy were calculated to examine the structural stability of the nanotubes. In NBO calculation, graphs of number occupied orbital p of atoms B and N were plotted versus the coefficients linear combinations. Keywords Nanotube, boron nitride, Density Functional Theory, Natural Bond Orbital, highest occupied molecular orbital, lowest unoccupied molecular orbital

1. Introduction Boron nitride (BN) is one of the most interesting III–V compounds due to its unique properties, such as low density, high thermal conductivity, excellent mechanical strength wear resistance, stability at high temperatures and possibility of easy doping with silicon (n-type) and beryllium (p-type). Thus, the material appears as a good alternative for carbon-related materials in several applications (1–3). BN is a structural equivalent of carbon .It is mostly found in the same phases and produces similar nanostructures. This is probably because the B-N bonding tends to be dipolar and is average the number of electron per atom to 2 in the 2P layer as for carbon (carbon is 2P2 , nitrogen is 2P3 , boron is 2P1 ) (4). BN is intensively used as a carbon substitute for its much higher chemical inertness especially at high temperature. BN is non-reactive to molten metals (Al, Fe, Cu, Zn), to hot Si and stable against air oxidation up to 1000◦ C (for comparison, graphite burns from 500◦ C, MoS2 from 350◦ C and WS2 from 420◦ C). BN is typically an interesting material for high temperature applications (5,6). BN also offers an electrically resistant counterpart to the semi-metallic graphite. This difference is more or less preserved for nanotubes. The mechanical and wear-resistant Address correspondence to M. Monajjemi, Department of Chemistry, Science and Research Branch, Islamic Azad University, Tehran, Iran. E-mail: [email protected]

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properties of both materials are of the same impressive order (e.g., the Young’s modulus is in the terapascal range (7)) while the electronic properties of BN nanotubes (BNNTs) can be more attractive (Figure 1). Carbon nanotubes (CNTs) are either metals or semiconductors depending on their chirality, while BNNTs are always semiconductors (8,9) with the gap (∼5.5 eV) practically independent of the nanotube chirality and its diameter (8). Its resistive character is not much affected by the structural specificity of the tube (e.g., helicity, defects, multi-layering). As hexagonal boron nitride (h-BN) is very resistant to oxidation (10,11). BNNTs which inherit these properties are suitable for shielding and coating at the nanoscale. Despite these prospects, BNNTs have received little attention compared to CNTs due to various difficulties in their reproducible and efficient synthesis (12). Armchair nanotubes are formed when n = m and the chiral angle is 30◦ (see Figure 2). All other nanotubes, with chiral angles intermediate between 0◦ and 30◦ , are known as chiral nanotubes. These nanotubes are found to be chiral or nonchiral; however, a preference toward the armchair and zigzag configurations is suggested. Electron energy loss spectroscopy yields a B/N ratio of approximately 1 and a perfect chemical homogeneity (13). This paper focuses on the tubes generated with the single-walled boron nanotube (SWBNNT) from a MWNT = 1 as an armchair nanotube (n,m) with various chirality (m = 5, n = 5), (m = 4, n = 4), (m = 3, n = 3) and (m = 2, n = 2) are displayed in Figure 2.

(B)

(A)

Figure 1. A) Possible choices of circumference to close a hexagonal layer as a cylinder, satisfying the continuity of hexagons; B) one type of BN SWNT armchair (10,10) (color figure available online).

Figure 2. The optimized structure of nanotubes B8 N8 , B12 N12 , B16 N16 , B20 N20 at the B3LYP/EPR-II level of theory (color figure available online).

Boron Nitride Nanotubes with Armchair Forms

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2. Computational Details The geometry of nanotubes B8 N8 , B12 N12 , B16 N16 , B20 N20 has been optimized by Beck’s hybrid three-parameter exchange functional and the nonlocal correlation functional of the Lee, Yang, and Parr (B3LYP) method (15,16) with the EPR-II basis sets of Baron (16). The Gaussian quantum chemistry package was used for all calculations (18). EPR-II is a double-basis set with a single set of polarization functions and an enhanced S part (19,20), for H and (19,8) for B-F. It has been demonstrated how this mechanistic question may be addressed in the framework of modern electronic structure methods, specifically with the B3LYP hybrid density functional method and EPR-II basis set. Natural bond orbital (NBO) analysis has been employed to analyze the calculated electron density in terms of localized Lewis structure and resonance theoretical concepts (21). As a check on the quality of the calculated geometrical parameters and their stability with respect to the level of theory, the HOMO and the LUMO differences have been explored. In the course of determining hyperfine parameters and relating them to the underlying electronic structure of the considered system, anisotropic magnetic effects have been explained and provided useful information on the interaction characteristics (23). The HOMO corresponds to a combination of lone pair orbitals on the N atoms as well as the LUMO, which is characterized by large contributions from vacant p orbitals on B atoms with some admixture of N-based orbitals having been calculated (22). The NBO analysis has been performed using NBO as implemented in the Gaussian quantum chemistry package (21). Nuclear magnetic resonance (NMR) spectroscopy is a powerful technique to determine the three-dimensional (3D) structures and dynamics of molecules and a valuable complementary technique to that of X-ray crystallography. All the parameters that can be measured by NMR spectroscopy are sensitive to molecular structure and dynamics and can be employed as restraints to construct models of the 3D structures of bimolecular. The chemical shift is one of the most often observed parameters in NMR, which encodes information about the chemical and electronic environment of a nucleus via a shift (hence the term chemical shift) in resonant frequency from the reference frequency. This local field shields the nucleus from the external field, resulting in a shift in the observed frequency. Electronic distribution is rarely spherically symmetric and the resulting local field is usually anisotropic. The chemical Shift Anisotropy (CSA) tensor contains structural information and is directly measured in NMR experiments (23, 24).

3. Results and Discussion 3.1. Energy To investigate the structural stability, we first optimized the structure of nanotubes with a formula BxNx (x = 2,3,4,5) with hybrid density functional theory (B3LYP) using the EPR-II basis set. Energy calculated for different forms is presented in Table 1. As shown in Table 1, the nanotube with structure (m = 5, n = 5) has more structural stability: B20 N20 > B16 N16 > B12 N12 > B8 N8 3.2. HOMO-LUMO Gap of the System The LUMO-HOMO band gap is a gap between the LUMO (the lowest unoccupied molecular orbital) and HOMO (the highest occupied BN molecular orbital). Nanotubes have a

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(1,1,2)

(1,1,2)

(1,1,2)

(1,1,2)

Formula

B8 N8

B12 N12

B16 N16

B20 N20

(2,2)

(3,3)

(4,4)

(5,5)

Set cell_count

BN Nano tube 4 hexagonal sub-cells 6 hexagonal sub-cells 8 hexagonal sub-cells 10 hexagonal sub-cells

Hexagonal nanotube lattic consists of

EPR-II

EPR-II

EPR-II

EPR-II

Basis Set

Dipole Moment (Debye) 0.0000 0.0000 0.0017 0.0000

E(RB + HF + LYP) a.u. −637.19117 −956.03605 −1274.82250 −1593.58903

Table 1 Energy, band gaps, Set cell count and dipole moment of BNNTs


S10

S8

S6

S4

Point Group

0.20678(5.627ev)

0.20877(5.681ev)

0.21473(5.843ev)

0.20057(5.458ev)

HOMO-LUMO (in a.u. and ev) Band gaps


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wide band gap (E) of ∼5.5ev and non-magnetism independent of the tube diameters (12). The large LUMO-HOMO gap is often regarded as a molecule stability condition. In BN interlayer, B and N atoms are arranged staggered, and the electrons mainly localized on π -orbitals of N in valence band can hardly be promoted over a wide gap to the conduction band. Therefore, BN shows poor conductivity. The energy band structures can be given from calculated orbital energies. The calculated energies and the band gaps of BNNT are given in Table 1. It can be seen that BNNTs all have wide band gaps (∼5.5–5.8). This result is consistent with experimental data (13). A comparison indicates that band gap is decreased from B12 N12 to B20 N20 , but B8 N8 has less gap energy, so the electrical conductance in B8 N8 is more than the other. This could be due to the unstable structure of B8 N8 .


3.3. Natural Bond Orbital (NBO) Analysis The concepts of natural atomic orbital (NAO) and NBO analyses are useful for distributing electrons into atomic and molecular orbitals used for the one-electron density matrix to define the shape of the atomic orbitals in the molecular environment and then derive molecular bonds from electron density between atoms. The optimal condensation of occupancy in the natural localized orbitals leads to partitioning into high- and low-occupancy orbital types (reduction in dimensionality of the orbitals having significant occupancy), as reflected in the orbital labeling. Each pair of valence hybrids hA , hB in the natural hybrid orbitals (NHO) basis give rise to a bond (σ AB ) and antibond (σ ∗ AB ) in the NBO basis: σAB = cA hA + cB hB ∗ σAB = cB hA − cA hB

At each considered coordination, the bonding coefficients of s and p orbitals of B-N bonds are reported in Table 2. As shown in Table 2, in B8 N8 , the coefficients’ linear combinations are between 0.4357 and 0.4907 for boron and between 0.8713 and 0.9001 for nitrogen atoms. Therefore, nitrogen with the higher electronegativity have larger coefficient linear combination. In the nanotube B12 N12 , coefficient orbitals are between 0.4600 and 0.5070 for boron and 0.8619 and 0.8879 for nitrogen. In B16 N16 , coefficients are 0.4630– 0.5110 for boron atoms and 0.8596–0.8863 for nitrogen atoms. In B20 N20 structure, coefficients for boron and nitrogen atoms are 0.4654–0.5127 and 0.8586–0.8851, respectively. In Figure 3, the number of occupied p orbital versus coefficients linear combinations of atoms B and N are shown for four structures of nanotubes. As is evident from Figure 3, with increasing coefficient of linear in B atoms, the number of occupied orbitals p is reduced and is a minimum value when coefficients of atoms B are about 0.48 (in the structure of B8 N8 is about 0.46). The number of occupied p orbitals in coefficient 0.5 for B atoms (left graphs) is p1.8 for (3,3), (4,4), (5,5) BNNTs. It finally decreases to p0.8 in the higher coefficients. In N atoms, the orbital occupation numbers p increased to p2.5 with increasing coefficients of the nitrogen atom (about coefficients 0.870) then decreased but finally increased to about p2.6 in coefficients 0.890. The average number of electron per p orbital in BNNTs B8 N8 , B12 N12 ,B16 N16 , B20 N20 is p2.16 , p1.64 , p1.65 , p1.63 for B atoms, and p1.64 , p2.17 , p1.99 , p1.98 for N atoms, respectively. Also three-dimensional graphs of number-occupied orbitals p and d versus distance are drawn (Figure 4). It was clear that all curves have a minimum plate, and this plate is a characteristic line. A set of appropriate powers for linear combinations can be found on the characteristic line.

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B9–N10

N8–B9

B7–N8

N6–B7

B5–N6

N4–B5

B3–N4

N2–B3

B1–N2

bond

Nanotube (3,3) 0.5070∗ (sp1.23 d0 )B + 0.8619∗ (sp1.58 d0.01 )N 0.8673∗ (sp2.4 d0.01 )N + 0.4977∗ (sp1.81 d0 )B 0.4646∗ (sp2.04 d0.01 )B + 0.8855∗ (sp2.03 d0 )N 0.8733∗ (sp2.34 d0 )N + 0.4871∗ (sp0.99 d0 )B 0.5070∗ (sp1.22 d0 )B + 0.8619∗ (sp1.58 d0.01 )N 0.8673∗ (sp2.4 d0.01 )N + 0.4977∗ (sp1.8 d0 )B 0.4646∗ (sp2.04 d0.01 )B + 0.8855∗ (sp2.03 d0 )N 0.8733∗ (sp2.34 d0 )N + 0.4871∗ (sp0.99 d0 )B 0.5070∗ (sp1.23 d0 )B + 0.8619∗ (sp1.58 d0.01 )N

Nanotube (2,2)

0.4843∗ (SP1.98 )B + 0.8749∗ (sp1.31 d0.01 )N 0.8789∗ (sp0.79 )N + 0.4770∗ (sp2.23 d0.01 )B 0.4357∗ (sp3.49 d0.02 )B + 0.9001∗ (sp1.97 )N 0.8713∗ (sp2.17 )N + 0.4907∗ (sp1.04 )B 0.4843∗ (sp1.98 )B + 0.8749∗ (sp1.31 d0.01 )N 0.8789∗ (sp0.79 )N + 0.4770∗ (sp2.23 d0.01 )B 0.4357∗ (sp3.49 d0.02 )B + 0.9001∗ (sp1.97 )N 0.8884∗ (sp1.96 )N + 0.4590∗ (sp2.06 d0.01 )B 0.4357∗ (sp3.49 d0.02 )B + 0.9001∗ (sp1.97 )N

0.5104∗ (sp1.08 d0 )B + 0.8599∗ (sp1.5 d0.01 )N 0.8653∗ (sp2.35 d0.01 )N + 0.5013∗ (sp1.82 d0 )B 0.4630∗ (sp2.13 d0.01 )B + 0.8863∗ (sp1.65 d0 )N 0.8735∗ (sp2.31 d0 )N + 0.4868∗ (sp1 d0 )B 0.5110∗ (sp1.12 d0 )B + 0.8596∗ (sp1.5 d0.01 )N 0.8653∗ (sp2.35 d0.01 )N + 0.5013∗ (sp1.82 d0 )B 0.4630∗ (sp2.13 d0.01 )B + 0.8863∗ (sp1.65 d0 )N 0.8735∗ (sp2.31 d0 )N + 0.4868∗ (sp1 d0 )B 0.5110∗ (sp1.12 d0 )B + 0.8596∗ (sp1.5 d0.01 )N

Nanotube (4,4)

Table 2 NBO analysis of BN nanotubes with different coordinates at B3LYP/EPR-II level of theory


0.5123∗ (sp1.04 d0 )B + 0.8588∗ (sp1.47 d0.01 )N 0.8644∗ (sp2.32 d0.01 )N + 0.5028∗ (sp1.8 d0 )B 0.4654∗ (sp2.09 d0.01 )B + 0.8851∗ (sp1.62 d0 )N 0.8738∗ (sp2.3 d0 )N + 0.4863∗ (sp1 d0 )B 0.5127∗ (sp1.07 d0 )B + 0.8586∗ (sp1.47 d0.01 )N 0.8644∗ (sp2.32 d0.01 )N + 0.5028∗ (sp1.8 d0 )B 0.4654∗ (sp2.09 d0.01 )B + 0.8851∗ (sp1.62 d0 )N 0.8738∗ (sp2.3 d0 )N + 0.4863∗ (sp1 d0 )B 0.5127∗ (sp1.07 d0 )B + 0.8586∗ (sp1.47 d0.01 )N

Nanotube (5,5)

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B15–N16

N14–B15

B13–N14

N12–B13

B11–N12

N10–B11

0.8713∗ (sp2.17 )N + 0.4907∗ (sp1.04 )B 0.4843∗ (sp1.98 )B + 0.8749∗ (sp1.31 d0.01 )N 0.8789∗ (sp0.79 )N + 0.4770∗ (sp2.23 d0.01 )B 0.4357∗ (sp3.49 d0.02 )B + 0.9001∗ (sp1.97 )N 0.8713∗ (sp2.17 )N + 0.4907∗ (sp1.04 )B 0.4843∗ (sp1.98 )B + 0.8749∗ (sp1.31 d0.01 )N

0.8673∗ (sp2.4 d0.01 )N + 0.4977∗ (sp1.81 d0 )B 0.4646∗ (sp2.04 d0.01 )B + 0.8855∗ (sp2.03 d0 )N 0.8879∗ (sp2.51 d0 )N + 0.4600∗ (sp2.16 d0.01 )B 0.4646∗ (sp2.04 d0.01 )B + 0.8855∗ (sp2.03 d0 )N 0.8733∗ (sp2.34 d0 )N + 0.4871∗ (sp0.99 d0 )B 0.5070∗ (sp1.23 d0 )B + 0.8619∗ (sp1.58 d0.01 )N

0.8653∗ (sp2.35 d0.01 )N + 0.5013∗ (sp1.82 d0 )B 0.4630∗ (sp2.13 d0.01 )B + 0.8863∗ (sp1.65 d0 )N 0.8735∗ (sp2.31 d0 )N + 0.4868∗ (sp1 d0 )B 0.5110∗ (sp1.12 d0 )B + 0.8596∗ (sp1.5 d0.01 )N 0.8653∗ (sp2.35 d0.01 )N + 0.5012∗ (sp1.77 d0 )B 0.4662∗ (sp2.07 d0.01 )B + 0.8847∗ (sp1.62 d0 )N


0.8644∗ (sp2.32 d0.01 )N + 0.5028∗ (sp1.8 d0 )B 0.4654∗ (sp2.09 d0.01 )B + 0.8851∗ (sp1.62 d0 )N 0.8738∗ (sp2.3 d0 )N + 0.4863∗ (sp1 d0 )B 0.5127∗ (sp1.07 d0 )B + 0.8586∗ (sp1.47 d0.01 )N 0.8644∗ (sp2.32 d0.01 )N + 0.5028∗ (sp1.77 d0 )B 0.4673∗ (sp2.05 d0.01 )B + 0.8841∗ (sp1.61 d0 )N

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A

B

Figure 3. Graphs of number occupied orbital p versus coefficients linear combinations of atoms Bore (A) and Nitrogen (B), from up to down nanotube (2,2), (3,3), (4,4), (5,5), respectively.

3.4. Analysis of Chemical Shift and Chemical Shielding in NMR In the standard convention, the principal components of the chemical shift tensor, (δ 11 , δ 22 , δ 33 ), are labeled according to IUPAC (International Union of Pure and Applied Chemistry) rules (25). They follow the high frequency-positive order. Thus, δ 11 corresponds to the direction of the lowest shielding, with the highest frequency, while δ 33 corresponds to the direction of highest shielding, with the lowest frequency. NMR shielding constants and corresponding parameters for BNNTs are shown in Table 3.

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2,2 3,3 4,4 5,5 2,2 3,3 4,4 5,5 2,2 3,3 4,4 5,5 2,2 3,3 4,4 5,5

Nano tube

B1 B1 B1 B1 N2 N2 N2 N2 B3 B3 B3 B3 N4 N4 N4 N4

atom’s type

11.6107 7.6548 3.9168 1.1637 −34.5268 −3.7577 13.5212 23.2331 34.9493 40.6089 42.2469 42.3921 43.4947 88.7227 96.677 99.175

σ 11 ppm

23.5631 25.3472 24.6099 23.3201 −1.3158 43.543 63.4887 74.5325 68.104 81.3289 85.1364 87.1507 119.2239 144.6734 159.0063 164.2944

σ 22 ppm 188.7016 187.9043 185.7013 184.5498 281.3736 254.4498 230.2542 212.9019 97.5443 93.9547 93.0533 92.0069 183.0956 173.4696 172.43 171.9614

σ 33 ppm 74.6251 73.6354 71.4094 69.6778 81.8437 98.0784 102.4213 103.5558 66.8659 71.9641 73.4789 73.8499 115.2714 135.6219 142.7044 145.1436

δ iso ppm 177.0909 180.2495 181.7845 183.3861 315.9004 258.2075 216.733 189.6688 62.595 53.3458 50.8064 49.6148 139.6009 84.7469 75.753 72.7864

ppm

Muliken atomic charges −0.12039 −0.07841 −0.02444 −0.00354 −0.06774 −0.10814 −0.131 −0.14348 0.06162 0.008602 −0.0035 −0.00249 0.126509 0.177707 0.158936 0.149516

K rad −0.865013 −0.80369 −0.77233 −0.75836 −0.78974 −0.63362 −0.5389 −0.45906 0.059339 0.526647 0.688348 0.804244 0.084939 0.320419 0.645594 0.789329

Table 3 NMR shielding constants and corresponding parameters for BNNTS


171.1147 171.4033 171.43795 172.3079 299.2949 234.5572 191.7493 164.0191 −47.8749 −3.212 −46.848 −47.1867 −107.665 9.18695 −69.0412 −68.9529

δ

0.189677 0.268145 0.3065981 −0.32338453 0.28539 0.464479 0.5620635 −0.63866628 0.922413 0.40267 1.373255 0.154371889 0.889867 0.614002 1.3541782 0.166787764

η


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Figure 4. Three-dimensional graphs of number occupied in orbitals p and d versus distance in BNNTS (BD and BD∗ ) (color figure available online).

Changes of this parameter versus muliken charge are drawn for all nanotubes versus muliken charge (Figure 6) and separately for every nanotube by matrix chart (Figure 7). For all types of curves, a cubic polynomial fit is quite appropriate. The isotropic values, σ iso , are the average values of the principal components and correspond to the center of gravity of the line shape. The Haeberlen-Mehring-Spiess convention uses different combinations of the principal components to describe the line shape (26,27). This convention requires that the principal components are ordered according to their separation from the isotropic value (Figure 5). The center of gravity of the line shape is described by the isotropic value, which is the average value of the principal components.

Figure 5. Standard convention and Herzfeld-Berger convention and Haeberlen convention from left to right (color figure available online).

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Figure 6. Graphs of NMR shielding constants and corresponding parameters for BNNTS (color figure available online).

The anisotropy and reduced anisotropy describe the largest separation from the centre of gravity. The sign of the anisotropy indicates on which side of the isotropic to find the largest separation. The asymmetry parameter indicates by how much the line shape deviates from that of an axially symmetric tensor. In the case of an axially symmetric tensor, a = (δ yy − δ xx ) will be zero and hence η = 0. The nanotube (2, 2) graph of σ iso versus muliken charge shows that the amount of σ iso is maximum in the range of positive charges and for (muliken charge of =0.04). The minimum amount is around −0.07, but the nanotube (3, 3), (4, 4) curves have concave shapes and the amount of σ iso is minimum in the range of negative charges and about −0.035. In the graph of nanotubes (5,5), curve is completely symmetric and the convex


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Figure 7. Graphs of σ iso , η, κ, , δ versus muliken charge in analysis of NMR (color figure available online).

shape in positive charges and concave shape in negative charges, have a maximum amount σ iso about 0.07 and minimum value at −0.07. In the study of curves asymmetry parameter (η), skew (κ) versus muliken charge, it is observed that in the nanotube (2, 2) amounts of κ, η increase with increasing charge, but in nanotubes (3, 3) and (4, 4) the changes of graphs of η and κ in negative charges is a concave shape and in positive charges is a convex shape. Also in nanotubes (5, 5), changes of skew (κ) are similar to nanotubes (3, 3) and (4, 4) but curve is completely symmetric with minimum and maximum amount about ±0.07, just at similar to graph of asymmetry parameter (η) in nanotubes (5, 5). Minimum amount and maximum amount in muliken charge is curve skew (κ) but opposite in sign.

4. Conclusion We have theoretically studied the properties of BNNTs by NMR and NBO. Our results in NBO calculation indicate that the average the number of electron per p orbital in BNNTs B8 N8 , B12 N12 , B16 N16 , B20 N20 is p2.16 , p1.64 , p1.65 , p1.63 for B atoms and p1.64 , p2.17 , p1.99 , p1.98 for N atoms, respectively. In HOMO-LUMO calculation a comparison indicates that the band gap decreases from B12 N12 to B20 N20 , but B8 N8 has less gap energy. In NMR calculation, we studied graph of shielding constants iso , η, κ, , δ versus muliken charge.

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