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

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). e calculated structural energies yield similar values for two models of DBD-BNNTs. Isotropic (CS) and anisotropic (CS) chemical shielding parameters of the optimized BNNT andDBD-BNNTs are calculated.e results illustrate that the changes in chemical shielding tensors of Band Nnuclei aremore signi�cant in the nearest neighborhood of the diborinin ring due to doping process.e changes of the electronic sites of theN atoms are alsomore signi�cant than those of the B atoms.e dipolemoments of the diborinin-doped BNNT structures show changes with respect to the pristinemodel. 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.


Introduction
Nanostructures such as nanotube are currently the subject of intense research because of the potential applications in nanoscale electronic and optoelectronic �elds [1][2][3][4].Aer 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 aer 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, smallgap semiconductor, and modest-gap semiconductor) rely on diameter and chirality, �rst approximation of BNNTs are electrically uniform with an energy gap of about 4-5 eV [9].is energy gap is independent of wall number, diameter, or chirality.For low applied electric �elds, 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.ese properties make BNNTs one of most promising materials for nanotechnology applications, especially under oxidative, hazardous and hightemperature environments.But there have been quite a few attempts to control the properties by incorporating extrinsic foreign atom doping.ese substitutions in BNNT signi�cantly modify the chemical binding con�guration, physical, chemical, and optical properties in comparison to pure BNNT [13].
Carbon-, Si-, Ti-and Pt-doped [14][15][16][17][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.e 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).

Models and Computational Details
DFT calculations were carried out using the Gaussian 98 program [19] on the structure of pure and DBD-BNNT BNNTs.DFT has become extremely popular for molecular applications because it accounts for the correlation energy in computationally efficient manner and offers a substantially improved accuracy over conventional approaches.Subsequently, frequency calculations (keyword: FREQ = NORAMAN) were carried out by standard techniques on the optimized structures.For minimum state species, only real frequency values (with a positive sign) are accepted.
As was pointed out in the previous section, calculations have been performed on (a), (b), and (c) models (Figure 1).Two structural isomers of DBD-BNNTs ((b) and (c) models) were considered in the calculations within four sp 2hybridized carbon and two borons atoms (diborinin ring) were substituted instead of three boron and three nitrogen atoms in the middle of the nanotube.
At the �rst 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.e geometries were optimized at the B3LYP/6-311G * * level of theory.Subsequently, the NBO analysis was carried out on the B3LYP/6-311G * * wave functions.From the NBO calculations, highest-occupied molecular orbital (HOMO) and lowest-unoccupied molecular orbital (LUMO) energies, the band gap energies, dipole moments and electronegativity () for (a), (b), and (c) models of BNNTs were obtained.
Also, we investigated electronegativity () in the optimized structures.Within the conceptual framework of DFT, the electronegativity of a system of  particles, with total energy  and subject to the external potential (), is de�ned as In (1),  is the electronegativity [20][21][22][23][24][25].Pauling introduced the concept of electronegativity as the power of an atom in a molecule to attract electrons [20].Using the method of �nite difference, an operational and approaching de�nition of  is: where IP is the ionization potential and EA is the electron affinity of the system.Within the validity of Koopman's theorem for closed-shell species, the frontier orbital energies are given by erefore, on the basis of orbitals, we can write LUMO and  HOMO are the energies of the lowest unoccupied and the highest occupied molecular orbitals LUMO and HOMO, respectively.Finally nuclear magnetic resonance (NMR) parameters at 11 B and 15 N 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 shis are described by a 3 by 3 matrix.In this principal axis system, the chemical shi tensor is fully described by the three diagonal elements-the principal components ( 33 >  22 >  11 )-and the three eigenvectors or Euler angles describe the orientation of the principal axes with respect to an arbitrary frame.erefore, ( 5) and ( 6) are used to convert the calculated chemical shielding (CS) tensors to the isotropic (CS  ) and anisotropic (CS  ) parameters.e 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.e 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.e following are equations ( 5) and ( 6): At the �rst 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.e optimized geometries of pure and doped models of the BNNTs are listed in Figures 2 and 3. ese �gures 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].is 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.

Result and Discussion
However, the effects of this deformation are consequential, just at the geometrical properties of the nearest atoms to the diborinin-doped ring, whereas those of other atoms are almost remained unchanged.As shown in Figures 2(b) and 2(c), the average C=C and B-C bond lengths (1.36 Å and 1.56 Å, resp.) are different from B-N bond length (1.46 Å).Moreover, the changes of the bond angles are more than those of the bond lengths in the (6,0) zigzag DBD-BNNT (Figures 2 and 3).
e calculated structural energies, LUMO-HOMO gaps, electronegativity (), and dipole moments for three models of the investigated BNNTs have been listed in Table 1.
e 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.e energies of both the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) are negative in all of  1).In comparison to the pure systems, the energy gaps between HOMO and LUMO, (Δ (LUMO-HOMO) ), have small values in (b) and (c) models of DBD-BNNT.e 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.e electronic structures observed near Fermi level of the pure BNNT (Figure 4(a)) also show signi�cant 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.e HOMO and LUMO, the pure and diborinin-doped models are plotted in Figure 5.For the pure model, the HOMO is located on the nitrogen atoms of the (6,0) zigzag BNNT model and corresponds to the lone pair of electron on nitrogen atoms.In contrast, the LUMO is uniformly distributed throughout the B-N bonds.For the diborinindoped models, the majority of the HOMO and LUMO are located at the diborinin-doped regions.
e 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.e B atoms are slightly positive and the N atoms are slightly negative.erefore, 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 signi�cantly increased (D = 9.28 Debye) whereas for (c) model is signi�cantly reduced (D = 6.98 Debye), compared with the pure model (D = 7.47 Debye), which means that the orientations of diborinin ring in two diborinindoped models foundation diverse dipole moment for these models (Figure 1 and Table 1).

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

Pure Model.
Tables 2 and 3 present the calculated NMR parameters for various 11 B and 15 N nuclei in the pure (a) model of BNNT.is model includes 24 B and 24 N atoms, where the edges are saturated by 12 H atoms (Figure 1).e 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, 11 B and 15 N 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 CS  and CS  parameters [29].Almost no signi�cant difference is observed in the calculated NMR parameters for the atoms of each layer; hence, just the average values in each layer for 15 N and 11 B nuclei are reported in Tables 2 and 3.
e �rst 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.e values of NMR properties for the 11  e 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.erefore, different behaviors of the CS properties are expected and are also observed for these atoms.For these reasons, the average values of CS  are greater atoms respectively, hence, their CS parameters detect some changes due to the diborinin doping.is observation was more signi�cant for N�, N9, and N20 atoms which were directly bonded to the diborinin ring.is 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.e results of Tables 2 and 3 reveal the signi�cant e�ect of diborinin-doping at the sites of those 11 B and 15 N nuclei located in the nearest neighborhood (closer distance) of the DBD-BNNTs ((b) and (c) models), but negligible in�uence at the sites of those nuclei farther from the diborinin-doped rings.Also, in (b) and (c) models, the CS  parameters are changed by diborinin-doping, the magnitude of the change for 15 N being more signi�cant rather than that for the 11 B nuclei.
e CS  parameters of B20 and B21 which were located in the B-tip of the (c) model are in�uenced indirectly by the diborinin-doping, whereas those of B20 and B21 in the (b) model remained unchanged.
Meanwhile, the magnitude of changes of the CS tensors at the sites of 15 N 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 15 N nuclei was placed in the �rst neighborhood of diborinin ring is larger for the form (c) than the form (b).
In the diborinin-doped models, when compared to the pure model, changes are greater in the values of CS parameters of those N atoms (N7, N9 and N20) which are directly bonded to diborinin ring in the (b) model borininthan in the (c) model whereas, the magnitude of changes of CS parameters of those B atoms (B2, B13, and B15) which are directly bonded to diborinin ring are more in (c) model borininthan in (b) model.
Table 4 shows the average deviations of (b) model (and (c) model in bracket) for CS  and CS A of 11   As a result, Table 4 shows changes in the average deviations of N atoms are greater than those of B atoms.Also changes of CS  and CS  of 11 B and 15 N in layer 2 and 3 (directly bonded) are more than N-tip and B-tip of DBD-BNNT.

Conclusion
In this study, we have used DFT calculations to investigate the properties of the electronic structure of pure and DBD-BNNTs through to simulate the 11 B and 15 N spectra.e 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 signi�cantly changed.CS parameters detect the effects of diborinin-doping on the properties of nanotubes in comparison with the pure model.Our results show that changes in the average deviations of N atoms are greater than those of B atoms.Also, changes of CS  and CS  of 11 B and 15 N 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 signi�cant 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.

F 1 :
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.On the other hand, the BNNTs are produced through heating of C templates with B 2 O 3 in a �owing N 2 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 and15 N 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 of11 B and 15 N nuclei for pure (6,0) singlewalled zigzag BNNT ((a) model) and DBD-BNNT ((b) and (c) models) via density functional theory method (DFT).

3. 1 .
Geometries.As shown in Figure 1, by substituting three B and three N atoms of pure BNNT ((a) model) with four sp 2hybridized carbons and two boron atoms, in the middle of the nanotube, (b) and (c) models of DBD-BNNTs are produced.
B and 15 N nuclei of the pure (a) model indicate that the B-tip has the smallest value of CS  for both 11 B (64 ppm) and 15 N (75 ppm) nuclei.Similarly N-tip has the smallest value of CS  for both 11 B (44 ppm) and 15 N (95 ppm) nuclei, among the other layers of nuclei.
B and 15 N in all layers of DBD-BNNT.e positive average deviations show increasing the values of CS  and CS  in DBD-BNNT models relative to pure model.e changes of CS parameters of B atoms in the diborinin-doped (c) model are generally greater than (b) model.ese orders are reverse for N atoms.

T 4 :F 5 :
e average deviations of (b) model (and (c) model in brackets) for CS  and CS  of 11 B and 15 N in N-tip and B-tip of DBD-BNNT.HOMO and LUMO orbitals for different models of the BNNTs; (a) pure model, (b) and (c) diborinin-doped models.
For the (b) and (c) models, both of the CS  and CS  parameters were signi�cantly changed due to the diborinin-doped ring.e changes in the NMR (CS  ) parameters due to the diborinin doping are more signi�cant for the N atoms than the B atoms regarding to the pure model.Results show the Average deviations of (b) model [and (c) model in bracket] for CS  and CS  of 11 B and 15 N in all layers of DBD-BNNT.e positive average deviations show increasing the values of CS  and CS  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.ese orders are reverse for N atoms.
T 3: e CS  and CS  parameters of the (c) model of DBD-BNNT.