All calculations were performed using Gaussian 98 computational package (Gaussian INC, Wallingford, CT, USA) [16] with density functional theory (DFT) method using Becke’s three-parameter hybrid-exchange functions with the correlation functions of Lee, Yang, Parr (B3LYP) [17, 18] using 6-31G (d) basis set [19]. Previously, it is found that the calculated NMR parameters at the B3LYP and B3PW91 levels have a good agreement with the experiment [20]. It is shown that B3LYP gives reasonable and even accurate band gap values for nanotubes [20], and hence, this function is chosen for band gap calculations.

In this study, we considered a pristine (6,3) chiral BNNTs of diameter 6.6 Å and 10.1 Å length. This BNNT model consists of 42 boron, 42 nitrogen, and 18 hydrogens (B42N42H18) B and N sites of this BNNT are doped by C, Si, Ge (Fig. 1).

Consider the following seven models, namely pristine (Fig. 1a), or with a B or N atom doped by C, that is, the B–C–B or N–C–N model (Fig. 1b, c), doped by a Si atom, that is, the B–Si–B or N–Si–N model (Fig. 1d, e), doped by a Ge atom, that is, the B–Ge–B or N–Ge–N model (Fig. 1f, g). We investigated the influence of the C, Si, and Ge doping on the properties of the (6,3) chiral BNNTs. The hydrogenated models of the pristine (6,3) chiral BNNTs and the three atoms doped models of BNNTs consisted of 102 atoms with the formulas of B42N42H18 (pristine), CB41N42H18 and CB42N41H18 (B–C–B or N–C–N model), SiB41N42H18 and SiB42N41H18 (B–Si–B or N–Si–N model), GeB41N42H18 and GeB42N41H18 (B–Ge–B or N–Ge–N model). The calculated CS tensors in the principal axis system (PAS) with the order of *σ*_{33}>*σ*_{22}>*σ*_{11} [21] for C, Si, and Ge doping for the investigated models of the (6,3) chiral BNNTs were converted into measurable NMR parameters [isotropic chemical shielding (CS^{I}) and anisotropic chemical shielding (CS^{A}) parameters] using (1) and (2) [22], summarised in Tables 3–6.

$${\text{CS}}^{\text{I}}\text{(ppm)}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\frac{1}{3}\mathrm{(}{\sigma}_{11}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}{\sigma}_{22}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}{\sigma}_{33}\mathrm{)}\text{\hspace{1em}(1)}$$(1)

$${\text{CS}}^{\text{A}}\mathrm{(}\text{ppm}\mathrm{)}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}{\sigma}_{33}\text{\hspace{0.17em}}-\text{\hspace{0.17em}}\frac{1}{2}\mathrm{(}{\sigma}_{11}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}{\sigma}_{22}\mathrm{)}\text{\hspace{1em}(2)}$$(2)

For nuclear quadrupole resonance (NQR) parameters, computational calculations do not directly detect experimentally measurable NQR parameters, nuclear quadrupole coupling constant (*C*_{Q}), and asymmetry parameter (*η*_{Q}). Therefore, (3) and (4) are used to convert the calculated electric field gradient (EFG) tensors in the principal axis system (PAS) with the order of |*q*_{zz}|>|*q*_{yy}|>|*q*_{xx}| to their proportional experimental parameters; *C*_{Q} is the interaction energy of nuclear electric quadrupole moment (*eQ*) with the EFG tensors at the sites of quadrupole nuclei (nuclei with nuclear spin angular momentum greater than >1/2), but the asymmetry parameter (*η*_{Q}) is a measure of the EFG tensors, which describes the deviation from tubular symmetry at the sites of quadrupole nuclei. The standard *Q* value [*Q* (^{11}B)=40.59 mb] reported by Pyykkö [23] is used in (3). The NQR parameters of ^{11}B nuclei for the investigated models of the (6,3) BNNTs are summarised in Table 7.

$${C}_{Q}\mathrm{(}\text{MHz}\mathrm{)}={e}^{2}Q{q}_{zz}{h}^{-1}\text{\hspace{1em}(3)}$$(3)

$${\eta}_{Q}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}|\mathrm{(}{q}_{xx}\text{\hspace{0.17em}}-\text{\hspace{0.17em}}{q}_{yy}\mathrm{)}/{q}_{zz}|0\u3008{\eta}_{Q}\u30081\text{\hspace{1em}(4)}$$(4)

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