### Abstract

- Top of page
- Abstract
- 1 Introduction
- 2 Computation details
- 3 Results and discussion
- 4 Summary and conclusions
- Acknowledgements
- Biographical Information

The first-principles calculations have been performed to investigate the ground-state properties of monoperiodic boron nitride (BN), TiO_{2}, and SrTiO_{3} single-walled nanotubes (SW NTs) containing extrinsic point defects. The hybrid exchange–correlation functionals PBE, B3LYP, and B3PW within the framework of density functional theory (DFT) have been applied for large-scale *ab initio* calculations on NTs with the following substitutional impurities: Al_{B}, P_{N}, Ga_{B}, As_{N}, In_{B}, and Sb_{N} in the BN NT, as well as C_{O}, N_{O}, S_{O}, and Fe_{Ti} in the TiO_{2} and SrTiO_{3} NTs, respectively. The variations in formation energies obtained for equilibrium defective nanostructures allow us to predict the most stable compositions, irrespective of the changes in growth conditions. The changes in the electronic structure are analyzed to show the extent of localization of the midgap states induced by defects. Finally, the electronic charge redistribution was calculated in order to explore the intermolecular properties, which show how the reactivity of the NTs under study was affected by doping and orbital hybridization.

### 1 Introduction

- Top of page
- Abstract
- 1 Introduction
- 2 Computation details
- 3 Results and discussion
- 4 Summary and conclusions
- Acknowledgements
- Biographical Information

Inorganic nanotubes (NTs) are important and widespread materials in modern nanotechnology. Moreover, imperfect NTs with reproducible distribution of point defects attract enhanced interest, due to potential generation of novel innovative nanomaterials and devices. A variety of experimental conditions accompanying their synthesis can certainly promote the appearance of point defects: native vacancies or antisites as well as substitutional impurities. These and other types of irregularities may occur in inorganic NTs as a result of the growth process or intentionally induced to modify their properties. Point defects also play the role of chemically active sites for NT-wall functionalization 1.

Boron nitride (BN), titania (TiO_{2}), and strontium titanate (SrTiO_{3} or STO) are well-known semiconductors comprehensively studied in materials science, thanks to their widespread technological applications. During recent years NTs of different morphology obtained from these compounds were systematically synthesized and carefully studied as prospective technological materials (see *e.g*., Refs. 2, 3 for BN, Ref. 4 for TiO_{2}, and Ref. 5 for STO). The doped BN NTs, which exhibit substantial changes in electronic properties with respect to their pristine counterparts, further enlarge applications in the nanosize range. For example, either a single boron or a single nitrogen atom substituted in the C-doped BN NTs was found to induce spontaneous magnetization 6, while an insulator-to-semiconductor transition has been observed on the successfully synthesized F-doped BN NTs 7. Very recent experimental studies performed on Nb-doped TiO_{2} NTs, fabricated by anodization of TiNb alloys 8, and Gd^{3+}N codoped trititanate NTs prepared using the hydrothermal method 9 demonstrate strongly enhanced photoelectrochemical water splitting without considerable photodegradation. Analogously, STO NTs after doping are potentially promising photoelectrodes for visible-light-driven photocatalytic applications 10, 11.

In spite of large (mainly experimental) efforts the current understanding of fundamental changes in electronic structure with atomic composition of doped semiconducting NTs is still insufficient to rationally design the atomic composition of these prospective nanomaterials. To guide the search, a theoretical prediction is needed to prudently suggest the electronic structure and charge transition in tubular nanostructured materials. Although point defects in BN NTs are much better described from the theoretical point of view (see Refs. 1, 3 and references therein), the extrinsic isoelectronic substitutional impurities in BN NT walls 12 were not sufficiently studied from first principles. Theoretical simulations performed so far dealt, *e.g*., with doped and codoped TiO_{2} 13, 14 and STO 15, 16 bulk, as well as titania anatase- and rutile-type low-index surfaces (101) and (110), respectively 17, 18, or nanoparticles 19. However systematic theoretical studies performed on doped semiconducting metal-oxide NTs are rather scarce in the literature.

In this paper, we continue to present a series of results obtained using *ab initio* simulations on both perfect and defective BN NTs 20–23, as well as on perfect TiO_{2} and STO NTs 24–27. Using hybrid exchange–correlation functionals applied within the density functional theory (DFT) we have calculated the following extrinsic isoelectronic substitutional impurities in BN NT: Al_{B}, P_{N}, Ga_{B}, As_{N}, In_{B}, and Sb_{N} as they may produce a strong effect in the luminescence spectra of nanostructured BN 12. Moreover, C_{O}, N_{O}, S_{O}, and Fe_{Ti} extrinsic substitutional impurities in the TiO_{2} and SrTiO_{3} NTs have been calculated too since they essentially enhance photocatalytic activity of both NT types 28. The calculated changes in the electronic structure of nanomaterials under study, *e.g*., the electronic charge redistribution around substitutional defects, are thoroughly discussed.

The paper is organized as follows. In Section 2, the computational details of first-principles calculations are described. Section 3 presents the calculated electronic properties, *e.g*., electronic charge redistribution around extrinsic substitutional point defects in the aforementioned NTs. Finally, a short summary is given in Section 4.

### 2 Computation details

- Top of page
- Abstract
- 1 Introduction
- 2 Computation details
- 3 Results and discussion
- 4 Summary and conclusions
- Acknowledgements
- Biographical Information

Rather scarce results were reported so far on computer simulations of realistic defective NTs since the lack of periodicity makes their calculations space- and time-consuming. In this study, we have performed the first-principles simulations on doped NTs using the formalism of the localized Gaussian-type functions (GTFs), which form the basis set (BS), and exploiting periodic rototranslation symmetry for efficient ground-state calculations as implemented in the *ab initio* code CRYSTAL developing the formalism of localized atomic orbitals (LCAO) for calculations on periodic systems 29. Earlier, this approach was successfully applied by us for simulations on single- (SW) and multiwalled BN, TiO_{2}, and STO NTs 20–27.

We employ the hybrid exchange–correlation scheme that accurately reproduces the basic bulk and surface properties of BN 20–22 as well as a number of perovskites 30–32. Our calculations on defective BN NTs have been performed using the hybrid Hartree–Fock/Kohn–Sham (HF/KS) exchange–correlation functional PBE0 of Perdew–Becke–Erzerhof 33, 34 combining exact HF nonlocal exchange and KS exchange operator within the generalized gradient approximation (GGA) as implemented in CRYSTAL code 29. For calculations on defective TiO_{2} and STO NTs we have employed the hybrid B3LYP and B3PW exchange–correlation functional, respectively. They consist of the nonlocal HF exchange, DFT exchange, and GGA correlation functionals as proposed by Becke 35. The main advantage of the hybrid DFT calculations is that they make the results of the band-structure calculations more plausible.

To perform calculations, the following configurations of BSs have been adopted. An all-valence BS in the form of 6s–21sp–1d and 6s–31p–1d has been used for B and N atoms, respectively 22. For substitutional impurity atoms in BN NTs, the 21sp–1d BSs with an effective core pseudopotential (ECP) from Durand and coworkers 36–38 have been used. For Sr and Ti atoms in TiO_{2} and STO NTs, the BSs have been chosen in the form of 311sp–1d and 411sp–311d, respectively, using ECP from Hay and Wadt 39, while full-electron BSs were adopted for all other atoms in calculations of defective titania and strontium titanate NTs, *i.e*., O: 8s–411sp–1d; C: 6s–411sp–11d; N: 6s–31p–1d, S: 8s–63111 sp-11d, and Fe: 8s–6411 sp–41d (see Refs. 29, 40).

To provide the balanced summation over the direct and reciprocal lattices of BN NT, the reciprocal-space integration has been performed by sampling the Brillouin zone (BZ) with the 10 × 1 ×1 Pack–Monkhorst *k*-mesh 41 that results in six eventually distributed *k*-points at the segment of irreducible BZ. Extended 2 × 2 supercells have been used to simulate quasi-isolated point defects in TiO_{2} and STO NTs. Therefore, BZ sampling for these NTs have been chosen with the 6 × 1 × 1 Pack–Monkhorst *k*-mesh or four *k*-points per segment. Threshold parameters of CRYSTAL code (ITOLn) for evaluation of different types of bielectronic integrals (overlap and penetration tolerances for Coulomb integrals, ITOL1 and ITOL2, overlap tolerance for exchange integrals ITOL3, as well as pseudo-overlap tolerances for exchange integral series, ITOL4 and ITOL5) 29 have been set to 8, 8, 8, 8, and 16, respectively. (If the overlap between the two atomic orbitals is smaller than 10^{–ITOLn}, the corresponding integral is truncated.) Truncation parameters in the case of TiO_{2} and STO NTs have been set to 7, 8, 7, 7, and 14, respectively. Further increase of *k*-mesh and threshold parameters results in much more expensive calculations, yielding only a negligible gain in the total energy (∼10^{−7} a.u.). Calculations are considered as converged when the total energy obtained in the self-consistent field procedure differs by less than 10^{−7} a.u. in the two successive cycles. Effective charges on atoms as well as net bond populations have been calculated according to the Mulliken population analysis 29.

Equilibrium lattice constants calculated for the bulk of hexagonal BN have been found to be qualitatively close to their experimental values (*a*_{0} of 2.51 vs. 2.50 Å obtained in experiment and *b*_{0} of 7.0 vs. 6.7 Å 42), thus, indicating reliable geometry optimization of BN BSs. The optical bandgap (*δ*) measured experimentally for hexagonal BN bulk is 5.96 eV 43, the value of *δ* calculated by us is found to be somewhat overestimated (6.94 eV), which is rather typical of hybrid methods considered in the current study. The value of *δ* calculated for bulk TiO_{2} in anatase phase yields 3.64 vs. 3.18 eV in experiment, while *δ* calculated for bulk STO in high-symmetry cubic phase yield 3.63 vs. 3.25 eV. A reasonable agreement between measured and calculated equilibrium lattice constants of both TiO_{2} and STO bulk solids is also obtained (see Refs. 27 and 40).

### 4 Summary and conclusions

- Top of page
- Abstract
- 1 Introduction
- 2 Computation details
- 3 Results and discussion
- 4 Summary and conclusions
- Acknowledgements
- Biographical Information

In this study, we have presented the results of defect-engineering modeling of boron nitride, titanium dioxide, and strontium titanate nanotubes (NTs) using first-principles calculations based on hybrid DFT. The variations in formation energies obtained for equilibrium defective nanostructures allow us to predict the most stable compositions, irrespective of the changes in growth conditions. Calculated charge–density maps of the different tubular nanostructures containing extrinsic substitutional impurity atoms highlighted changes in the charge distribution caused by doping. This means that the increased covalency in defect–host atom bonds may lead to an enhancement of adsorption properties. This would imply that defective NTs can be used in gas-sensing devices.

On the basis of the performed first-principles calculations, one may conclude that the presence of isoelectronic impurities significantly affects the band structure of the NTs under study, which must be taken into account when constructing nanoelectronic devices based on these NTs. All the mentioned effects can be observed by optical and photoelectron spectroscopy methods, as well as by measuring the electrical properties of the NTs. Midgap levels positioned inside the optical bandgap of defective NTs make them attractive for bandgap engineering in, for example, photocatalytic applications.

### Biographical Information

- Top of page
- Abstract
- 1 Introduction
- 2 Computation details
- 3 Results and discussion
- 4 Summary and conclusions
- Acknowledgements
- Biographical Information

**Yuri Zhukovskii** obtained his B.Sc. and M.Sc. degrees from the Department of Physics and Mathematics at the University of Latvia, Riga. In 1993, he gained the Ph.D. degree (Dr. Chem.) from Institute of Inorganic Chemistry, Latvian Academy of Sciences, Latvia, and Institute of Physics, St. Petersburg State University, Russia, for his thesis “Quantum-chemical study of water chemisorption on aluminum surface”. Between 1995 and 2007, he was Fellow at the Helsinki University of Technology, Espoo (Finland), the University of Western Ontario, London (ON, Canada), and the Northwestern University, Evanston (IL, USA). Dr. Zhukovskii has extended teaching experience and has participated in several international research activities, among them the EC Framework 7 Project on Nanoscale ICT Devices and Systems, the EUROATOM ACTINET networking Project on Nuclear Fuels, and the FP 7 Marie Curie CACOMEL Project (Nano-carbon based components and materials for high frequency electronics). From 2012 he is Head of the Laboratory of Computer Modeling of the Electronic Structure of Solids at the Institute of Solid State Physics at University of Latvia, Riga. His main research interests include the physics and chemistry of crystalline solids, surface science, adsorption and surface reactivity, physics and chemistry of nanostructures, quantum chemistry, and computational materials science.