**1. Introduction**

This is a chapter on electronic structure calculations for nano materials based on first‐principles density functional theory (DFT) [1, 2]. The DFT has become the primary tool for electronic structure calculations for solids and has also become popular for atoms and molecules. There are many reviews and books on theDFT [3‐5].In this chapter,the works ofOhno and coworkers on electronic structure calculations for deformed boron nitride nanotubes (BNNTs) using the DFT are described [6, 7].

The existence of BNNTs was theoretically predicted by Rubio et al. [8, 9] and then multi‐walled (MW) BNNTs were first synthesized by Chopra et al. [10]. Since then, BNNTs have attracted the attention of many researchers owing to their important properties [11]. The mechanical strength [12, 13] and thermochemical stability [14] of BNNTs are comparable to those of carbon nanotubes (CNTs) [15]. For instance, experiments (using a thermal vibrational amplitude technique [12] and an electric field‐induced resonance method [16]) and atomistic simulations (first‐principles [17‐20], tight‐binding [21, 22], and classical molecular mechanics [23, 27] calculations) measured the Youngʹs modulus of BNNTs to be in the range 0.7‐1.2 TPa, which is close to that of CNTs (e.g., the average value is 1.8 TPa [28] and 1.25 TPa [29]). In contrast, the electrical conductivity of BNNTs is completely dissimilar to that of CNTs. While CNTs become either metallic or semiconductive depending on the chirality, BNNTs are electrically insulating regardless of the diameter and chirality [11]. This is a notable characteristic of BNNTs that is different from CNTs. Therefore, BNNTs are expected to be used as electrical insulation coatings for conducting or semiconducting nanochains, nanowires, and nanotubes in severeconditions such as high temperatures and chemically hazardous environments.

However, a recent experimental study indicated that a bent MWBNNT was electrically conductive [30], and a theoretical study showed that flattening decreased the energy gap of a zigzag single‐walled (SW) BNNT [31]. These results indicate that the usefulness of BNNTs as nanocoatings might be lost under certain conditions (e.g., deformation caused by thermal

**Figure 1.** Simulation model of (8,0) SWBNNT.

stress or by a substrate constraint). Alternatively, BNNTs can be used in nanoelectronic devices by introducing deformation. In any case, our aim is to elucidate the electronic structures of deformed BNNTs. In the following sections, electronic structure calculations for SWBNNTs under tension, torsion, and flattening (Section 2) and for MWBNNTs under flattening (Section 3) will be discussed.
