Introduction

Borazine (B3N3H6), which is generally introduced in textbooks as “inorganic benzene” under aspects of the isoelectronic relationship [1], is an ideal precursor for boron nitride materials because it only contains elements of boron, nitrogen, and hydrogen [2]. It has been used as the precursor for preparation of both boron nitride ceramic matrix composites by precursor infiltration pyrolysis (PIP) and boron nitride coatings by chemical vapor deposition (CVD) [3]. Borazine was originally discovered by the thermal decomposition of the diammoniate of diborane [4]. Both experimental [5, 6] and theoretical [7, 8] works have been performed widely. The thermal decomposition of B3N3H6 in unsaturated vapor has been studied [9], showing that the gaseous B3N3H6 was decomposed on the reaction vessel surface along with the formation of volatile intermediates. The nature of chemical bond [10], ring current strengths [11], and anion-π interactions [12] of B3N3H6 were investigated, indicating its wide applications such as active molecule for electrodes [13], reactant for boron nitride nanowalls [14], low-dimensional spin filters [15, 16]. etc.

Kalemos [10] compared the nature of the chemical bond in B3N3H6, B3O3H3, B2N2C2H6, and related species by considering the excited states of the constituent fragments, which told us that these molecules isoelectronic to benzene were formed due to that BH, CH, NH binded together in their excited states. Rabanal-León et al. [11] investigated the ring current strengths of B3N3X6 (X = H, F, Cl, Br, I, At) by using the magnetically induced current density method, which were used to evaluate the corresponding contributions to aromaticity. Bauzá et al. [12] studied the rings of N6, B3O3H3, B3N3H6, B3N3, and B3S3H3 with the anion-π interactions, which were important to crystal packing and three-dimensional structure. Sen [13] used B3N3H6 as active molecule to investigate the role of asymmetric magnetic electrodes. Merenkov et al. [14] synthesized hexagonal boron nitride nanowalls from B3N3H6 and NH3 gas mixture.

However, there are few studies in the literatures about physical properties of B3N3H6. For example, the optical and vibrational properties associated with the material’s structure are important to the military and civilian applications [17, 18], which have not been reported systematically. The optical properties of the material are critical to the application of laser guidance, optical information processing, telecommunications, infrared countermeasures, radar detection, etc. [19,20,21]. The vibrational properties are linked with the chemical reaction process, molecular bonding strength, Raman spectra, etc. [22,23,24], which are very important to understand the explosion process of energetic materials. Therefore, our purpose is to calculate the electronic structure, optical, and vibrational properties of B3N3H6 by using the first-principles density functional theory.

Computational details

The first-principles calculation with the Cambridge Sequential Total Energy Package (CASTEP) is employed in this paper [25]. The LDA of Ceperley-Alder-Perdew-Zunger (CAPZ) functional as well as GGA of Perdew-Burke-Ernzerhof (PBE) functional are applied as the exchange–correlation functional [26,27,28,29]. In order to consider the van der Waals interactions in B3N3H6 crystal, the DFT-TS [30] and DFT-D2 [31] methods are used. The pseudopotential is an effective potential constructed to replace the ionic core states, that is, the valence electrons are described by pseudo-wave functions [26,27,28,29]. For B3N3H6, the ionic cores are represented by ultrasoft pseudopotential. For B atom, the configuration is 1s22s22p1, where the 2s2 and 2p1 electrons are treated as valence electrons; for N atom, the configuration is 1s22s22p3, where the 2s2 and 2p3 electrons are treated as valence electrons; for H atom, the configuration is 1s1, where the 1s1 electron is treated as valence electron. The energy cutoff of 500 eV is applied in plane-wave basis. The Brillouin-zone integration is performed with 3 × 3 × 1 meshes using the Monkhorst–Pack method [32] for structure optimization. The values of the convergence thresholds for total energy, maximum force, maximum stress, and maximum displacement are 5.0 × 10−6 eV/atom, 0.01 eV/Å, 0.02 GPa, and 5.0 × 10−4 Å.

Results and discussion

Structural properties

The space group of tetragonal structure B3N3H6 is P43212. The crystal mode of B3N3H6 is shown in Fig. 1 after structural optimization, and it is an equilibrium crystal structure of Borazine. The optimized structural parameters of B3N3H6 are given in Table 1 as well as experimental data [1]. It can be seen that the values based on the GGA PBE-TS functional are in good agreement with the experimental results, indicating that this functional can well describe the crystal structure of Borazine. Hence, the physical properties of Borazine are solved by the GGA PBE-TS in the following work.

Fig. 1
figure 1

The crystal structure of B3N3H6 (B atoms are pink, N atoms are blue, and H atoms are white)

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Table 1 The optimized structural parameters of B3N3H6 along with the results of previous experimental data
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Electronic properties

The calculated band structure of B3N3H6 within the GGA PBE-TS is shown in Fig. 2. From the band structure, it is shown that B3N3H6 has an indirect band gap because the top of valence band is found at G point, while the bottom of conduction band is found at A point. The band gap is calculated to be 5.007 eV, so we can know that B3N3H6 is an insulator. The calculated band gap value is smaller than the experimental value of 6.5 eV [33]. The discrepancy is due to the well-known underestimation of DFT calculations. In order to solve this discrepancy, we use the B3LYP hybrid functional to recalculate the band structure. The calculated bandgap is 6.711 eV which is close to experimental value.

Fig. 2
figure 2

The band structure of B3N3H6 from the GGA PBE-TS calculation

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In the band structure, the valence bands are roughly divided into three regions: − 16.0 eV to − 14.0 eV (lower), − 7.5 eV to 6.0 eV (middle), and − 4.5 eV to 0 eV (higher). Figure 3 shows the total and the partial density of states (DOS) of B3N3H6. With the states between − 16 eV and − 12.5 eV, there is the interaction of N 2 s, B 2p and H 1 s. The states between – 8 eV and – 5 eV are predominantly composed of N 2p, B 2 s and all hydrogen’s 1 s. The valence bands basically arise from interaction of N 2p, B 2p and H 1 s states in the Fermi level.

Fig. 3
figure 3

The density of states of B3N3H6 from the GGA PBE-TS calculation

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Optical properties

The optical properties such as the complex dielectric function, complex refractive index, complex conductivity function, reflectivity, loss function, and absorption coefficient are important, which can be obtained from the complex dielectric function [34]:

$$\varepsilon (\upomega )={\varepsilon }_{1}(\upomega )+{i\varepsilon }_{2}(\upomega )$$
(1)

In this section, we present our results of optical properties of B3N3H6 at the equilibrium lattice constants in Figs. 4–9, up to an energy of 35 eV. We resolve the optical properties into two independent components: the polarization direction (001) component and the polarization direction (100) component. The calculated real part and imaginary part of complex dielectric function of B3N3H6 are shown in Fig. 4. From this figure, the real part of complex dielectric function is ε1 (001) = 2.209 and ε1 (100) = 2.298. There is a peak (ω (001) = 7.735 eV, ω (100) = 7.577 eV) from 4.5 eV to 9 eV for imaginary part, which is attributed to transition from the valence bands to conduction bands (t2g). There is a peak (ω (001) = 13.225 eV, ω (100) = 12.863 eV) for the calculated imaginary part, which is due to transition from the valence bands to conduction bands (eg). The complex refractive index of B3N3H6 is shown in Fig. 5. As shown in Fig. 5, we find that the static refractive index is n (001) (0) = 1.486 and n (100) (0) = 1.516. The refractive index reaches a peak at energy of 6.979 eV in (001) component, while it reaches a peak at energy of 6.806 eV in (100) component. Figures 6, 7, 8 and 9 show the absorption coefficient α(ω), complex conductivity function σ(ω), energy-loss function L(ω), and optical reflectivity R(ω). In each figure, as we can see, the optical anisotropy corresponds to the space group of B3N3H6.

Fig. 4
figure 4

The real and imaginary part of dielectric function of B3N3H6 for polarization direction (001) and (100)

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Fig. 5
figure 5

The real and imaginary part of refractive index of B3N3H6 for polarization direction (001) and (100)

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Fig. 6
figure 6

The absorption coefficient of B3N3H6 for polarization direction (001) and (100)

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Fig. 7
figure 7

The complex conductivity of B3N3H6 for polarization direction (001) and (100)

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Fig. 8
figure 8

The energy-loss function of B3N3H6 for polarization direction (001) and (100)

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Fig. 9
figure 9

The optical reflectivity of B3N3H6 for polarization direction (001) and (100)

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Vibrational properties

As shown in Fig. 10, there are 144 vibrations including 3 acoustic branches and 141 optical branches. The phonon spectra with no imaginary frequency reveal that B3N3H6 is dynamically stable. There is no significant splitting, which indicates that the B3N3H6 has no ability to change the strength of light as an optical device.

Fig. 10
figure 10

Calculated phonon dispersion of B3N3H6

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As shown in Fig. 10, the frequencies around 3450 cm−1 are referred to the vibrations of B-H and N–H, which are parallel to plane (111) , (111) , (111) and (111), including anti-symmetry and symmetry vibrations. It indicates that the B-H and N–H have a most dynamic strength. The frequencies around 2550 cm−1 are B-N anti-symmetric and symmetric vibrations, which are also parallel to above four planes. According to the calculated results, the vibrations of the frequencies above 896 cm−1 are parallel to four planes. The vibration of phonon is parallel to four planes at high frequencies; it shows that the crystal has a better dynamic stable when the optical radiation along those planes. Below 890 cm−1, the vibrations begin to be perpendicular and parallel to four planes as well as group vibration. It corresponds to a weak covalent bond strength, so the crystal has a low mechanical modulus and thermal conductivity. In a word, these vibrations can be used to present conformational changes and bonding and to reflect the initiation mechanism of energetic materials [24].

Conclusions

We have investigated the structural, electronic, optical, and vibrational properties of B3N3H6. We find that the accurate equilibrium volume of B3N3H6 from DFT calculations can be obtained by the TS correction to treat the van der Waals interactions. From the calculated band structure and density of states, we conclude that B3N3H6 is an insulator with an indirect band gap of 5.007 eV. The obtained optical properties show an optical anisotropy in (100) and (001) due to its tetragonal structure. These peaks associated with the transitions from the occupied to unoccupied states in the imaginary part of dielectric function are given. Moreover, the vibrational properties of B3N3H6 have been computed and these vibrations are discussed, indicating that B3N3H6 shows weak covalent bond strength.