Electronic, Optical and Vibrational Properties of B3N3H6 from First-Principles Calculations

The electronic, optical and vibrational properties of B 3 N 3 H 6 have been calculated by means of rst-principles density functional theory (DFT) calculations within the generalized gradient approximation (GGA) and the local density approximation (LDA). The calculated structural parameters of B 3 N 3 H 6 are in good agreement with experimental work. With the band structure and density of states (DOS), we have analyzed the optical properties including the complex dielectric function, refractive index, absorption, conductivity, loss function and reectivity. By the contrast, it is found that on the (001) component and (100) component have obvious optical anisotropy. Moreover, the vibrational properties have been obtained and analyzed.


Introduction
Borazine (B 3 N 3 H 6 ), 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 PIP and boron nitride coatings by 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 B 3 N 3 H 6 in unsaturated vapor has been studied [9], showing that the gaseous B 3 N 3 H 6 was decomposed on the reaction vessel surface along with the formation of volatile intermediates. The nature of chemical bond [10], ring current strengths [11], anion-π interactions [12] of B 3 N 3 H 6 were investigated, indicating its wide applications such as active molecule for electrodes [13], reactant for boron nitride nanowalls [14], low-dimensional spin lters [15,16]. etc. However, there are few studies in the literatures about physical properties of B 3 N 3 H 6 . 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. Therefore, our purpose is to calculate the electronic structure, optical and vibrational properties of B 3 N 3 H 6 by using the rst-principles density functional theory.

Computational Details
The rst-principles calculation with the Cambridge Sequential Total Energy Package (CASTEP) is employed in this paper [19]. LDA-CAPZ as well as GGA-PBE functional are applied as the exchangecorrelation functional [20][21][22][23]. In order to consider the van der Waals interactions in B 3 N 3 H 6 crystal, the DFT-D methods is used, including the TS [24] and G [25] corrections. The pseudopotential is an effective potential constructed to replace the ionic core states, that is, the valence electrons are described by pseudo-wave functions [20][21][22][23]. For B 3 N 3 H 6 , the ionic cores are represented by ultrasoft pseudopotentials. For B atom, the con guration is 1s 2 2s 2 2p 1 , where the 2s 2 and 2p 1 electrons are treated as valence electrons; for N atom, the con guration is 1s 2 2s 2 2p 3 , where the 2s 2 and 2p 3 electrons are treated as valence electrons; for H atom, the con guration is 1s 1 , where 1s 1 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 [26] for structure optimization. The values of the convergence thresholds for total energy, maximum force, maximum stress, maximum displacement are 5.0×10 − 6 eV/atom, 0.01eV/Å, 0.02 GPa and 5.0×10 − 4 Å.

Structural properties
The space group of tetragonal structure B 3 N 3 H 6 is P4 3 2 1 2. The crystal mode of B 3 N 3 H 6 is shown in Fig. 1 after structural optimization, it is an equilibrium crystal structure of Borazine. The optimized structural parameters of B 3 N 3 H 6 are given in Table 1

Electronic properties
The band structure of B 3 N 3 H 6 calculated within the GGA PBE-TS is shown in Fig. 2. From the band structure, it is shown that B 3 N 3 H 6 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 B 3 N 3 H 6 is an insulator. The calculated band gap value is smaller than the experimental value of 6.5 eV [27]. The discrepancy is due to the well-known underestimation of DFT calculations. 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).

Optical properties
The optical properties such as the complex dielectric function, complex refractive index, complex conductivity function, re ectivity, loss function and absorption coe cient are important, which can be obtained from the complex dielectric function [28]: In this section, we present our results of optical properties of B 3 N 3 H 6 at the equilibrium lattice constants in Figs. 4-9, up to a photon 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 B 3 N 3 H 6 are shown in Fig. 4.
From this gure, the real part of complex dielectric function is ε 1 (001) = 2.209 and ε 1 (100) = 2.298. There is a peak (ω (001) = 7.735 eV, ω (100) = 7.577 eV) from 4.5eV to 9eV for imaginary part, which is attributed to transition from the valence bands to conduction bands (t 2g ). 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 (e g ). The complex refractive index of B 3 N 3 H 6 is shown in Fig. 5. As shown in Fig. 5, we nd that the static refractive index are 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 6-9 show the absorption coe cient α(ω), complex conductivity function σ(ω), energy-loss function L(ω) and optical re ectivity R(ω). In each gure, as we can see, the optical anisotropy corresponds to the space group of B 3 N 3 H 6 .

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 B 3 N 3 H 6 is dynamically stable. There is no signi cant splitting, which indicates that the B 3 N 3 H 6 has no ability to change the strength of light as an optical device.
As shown in Fig. 10 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.

Conclusions
We have investigated the structural, electronic, optical and vibrational properties of B 3 N 3 H 6 . We found that the accurate equilibrium volume of B 3 N 3 H 6 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 concluded that B 3 N 3 H 6 is an insulator with an indirect band gap of 5.007 eV. Moreover, the optical and vibrational properties of B 3 N 3 H 6 have been computed, indicating that there is an optical anisotropy and B 3 N 3 H 6 shows weak covalent bond strength. Declarations