First-principles calculation of electronic, vibrational, and thermodynamic properties of triaminoguanidinium nitrate

In recent years, the important energetic material triaminoguanidinium nitrate (TAGN) has been widely used, and the process of synthesizing TAGN has become more and more perfect. However, there are relatively few theoretical studies on TAGN. This paper uses first-principles calculations to more systematically study the crystal structure, and electronic, vibrational, and thermodynamic properties of TAGN. The calculation results show that the calculated unit cell parameters are relatively consistent with the values obtained through X-ray diffraction experiments. This article describes in detail the state density of the valence electrons of each atom. By analyzing the vibrational properties of TAGN crystal, the vibration mode corresponding to each optical wave is obtained. At the same time, the vibration mode of each peak in the Raman spectrum and the infrared spectrum is described in detail. Then, the calculated value is compared with the experimental value; it can be seen that the error is relatively small. According to the vibration characteristics, a series of thermodynamic functions such as enthalpy (H), Debye temperature (Θ), free energy (F), and entropy (S) are calculated. These thermodynamic functions can provide a certain reference for future research.


Introduction
Nowadays, energetic materials have been widely used in military industry and national life fields. In order to meet all kinds of needs, all kinds of energetic materials are bred. Triaminoguanidinium nitrate (TAGN) is a very important energetic material. With its own superior properties, it is widely used in gas generating agents, propellants, and explosive additives [1,2]. At the same time, TAGN has good thermal stability and can be stored for a long time without deterioration [3][4][5].
Therefore, the synthesis of TAGN has always been the focus of research. In the 1960s, research reports on TAGN appeared for the first time [6]. According to literature reports, depending on the different reactants, there are four main methods for synthesizing TAGN: dicyandiamide method [6], calcium cyanamide method [7], cyanamide method [8], and guanidine nitrate method [9]. These four methods have high yields, but the purity of the reactants is too high and the reaction time is too long, which greatly limit the production of TAGN. In order to solve this problem, in 2006, Xu and Yang optimized and improved the nitric acid arc method and synthesized kilogram-level TAGN with a productivity of 94.8% [10]. A certain scale of mass production also creates certain conditions for the wide application of TAGN. Besides its own synthesis as the focus of research, TAGN is also an important intermediate for the synthesis of energetic materials. A series of tetrazine high-nitrogen energetic compounds were synthesized by TAGN [11][12][13]. Meanwhile, triaminoguanidinium nitrate is also one of the important raw materials for the synthesis of other triamino arc salts [14,15]. The wide application of TAGN means that the research on TAGN is particularly important. The molecular structure of TAGN is shown in Fig. 1 [5].
At present, there are many researches on the synthesis method and application performance of TAGN, but there are few researches on the electronic and thermal properties of TAGN. At the same time, lattice vibration is regarded as the basis of the microscopic theory and macroscopic process of studying the thermodynamic properties and structural phase transition of crystals. Therefore, this work research is based on first-principles calculations, focusing on the crystal structure, and electronic, vibrational, and thermodynamic properties of TAGN.

Calculational methods
The calculations were performed by using the CASTEP code [16]. This code was based on density functional theory (DFT) and used the norm-conserving pseudopotential method. The exchange correlation potential used the Perdew-Burke-Ernzerhof (PBE) in the generalized gradient approximation (GGA) [17]. The Grimme correction of the DFT-D method was used to deal with the van der Waals interactions [18]. At the same time, to ensure the calculation convergence, the plane wave cutoff energy was set to 830 eV. The H 1s 1 , C 2s 2 2p 2 , N 2s 2 2p 3 , and O 2s 2 2p 4 were treated as valence electrons, and the k-point of Brillouin zone was set to 2 × 1 × 2. The total energy, residual force, residual stress, and displacement were set in this article. The total energy was less than 5.0 × 10 −6 eV/atom. The force acting on each atom was not more than 0.1 eV/nm. The maximum stress was 0.02GPa, and the maximum displacement of atoms was 5 × 10 −4 Å.

Structure of triaminoguanidine nitrate
The crystal structure of TAGN is an orthorhombic unit cell composed of four TAGN molecules, its space group is Pbcm, and its molecular formula is CH 9 N 7 O 3 . As shown in Fig. 2, the red balls represent oxygen atoms, the white balls represent hydrogen atoms, and the blue balls represent nitrogen atoms. The structure of a single TAGN molecule is shown in Fig. 3. TAGN is composed of CH 9 N 6 + cation and NO 3 − anion. From Fig. 2, we can see that for a single TAGN molecule all nitrogen atoms are on the same plane, and this plane bisects the entire molecule. There are three amino groups on the CH 9 N 6 + cation. These are the same as described in the literature [19]. As shown in Table 1, this paper calculates the bond length of C-N. We can see that the bond length of C-N is between the lengths of the C-N single bond and the C-N double bond. This means that C-N is a partial double bond [5,20,21]. There are  Table 2, the unit cell parameters calculated in this paper are in good agreement with the experimental results [19]. The maximum error will not exceed 2.40%, indicating that the calculated crystal structure of TAGN in this paper is feasible and the optimized result is reasonable.

Electronic properties
The band structure of TAGN along the high symmetry point of the Brillouin zone is shown in Fig. 4. It can be seen from the figure that TAGN is a direct band gap because the lowest point of the conduction band and the highest point of the valence band are at the same symmetric point. In addition, the band gap of TAGN is calculated to be 3.039 eV. This value is very close to the calculated value 2.968 eV given by Qin [22]. Unfortunately, there is no experimental value to compare with the calculated value of the paper. However, it is well known that using GGA-PBE functional calculations will underestimate the band gap of the crystal, so the actual band gap of TAGN should be greater than 3.039 eV.
In order to better understand the electronic properties of TAGN, it is necessary to consider the contribution of the density of states of each atom to the density of states of the entire TAGN molecule. For the same kind of atom, the contribution to the total density of states is also different due to the difference in its occupation and the environment. This article considers the populations of atoms, then classifies all the atoms in the TAGN molecule. As shown in Fig. 3, nitrogen atoms in TAGN molecules can be divided into 7 types, oxygen atoms are divided into 2 types, and hydrogen atoms are divided into 6 types. Figure 5 shows the total density of state and the partial density of states of various types of atoms. It can be seen from the figure that the energy band from −27.5 to −24.4 eV is mainly contributed by O1-2s, O2-2s, and O2-2p states and N7-2s states.

Vibrational properties
The vibrational properties of TAGN are calculated based on the density functional perturbation theory. There are four TAGN molecules in the TAGN unit cell, and each TAGN molecule has 20 atoms, so there are 80 atoms in the TAGN unit cell. This means that there are 3 acoustic vibrational modes and 237 optical vibrational modes in this TAGN molecule. According to group theory analysis [23], the irreducible expression of optical vibration is as follows: Γ = 24A u + 23B 1u + 36B 2u + 36B 3u + 36A g + 36B 1g + 22B 2g + 24B 3g , among which the vibrational modes of B 1u , B 2u , and B 3u have infrared activity. Among them, the vibrational modes of A g , B 1g , B 2g , and B 3g have Raman activity. A u does not have Raman and infrared activity. As shown in Table 3, each frequency and the corresponding vibrational mode are recorded in the table and compared with the corresponding experimental values. However, considering that the vibration at some frequencies is the coupling effect of the unit cell's overall   vibration and chemical bond vibration or group vibration, the vibration form is relatively complicated and has no substantial meaning, so Table 3 does not list the corresponding frequencies at these frequencies of the form of vibration. This phenomenon is more obvious at low frequencies. At the same time, considering that this phenomenon is more obvious in the low-frequency range, so the vibrational mode with a frequency lower than 200 cm −1 does not appear in Table 3. Both infrared spectroscopy and Raman spectroscopy are highly characteristic and can be used to reflect the molecular structure and vibrational properties of chemical bonds [26]. Therefore, this paper also calculated the infrared spectra of TAGN, as shown in Fig. 6. The Raman spectrum is also calculated, as shown in Fig. 7. In the infrared spectrum, in the high-frequency range of 3000 to 3400 cm −1 , the vibration of TAGN is mainly composed of N-H stretch and NH 2 asymmetry stretch. Among the absorption peaks of the infrared spectrum, the vibrations at frequencies of 3268.40 cm −1 , 3328.82 cm −1 , and 3367.67 cm −1 are NH 2 asymmetry stretch. This is very close to the experimental values [24] of NH 2 asymmetry stretch 3110 cm −1 , 3214 cm −1 , and 3317 cm −1 , and the maximum error does not exceed 5.1%. The frequency is N-H stretch at 3207.89 cm −1 , which is very small and different from the experimental value [10,25] Fig. 6 The infrared spectra of TAGN Fig. 7 The Raman spectra of TAGN It can be clearly seen that the calculated value obtained by using density functional theory is in good agreement with the experimental value, and the maximum error does not exceed 5.4%. But in the calculations in this paper, the infrared absorption peak of C-N stretch is not observed like the experiment. This article believes that C-N stretch exists, but C-N is relatively stable, with a low vibration frequency, so the infrared absorption peak is covered by other infrared absorption peaks with large vibrational frequencies. At the same time, this paper also determined the infrared absorption peaks of N-O stretch, which can be used as the infrared characteristic peaks of TAGN and also will play an important role in the future research of TAGN.
For Raman spectroscopy, in the high-frequency range, the Raman peaks at 3194.95 cm −1 , 3227.83 cm −1 , and 3293.33 cm −1 are N-H stretch. The Raman peak with a frequency of 3284.69 cm −1 is NH 2 symmetry stretch. In the intermediate frequency range, the Raman peak NO 3

Thermodynamic properties
Thermodynamic properties are one of the important parameters of materials, which play an important role in the thermal conductivity and thermal control of materials. Therefore, it is necessary to calculate the thermodynamic properties of the title compound. According to the vibration of atoms, this article calculates the Helmholtz free energy (F), enthalpy (H), entropy (S), and Debye temperature (Θ) of TAGN using statistical methods. The specific expressions are as follows [27]: where E tot is the total energy of the TAGN crystal ground state, E zp is the zero-point vibration energy, ℏ is the reduced Planck constant, T is the thermodynamic temperature, k B is the Boltzmann constant, and N(ω) is the state density of the Fig. 8 Thermodynamic function Fig. 9 Debye temperature function phonon. The relationship between thermodynamic quantity and temperature in the range of 5 to 1000 K is shown in Figs. 8 and 9. F i g u r e 8 c l e a r l y s h o w s t h a t e n t h a l p y a n d temperature*entropy increase with the increase of temperature. The growth rate of temperature*entropy is higher than enthalpy, and the relationship between enthalpy and temperature is almost linear. Helmholtz free energy decreases with increasing temperature. The main reason is that as the temperature increases, the irregular thermal motion of the molecules becomes more intense, and the distance between the molecules becomes larger. The macro performance is the increase in system energy and entropy. Figure 9 clearly shows that the Debye temperature increases as the temperature increases. In the lower temperature range, the Debye temperature increases faster, and in the high temperature range, the Debye temperature increases slowly. The main reason is that the heat capacity of a solid is mainly contributed by two parts [28]: one is the thermal vibration of the crystal lattice; the other is the thermal movement of electrons. The contribution of the thermal motion of electrons is only obvious at low temperatures, and it can be almost ignored when the temperature is high.

Conclusions
In this paper, the crystal structure, electronic properties, vibrational properties, and thermodynamic functions of TAGN are calculated by first-principles calculations. The following conclusions are obtained: the lattice parameters are not much different from the experimental values, which shows the rationality of the calculation results in this paper. It can be seen from the energy band diagram that TAGN is a direct band gap with a band gap of 3.039 eV. Combined with the total density of states diagram and the partial density of state diagram, the electronic properties of each atom are analyzed. The infrared and Raman spectra of TAGN are calculated. The vibration frequency of each group and chemical bond consistent with the experimental value was obtained from the infrared spectrum. The thermodynamic functions are calculated. Enthalpy and temperature*entropy increase with increasing temperature, and Helmholtz free energy decreases with increasing temperature. The Debye temperature increases with the increase in temperature, but it increases faster at low temperatures and slower at high temperatures.
Author contribution Wen-Guang Li: conceptualization, data curation, formal analysis, investigation, methodology, writing-original draft Yun-Dan Gan: investigation, methodology, writing-review and editing Zhi-Xin Bai: formal analysis, investigation, methodology, writingreview and editing Ming-Jian Zhang: conceptualization, funding acquisition, methodology, writing-review and editing Fu-Sheng Liu: conceptualization, methodology, writing-review and editing Bin Tang: methodology, software, writing-review and editing Qi-Jun Liu: conceptualization, resources, writing-review and editing Xiang-Hui Chang: conceptualization, investigation, methodology, project administration, supervision, writing-review and editing Funding This work was supported by the Fund of the Key Laboratory of N a t i o n a l D e f e n s e S c i e n c e a n d T e c h n o l o g y ( G r a n t N o . 6142A03182008) and the National Key Laboratory for Shock Wave and Detonation Physics of China (Grant No. JCKYS2019212007).
Data availability The datasets used or analyzed during the current study are available from the corresponding author on reasonable request.