3.1. Structure of triaminoguanidine nitrate
The crystal structure of TAGN is an orthorhombic unit cell composed with four TAGN molecules, its space group is Pbcm, and its molecular formula is CH9N7O3. As shown in Fig. 1, 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. 2. TAGN is composed of CH9N6+ cation and NO3− anion. From Fig. 1 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 CH9N6+ cation. These are the same as described in the literature [19]. As shown in Table 1, this paper calculates the bond length of CN. We can see that the bond length of CN is between the length of the CN single bond and the CN double bond. This means that CN is a partial double bond [5, 20, 21]. There are two types of hydrogen bonds in the TAGN unit cell. [N(2)H(2)…N(6)], [N(5)H(5)…N(4)], [N(3)H(3)…N(1)], and [N(2)H(2)…O(1)] form intramolecular hydrogen bonds. At the same time, each cation will also form intermolecular hydrogen bonds with other anions. The presence of hydrogen bonds reduces the sensitivity of TAGN and makes the title compound more stable.
Table 1
The CN bond length of TAGN.
Bond

Length(Å)

CN2

1.34387

CN3

1.34769

CN5

1.34790

As shown in 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.
Table 2
The experimental and calculated lattice parameters of TAGN.
Methods

a(Å)

b(Å)

c(Å)

V(Å3)

This work

8.43017

12.7080

6.38597

684.134

Expt. [19]

8.389

12.684

6.543

696.21

3.2. Electronic properties
The band structure of TAGN along the high symmetry point of the Brillouin zone is shown in Fig. 3. 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 2.968eV 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 GGAPBE 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. 2, 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 4 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 24.4eV is mainly contributed by O12s, O22s, O22p states and N72s states. From − 21.4 to 17.7eV, mainly contributed by a series of state contributions such as C2s, C2p, O12s, O22s, N72p and N(1–6)2s. From − 16.4 to 12.8eV, mainly by N(1–6)2s, C2s, C2p and H(1–6)1s and other state contributions. From − 10.8 to 5.4eV, the total density of states is mainly composed of N72s, N(1–7)2p, C2s, C2p, O(1–2)2s, O(1–2)2p, and H(1–6)1s. From − 5.35 to 3.15eV, mainly composed of N(1–7)2p, C2p, and H(1–6)1s. The valence band near the Fermi level is mainly composed of N(1–6)2s, N(1–6)2p, O12p, O22p, and H(1–6)1s. The conduction band is mainly composed of N(1–7)2s, N(1–7)2p, C2p, O(1–2)2p, H(1–6)1s and other state contributions.
3.3. 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 = 24Au + 23B1u + 36B2u + 36B3u + 36Ag + 36B1g + 22B2g + 24B3g, among which the vibrational modes of B1u, B2u, and B3u have infrared activity. Among them, the vibrational modes of Ag, B1g, B2g, and B3g have Raman activity. Au 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 200cm− 1 does not appear in Table 3.
Table 3
The calculated and experimental vibrational modes and frequencies of TAGN
symmetry

Frequency(cm− 1)

Assignments

Mode

Expt

B1u

200.47

NH2 inplane rocking

IR


B2g

204.03

NH2 inplane rocking

Raman


Ag

210.00

NO rocking

Raman


B1g

210.81

NO rocking

Raman


B2u

216.45

NO rocking

IR


B3u

217.22

NO rocking

IR


B3g

222.23

NH2 inplane rocking

Raman


Au

223.15

NH2 inplane rocking



B2u

238.52

NH2 outplane torsion

IR


Ag

239.45

NH2 outplane torsion

Raman


B1g

246.65

NH2 outplane torsion

Raman


B1u

248.78

NH2 outplane torsion

IR


B3u

250.0.

NH2 outplane torsion

IR


B2u

254.36

NH2 outplane torsion

IR


Ag

254.86

NH2 outplane torsion

Raman


B3u

268.53

NH2 outplane torsion

IR


Ag

269.78

NH2 outplane torsion

Raman


B1g

270.08

NH2 outplane torsion

Raman


B2g

300.17

NH2 outplane torsion

Raman


B3u

309.13

NH2 outplane torsion

IR


B3g

310.05

NH2 outplane torsion

Raman


Au

315.25

NH2 outplane torsion



B1u

436.52

NH2 outplane torsion + NH rocking

IR


B2g

446.63

NH2 outplane torsion + NH rocking

Raman


Au

470.28

NH2 outplane torsion



B3g

471.81

NH2 outplane torsion

Raman


Au

509.51

NH2 outplane torsion



B1u

522.45

NH rocking

IR


B2g

524.57

NH rocking

Raman


B3g

524.96

NH2 outplane torsion

Raman


Au

570.50

NH rocking



B3g

570.91

NH rocking

Raman


B1u

622.79

NH2 outplane torsion

IR


B3g

651.19

NH rocking

Raman


Au

653.07

NH rocking



Au

659.54

NH rocking



B3g

664.65

NH rocking

Raman


B1u

679.07

NO− 3 inplane deformation
+NH rocking

IR


B2g

680.24

NO− 3 inplane deformation
+NH rocking

Raman


B3g

680.66

NO− 3 inplane deformation
+NH rocking

Raman


Au

681.33

NO− 3 inplane deformation



B1u

689.44

NH rocking

IR


B1u

690.00

NH rocking

IR


B1g

690.53

NO− 3 inplane deformation

Raman


B2g

690.54

NO− 3 inplane deformation

Raman


B2u

690.80

NO− 3 inplane deformation

IR


B3u

691.13

NO− 3 inplane deformation

IR


B1u

702.87

NH rocking

IR


B2g

711.08

NH rocking

Raman


Au

715.16

NH rocking



B3g

722.40

NH rocking

Raman


B1g

781.98

NO− 3 outplane deformation

Raman


Ag

782.31

NO− 3 outplane deformation

Raman


B3u

782.38

NO− 3 outplane deformation

IR


B2u

782.43

NO− 3 outplane deformation

IR


B1g

927.54

NH2 outplane rocking

Raman


B2u

936.15

NH2 outplane rocking

IR


Ag

947.33

NH2 outplane rocking

Raman


B2u

948.70

NH2 outplane rocking

IR


B3u

950.18

NH2 outplane rocking

IR


B3u

954.83

NH2 outplane rocking

IR


B1g

961.24

NH2 outplane rocking

Raman


B2u

968.17

NH2 outplane rocking

IR


Ag

976.93

NH2 outplane rocking

Raman


B1g

978.09

NH2 outplane rocking

Raman


B3u

985.32

NH2 outplane rocking

IR


B2u

1020.73

NO− 13 asymmetry stretch

IR

1078 [25]

B1g

1020.82

NO− 13 symmetry stretch

Raman


B3u

1021.43

NO− 13 asymmetry stretch

IR


Ag

1021.46

NO− 13 symmetry stretch

Raman


B2u

1114.28

NH2 outplane rocking+
NH rocking

IR


B1g

1115.61

NH2 outplane rocking+
NH rocking

Raman


Ag

1119.61

NH2 outplane rocking+
NH rocking

Raman


B2u

1125.35

NH2 outplane rocking+
NH rocking

IR


B3u

1126.93

NH2 outplane rocking+
NH rocking

IR


Ag

1133.84

NH2 outplane rocking+
NH rocking

Raman


B3u

1134.06

NH2 outplane rocking+
NH rocking

IR


B1g

1135.28

NH2 outplane rocking+
NH rocking

Raman


B1g

1176.56

NH2 outplane rocking+
NH rocking

Raman


B2u

1186.10

NH2 outplane rocking+
NH rocking

IR


B3u

1186.89

NH2 outplane rocking+
NH rocking

IR


Ag

1190.94

NH2 outplane rocking+
NH rocking

Raman


Au

1261.25

NH2 outplane torsion



B3g

1261.73

NH2 outplane torsion

Raman


B1u

1265.15

NH2 outplane torsion

IR


B2g

1267.46

NH2 outplane torsion

Raman


B2u

1273.91

NH rocking + NO stretch

IR


B2g

1273.95

NH2 outplane torsion

Raman


B1u

1279.13

NH2 outplane torsion

IR


B3g

1281.30

NH2 outplane torsion

Raman


Au

1282.61

NH2 outplane torsion



B1g

1285.28

NH rocking + NO stretch

Raman


B3u

1296.37

NH rocking + NO stretch

IR


Ag

1298.81

NH rocking

Raman


B1u

1305.51

NH2 outplane torsion

IR


B2g

1306.95

NH2 outplane torsion

Raman


Au

1312.11

NH2 outplane torsion



B3g

1319.03

NH2 outplane torsion

Raman


B1g

1329.84

NH rocking

Raman


B2u

1333.85

NH rocking

IR


B3u

1337.46

NH rocking

IR


B1u

1338.01

NH2 outplane torsion

IR


Ag

1344.32

NH rocking

Raman


Ag

1348.61

NH rocking

Raman


B2u

1349.84

NH rocking

IR


B2g

1352.10

NH2 outplane torsion

Raman


B3u

1354.59

NH rocking

IR


Au

1361.70

NH2 outplane torsion



B1g

1365.29

NH rocking

Raman


B3g

1367.48

NH2 outplane torsion+
NO stretch

Raman


B3u

1439.04

NH rocking

IR


B1g

1442.68

NH rocking

Raman


Ag

1447.93

NH rocking

Raman


B2u

1450.68

NH rocking

IR


B2u

1556.95

NH2 inplane shearing

IR


B1g

1561.08

NH2 inplane shearing + NH rocking

Raman


Ag

1579.11

NH2 inplane shearing + NH rocking

Raman


B3u

1580.92

NH2 inplane shearing + NH rocking

IR


B2u

1588.20

NH2 inplane shearing + NH rocking

IR


B1g

1596.95

NH2 inplane shearing + NH rocking

Raman


Ag

1597.69

NH2 inplane shearing + NH rocking

Raman


B3u

1599.20

NH2 inplane shearing + NH rocking

IR


B1g

1622.46

NH2 inplane shearing

Raman


B2u

1647.95

NH2 inplane shearing

IR

1615
[10, 25, 26]

B3u

1648.58

NH2 inplane shearing

IR


Ag

1659.28

NH2 inplane shearing

Raman


Ag

1665.03

NH2 inplane shearing

Raman


B3u

1667.16

NH2 inplane shearing + NH rocking

IR


Ag

1667.40

NH2 inplane shearing

Raman


B2u

1668.56

NH2 inplane shearing

IR


B2u

1669.67

NH2 inplane shearing + NH rocking

IR


B1g

1671.38

NH2 inplane shearing + NH rocking

Raman


B1g

1685.69

NH2 inplane shearing + NH rocking

Raman


B3u

1691.42

NH2 inplane shearing + NH rocking

IR


Ag

3194.95

NH stretch

Raman


B2u

3196.16

NH stretch

IR


B1g

3200.90

NH stretch

Raman


B3u

3207.89

NH stretch

IR

3211
[10, 26]

B3u

3226.31

NH stretch

IR


B1g

3226.59

NH stretch

Raman


Ag

3227.83

NH stretch

Raman


B2u

3229.27

NH stretch

IR


B1u

3249.04

NH2 asymmetry stretch

IR


B1g

3249.51

NH2 symmetry stretch

Raman


Ag

3250.97

NH2 symmetry stretch

Raman


B3u

3259.75

NH2 asymmetry stretch

IR


B3u

3268.40

NH2 asymmetry stretch

IR

3110 [25]

Ag

3268.92

NH2 symmetry stretch

Raman


B2u

3273.26

NH2 asymmetry stretch

IR


B1g

3273.83

NH2 symmetry stretch

Raman


Ag

3284.69

NH2 symmetry stretch

Raman


B1g

3286.81

NH2 symmetry stretch

Raman


B3u

3287.50

NH2 asymmetry stretch

IR


B2u

3290.84

NH2 asymmetry stretch

IR


B2u

3326.47

NH stretch

IR


B1g

3328.07

NH stretch

Raman


Au

3328.74

NH2 symmetry stretch



B3g

3328.77

NH2 symmetry stretch

Raman


B1u

3328.82

NH2 asymmetry stretch

IR

3214 [25]

B3g

3328.90

NH2 symmetry stretch

Raman


Ag

3329.33

NH stretch

Raman


B3u

3330.90

NH stretch

IR


B1u

3351.05

NH2 asymmetry stretch

IR


Au

3351.10

NH2 symmetry stretch



B3g

3351.31

NH2 symmetry stretch

Raman


B3g

3351.37

NH2 symmetry stretch

Raman


B2g

3367.43

NH2 symmetry stretch

Raman


B1u

3367.67

NH2 asymmetry stretch

IR

3317 [25]

B3g

3368.07

NH2 symmetry stretch

Raman


Au

3368.32

NH2 symmetry stretch



Both infrared spectroscopy and Raman spectroscopy are highly characteristic and can be used to reflect the molecular structure and vibrational properties of chemical bonds [24]. Therefore, this paper also calculated the infrared spectra of TAGN, as shown in Fig. 5. The Raman spectrum is also calculated, as shown in Fig. 6. In the infrared spectrum, in the high frequency range of 3000 to 3400cm− 1, the vibration of TAGN is mainly composed of NH stretch and NH2 asymmetry stretch. Among the absorption peaks of the infrared spectrum, the vibrations at frequencies of 3268.40cm− 1, 3328.82cm− 1and 3367.67cm− 1 are NH2 asymmetry stretch. This is very close to the experimental values [25] of NH2 asymmetry stretch 3110cm− 1, 3214cm− 1, 3317cm− 1, and the maximum error does not exceed 5.1%. The frequency is NH stretch at 3207.89cm− 1, which is very small different from the experimental value [10, 26] of 3211cm− 1, which is only 0.01%. The vibration of TAGN is mainly composed of NO3 − 1 asymmetry stretch, NH2 outplane rocking, NH rocking, NO stretch, NH2 inplane shearing, NO3 − 1 inplane rotation and NH2, Outplane torsion and other series of vibration composition in the intermediate frequency range of 1000 to 2000cm− 1. Among the absorption peaks of the infrared spectrum, the weak absorption peak at 1647.95cm− 1 is NH2 inplane shearing, which is only 2.0% away from the experimental value of 1615 cm− 1. The absorption peaks at frequencies of 1667.16cm− 1, 1669.67cm− 1 and 1694.42cm− 1 are the coupling effect of NH2 inplane shearing and NH rocking. The weak infrared absorption peak in the frequency range from 1020.43 to 1021.46cm− 1 is NO3− asymmetric stretch, which is only 5.4% errors from the experimental value of 1078cm− 1. The frequency range of 1114.28 to 1134.28cm− 1 is the coupling effect of NH2 outplane rocking and NH rocking, and the infrared absorption peaks are at the frequencies of 1134.06cm− 1 and 1114.28cm− 1. The frequencies from 1261.25 to 1282.61 cm− 1, from 1305.51 to 1319.03 cm− 1 and 1338.01cm− 1 are NH2 outplane torsion, of which 1265.15cm− 1, 1279.13cm− 1 and 1338.01cm− 1 are infrared absorption peaks. The infrared absorption peak at the frequency of 1296.37cm− 1 is NH rocking and NO stretch. The weak absorption peak with frequency at 1349.84cm− 1 is NH rocking. The frequency is in the lowfrequency range of 200 to 1000cm− 1. The vibration of TAGN is mainly composed of NH2 outplane rocking, NO3 − 1 outplane deformation, NH rocking, NO3 − 1 inplane deformation, NH2 outplane torsion, NO3 − 1 inplane rotation and other vibration forms. The infrared absorption peaks at frequencies of 936.15cm− 1, 948.70cm− 1, and 954.83 cm− 1 are NH2 outplane rocking. The weak infrared absorption peak at 782.43cm− 1 is NH2 outplane torsion. The strong infrared absorption peak of NH rocking is at 522.45 cm− 1. The infrared peaks at frequencies 248.78cm− 1 and 309.13 cm− 1 are NH2 outplane torsion. The infrared absorption peaks at frequencies 522.45cm− 1 and 216.45 cm− 1 are NO rocking.
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 CN stretch is not observed like the experiment. This article believes that CN stretch exists, but CN 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 NO 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 3194.95cm− 1, 3227.83cm− 1, and 3293.33 cm− 1 are NH stretch. The Raman peak with a frequency of 3284.69 cm− 1 is NH2 symmetry stretch. In the intermediate frequency range, the Raman peak NO3 − 1 symmetry stretch at the frequency of 1020.82 cm− 1. The Raman peaks of NH rocking are at 1298.81cm− 1 and 1348.61 cm− 1. The Raman peak with frequency at 1665.03cm− 1 is NH2 inplane shearing. In the low frequency range, the Raman peak at 42.02cm− 1 is NO3 − 1 inplane rotation. The Raman peak of NO rocking is located at 210.81cm− 1. In the low frequency range, under the coupling effect of the lattice vibration and the group vibration, it is difficult to distinguish which group or chemical bond vibration the Raman peak at low frequency belongs to. At present, there are few researches on TAGN Raman spectroscopy. Although there is no comparison between the experimental value and the calculated value in this article, the calculated value in this article can provide a certain reference for future research on TAGN Raman spectrum.
3.4. 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]:
$$H(T)={E_{tot}}+{E_{zp}}+\int {\frac{{\hbar \omega }}{{\exp \left( {\frac{{\hbar \omega }}{{{k_B}T}}} \right)  1}}} N(\omega )d\omega$$
1
$$F(T)={E_{tot}}+{E_{zp}}+{k_B}T\int {N(\omega )\ln \left[ {1  \exp (  \frac{{\hbar \omega }}{{{k_B}T}})} \right]} d\omega$$
2
$$TS(T)={k_B}T\left\{ {\int {\frac{{\hbar \omega }}{{\exp \left( {\frac{{\hbar \omega }}{{{k_B}T}}} \right)  1}}N\left( \omega \right)d\omega  \int {N\left( \omega \right)\left[ {1  \exp \left( {  \frac{{\hbar \omega }}{{{k_B}T}}} \right)} \right]} } d\omega } \right\}$$
3
$${C_V}(T)=9N{k_B}{(\frac{T}{{{\Theta _D}}})^3}\int\limits_{0}^{{{\Theta _D}}} {\frac{{{x^4}{e^x}}}{{{{({e^x}  1)}^2}}}} dx$$
4
$$x=\frac{{\hbar \omega }}{{{k_B}T}}$$
5
Where Etot is the total energy of the TAGN crystal ground state, Ezp is the zeropoint vibration energy, \(\hbar\)is the reduced Planck constant, T is the thermodynamic temperature, kB is the Boltzmann constant, and N(ω) is the state density of the phonon. The relationship between thermodynamic quantity and temperature in the range of 5K to 1000K is shown in Figs. 7 and 8.
Figure 7 clearly shows that enthalpy and 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 8 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.