Introduction

There is an ongoing need for powerful but insensitive high energetic materials. A specific goal [1] is to synthesize the materials that have performance better than that of 1,3,5,7- tetranitro-1,3,5,7-tetraazacyclooctane (HMX) and stability close to or higher than that of 1,3,5-triamino-2,4,6-trinitrobenzene (TATB). Heterocycles generally have higher heat of formation and density and better oxygen balance than their carbocyclic analogues [2]. So the synthesis of energetic heterocyclic compounds has received a great amount of interest in recent years [3–9].

Pyridine is a six-membered heterocyclic compound with one nitrogen atom. Compared to carbocyclic analogues, the derivatives of pyridine have higher nitrogen contents, enabling these compounds to release more nitrogen gases in explosion. On the other hand, since the presence of N atom in the aromatic ring can increase the density effectively, e.g., the density of benzene is only 0.897 g·cm-3, but that of pyridine is 0.982 g·cm-3, the presence of pyridine in molecule is supposed to improve its density and correspondingly increases the detonation velocity and pressure [10]. Therefore, the search for new potential high-energy density materials containing pyridine has attracted many attentions [11–21]. In addition, studies show that introducing nitramine group (N-NO2) into a molecule can improve its detonation performance, for example, there are 3, 4, and 6 N-NO2 groups in hexahydro-1,3,5-Trinitro-1,3,5-triazine (RDX), HMX, and 2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane (CL-20) respectively, and their deto- nation performance increase in the same order. In this study, two new nitramine molecules containing pyridine ring, i.e., 1,3,5,7-tetranitro-8-(nitromethyl)-4-imidazolino[4,5-b]4-imidazolino-[4,5-e]pyridine(I) and its N-oxide 1,3,5,7-tetranitro-8-(nitromethyl)-4-imidazolino[4,5-b]4-imidazolino-[4,5-e]pyridine-4-ol(II) were proposed to benefit from the high density characteristics of pyridine and high energy characteristics of nitramine. The molecular structures are shown in Fig. 1. To the best of our knowledge, these kinds of compounds have not been synthesized and reported to date, though their possible synthetic routines have been suggested [22]. Theoretical studies have not been performed yet. We believe it is of great meaning to carry out a systematic theoretical investigation before synthesis on their geometrical structures and various properties, such as heat of formation, infrared spectrum, density, detonation properties and sensitivity, which will be helpful for understanding the candidate to be synthesized.

Fig. 1
figure 1

The molecular structures of the designed nitramines containing pyridine ring (bond lengths are in nm)

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Computational methods

The density functional theory (DFT)-B3LYP method [23, 24] in combination with the 6-31G* [25] basis set which has been proved [26–32] to be able to give quite reliable energies, molecular structures, and other properties was used to fully optimize the molecular geometries of I and II with the Gaussian03 program package [33]. To characterize the nature of the stationary points and to determine the zero-point vibrational energies, harmonic vibrational analyses were performed subsequently on each optimized structure at the same level. According to the previous studies, the computed harmonic vibrational frequencies were scaled uniformly by 0.96 to take into account the systematic overestimation of B3LYP/6-31G* calculations [34]. Based on the principle of statistical thermodynamics [35], heat capacity (C θp,m ), entropy (S θm ), and thermal enthalpy (H θm ) ranging from 200 to 800 K were derived.

Detonation velocity and pressure, the most important parameters for evaluating the detonation characteristics of energetic materials, were calculated using the Kamlet-Jacbos(K-J) equations [36, 37], which have been verified by many studies [26–32] to be suitable for organic explosives. The K-J equations are shown as follows:

$$ D = {1}.0{1}{\left( {N{{\overline M }^{{{1}/{2}}}}{Q^{{{1}/{2}}}}} \right)^{{{1}/{2}}}}\left( {{1} + {1}.{3}0\rho } \right) $$
(1)
$$ P = {1}.{558}{\rho^{{2}}}N{\overline M^{{{1}/{2}}}}{Q^{{{1}/{2}}}} $$
(2)

where P is the detonation pressure (GPa), D is the detonation velocity (km/s), ρ is the packed density (g/cm3), N is the moles of gas products per gram of explosives, M is the average molar weight of detonation products, and Q is the chemical energy of detonation (kJ/g). N, M, and Q are determined according to the largest exothermic principle [32].

Since Q and ρ are unknown for the unsynthesized hypothetical compounds, to predict their detonation properties, the modified K-J equations based on the calculation results of quantum chemistry were recommended [23, 24, 26, 38–43], in which the density of the explosive ρ was replaced by the crystal theoretical density (ρc) computed by the following equation:

$$ {\rho_c} = \frac{\text{M}}{{{\text{V}}\left( {0.001} \right)}}. $$
(3)

In which M is the molecular mass (g/molecule), and V(0.001) is the volume (cm3/molecule) defined as the space inside a contour of electron density of 0.001e · Bohr-3. However, the results obtained using this equation may have quite big errors for some systems, for example, molecules that can form strong hydrogen bonds. Politzer et al. [44] suggested that Eq. 3 should be corrected to better reflect the effects of intermolecular interactions in crystals. They have proposed two modified equations and the better one is shown as follows [44]:

$$ {\rho_{\text{p}}} = \alpha \left[ {\frac{\text{M}}{{{\text{V}}\left( {0.001} \right)}}\quad + \beta \left( {{\text{v}}{\sigma_{\text{tot}}}^2} \right) + \gamma } \right. $$
(4)

where α, β and γ are regression coefficients and their values are taken from ref. [44].

In this paper, both (3) and (4) have been used to predict the density of the title compounds for comparison.

The chemical energy of the detonation reaction Q was calculated as the difference between the heats of formation (HOFs) of products and reactants. In this paper, the HOFs of the title compounds were calculated with the help of the following reactions at the B3LYP/6-31G* level:

$$ \begin{array}{*{20}{c}} {7{\text{c}}\left( {\text{s}} \right) + 2{{\text{H}}_{{2}}}\left( {\text{g}} \right) + 5{{\text{O}}_{{2}}}\left( {\text{g}} \right) + 5{{\text{N}}_{{2}}}\left( {\text{g}} \right) \to {{\text{C}}_{{7}}}{{\text{H}}_{{4}}}{{\text{O}}_{{{10}}}}{{\text{N}}_{{{10}}}}\;\left( {\text{I}} \right)} \hfill \\ {7{\text{C}}\left( {\text{s}} \right) + 2{{\text{H}}_{{2}}}\left( {\text{g}} \right) + 5.5{{\text{O}}_{{2}}}\left( {\text{g}} \right) + 5{{\text{N}}_{{2}}}\left( {\text{g}} \right) \to {{\text{C}}_{{7}}}{{\text{H}}_{{4}}}{{\text{O}}_{{{11}}}}{{\text{N}}_{{{10}}}}\;\left( {\text{II}} \right)} \hfill \\ \end{array}. $$

With the calculated enthalpies of all species and the experimental sublimation enthalpy of graphite, it is easy to obtain the HOFs of the title compounds.

It should be noted, however, Q obtained in this way is the detonation enthalpy of the compound in gas phase, which is somewhat higher than that in solid phase used in K-J equations. The detonation velocity and pressure for the title compounds in solid state should be a little lower.

Results and discussion

Molecular geometry

With regard to the new designed compound, it is especially necessary to examine the geometric structures before discussing the other properties. Some bond lengths obtained from the B3LYP/6-31G*calculations are shown in Fig. 1.

According to the calculation results, the pyridine ring and the imidazole rings are essentially but not completely planar, e.g., C(4)-C(3)-C(6)-C(7) and C(1)-N(2)-C(3)-C(4) in I are −5.3° and −12.3°, respectively, and corresponding values are −11.1° and 5.8° for II. Dihedral angles about C(6)-N(11) in I are about 5° and in II are about 10°, which indicates the nitro groups linked with pyridyl slightly depart the plane of pyridine because of the steric hindrance effect.

The corresponding bond lengths of the two compounds are quite close to each other. Some discrepancies are obviously raised by the formation of N→O coordination bond in II. Because of the conjugation effect, the bond lengths of C-C (0.139 ∼ 0.141 nm) in the pyridine ring are between the usual lengths of C = C double bond (0.134 nm) and C-C single bond (0.154 nm). The same is true for the C-N bonds. In addition, the C-N bond in the pyridyl unit of II (0.137 nm) is a little longer than that of I (0.132 nm) because of the electron withdrawing inductive effect of the coordination O atom. The length of N→O bond is 0.125 nm. The lengths of these bonds are not very different from those in pyridine and N-oxide of pyridine. In pyridine, the experimental lengths of C-C and C-N bonds are 0.139 ∼ 0.140 nm and 0.134 nm [45], respectively. The corresponding results at the B3LYP/6-31G* level are completely the same. For the N-oxide of pyridine, the experimental determined bond lengths are 0.138 ∼ 0.139 nm for C-C, 0.138 nm for C-N, and 0.129 nm for N→O bond [46]. The corresponding calculated results are 0.138 ∼ 0.140 nm, 0.137 nm, and 0.127 nm. These results demonstrate once again that the method used in this study is reliable. The lengths of all N-NO2 bonds in the title compounds are longer than the usual N-N bond lengths (0.135-0.140 nm) in nitramines [47]. The N-NO2 bonds on the side of the N atom of pyridine in I (N(5)-N(12)) are shorter than those on the other side (N(2)-N(10)). However, this is not the case for II, in which the N-NO2 on the side of pyridyl N (0.149 nm) is longer than others (0.144 and 0.146 nm). Obviously, this change is caused by the introduction of the coordination O atom.

IR spectrum and thermodynamic property

It is well known that infrared spectrum (IR) is the basic property of a compound and an effective measure to analyze or identify the compound. It is also directly related with the thermodynamic properties. The simulated IR spectra of I and II based on the scaled harmonic vibrational frequencies are shown in Fig. 2. As there are no corresponding experimental results, no comparison and evaluation of the calculated results can be made. However, many previous studies [31, 38, 48] have shown that the calculated IR are usually in reasonable agreement with the experimental data. Our results may be used as reference data for future investigations of the title compounds.

Fig. 2
figure 2

The calculated infrared spectra of I and II at the B3LYP/6-31G* level

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For the complexity of the vibrational modes, it is difficult to assign all bands, so only some typical vibrational modes are analyzed. In the range of 1200–1300 cm-1, the characteristic symmetrical stretching vibrations of N=O in the nitro groups and out of plane wagging of C-H have the highest intensities. They appear at 1240 cm-1 and 1270 cm-1 in I and II, respectively, not much different from that in CL-20 and HMX (1260 cm-1 and 1250 cm-1, respectively). The next strongest absorption (1650 cm-1 in I and 1660 cm-1 in II) is raised by the asymmetrical stretching vibrations of nitro N=O and is also close to that in CL-20 and HMX (1650 cm-1 and 1630 cm-1 respectively). These two bands are both blue-shifted from I to II. The absorption band at 1580 cm-1 in II is resulted from the stretch of N→O coordination bond. It is blue-shifted compared with the N-oxide of pyridine for which the calculated value is 1320 cm-1 and the experimental value is 1265 cm-1 [49], which is consistent with the fact that the N→O length in II is shorter and stronger. The absorptions around 3000 cm-1 raised by the C-H symmetric and asymmetric stretching are very weak. The N-N stretching vibrations locate at the fingerprint region (800–900 cm-1). It is red-shifted from 850 cm-1 in I to 820 cm-1 in II due to the coordination of O to N. The corresponding values are 920 cm-1 and 870 cm-1 for CL-20 and HMX. Once again, this agrees with the fact that N-N in the title compounds are longer and weaker than those in CL-20 and HMX. In the range of 1000–1200 cm-1, there are absorptions raised by the symmetrical stretching vibrations of C-N in the imidazole ring and scissoring vibrations of C-H.

Thermodynamic functions, such as heat capacity, entropy, and enthalpy, which are important parameters and are necessary in predicting reactive properties, have been evaluated based on the scaled vibrational frequencies and the principle of statistic thermodynamics for I and II. The results are listed in Table 1.

Table 1 Thermodynamic functions of the title compounds at different temperatures
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At room temperature, the predicted C θp,m , S θm , and H θm of I are 345.95 J·mol-1·K-1, 644.43 J·mol-1·K-1, and 516.51 kJ·mol-1 respectively and corresponding values of II are 361.35 J·mol-1·K-1, 640.06 J·mol-1·K-1, and 528.86 kJ·mol-1. All these thermodynamic functions increase with temperature evidently. In addition, the values of C θp,m and H θm of II are all larger than that of I in the temperature range of 200 ∼ 800 K. However, the values of S θm are larger for II than for I only when the temperature is higher than 400 K. Analyzing the contribution of various movements, we see that this is mainly attributed to the contribution of vibration to entropy (Sv). The contribution of rotation (Sr) and translation (St) to entropy are always larger for II than for I, but the Sv of II is smaller than that of I when the temperature is lower than 400 K, so the sum of Sv, Sr, and St is smaller for II than for I at lower temperature. When the temperature increases, the Sv of II becomes bigger than that of I, and therefore the total entropy of II is larger. The temperature-dependent relationships for C θp,m , S θm , and H θm in the range of 200 ∼ 800 K can be expressed as shown in Table 2 and Fig. 3 (where SD is the standard deviation, the correlation coefficients (R2) are 1.000 for all equations). We think these will be helpful for the further studies on the other physical, chemical, and explosive properties of these two compounds.

Table 2 The correlation equations between the thermodynamic functions and temperature for the title compounds (the units of C θp,m , S θm , and H θm are J·mol-1·K-1, J·mol-1·K-1, and kJ·mol-1, respectively)
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Fig. 3
figure 3

Relationships between the thermodynamic functions and temperature for I and I (■,●, and▲ stand for C θp,m , S θm , and H θm and their units are J·mol-1·K-1, J·mol-1·K-1,and kJ·mol-1, respectively)

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The changes in energy (∆H) and Gibbs free energy (∆G) have been calculated for the oxidation reactions of I and pyridine, i.e., I + O → II, py + O → pyo, where py and pyo stand for pyridine and the N-oxide of pyridine, respectively. Results show that both are exothermic and spontaneous process with the ∆H being −131.86 and −259.75 kJ·mol-1, and ∆G being −141.83 and −219.75 kJ·mol-1, respectively. Since the oxidation from py to pyo has been achieved [50], the oxidation of I to II should also be feasible though it may be more difficult.

Detonation performance

To find a new HEDM, it is important to evaluate its detonation performance. Table 3 collects the predicted ρ, D, and P of the title compounds. For comparison, the calculated and experimental results of the famous explosives HMX [51] and CL-20 [52] are also listed. From Table 3 it can be seen that the densities obtained with the Eq. 4 is usually a little smaller than that obtained with the Eq. 3 and correspondingly, D and P predicted using the former are usually lower. For HMX, the densities obtained with Eqs. 3 and 4 are very close and both are smaller than the experimental value. The predicted D are a little bigger and P somewhat smaller than the corresponding experimental results. For CL-20, the density obtained from Eq. 3 is slightly larger and that from Eq. 4 is smaller than the experimental value with the former being somewhat better. The predicted D and P of CL-20 are all larger than the corresponding experiment values and those obtained using the density from Eq. 4 are better. As for the title compounds, II has better performances than I due to the improvement of oxygen balance. The detonation performances of II (D = 9.26 km•s-1, P = 39.70 GPa) are superior to HMX, though slightly inferior to CL-20. According to the criteria as an HEDM, i.e., ρ ≈ 1.9 g•cm-3, D ≈ 9 km•s-1, and P ≈ 40 GPa, compounds I and II are potential HEDMs and worth further investigations.

Table 3 Predicted detonation properties of the title compounds and two famous nitramine explosivesa
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Stability

Besides high energy, a good candidate of HEDM should also have a high stability. Bond overlap populations reflecting the electron accumulations in the bonding region can provide us detailed information about the strength of the bond and the thermal stability of the molecule. As a whole, the smaller the populations a bond has, the easier the bond breaks, and the lower stability the molecule has. In this paper, both Mulliken population analysis (MPA) [53], which is known to suffer from some shortcomings, especially the basis set dependence, and natural bond orbital analysis (NBO) [54] have been performed. The results are listed in Table 4.

Table 4 MPA and NBO results of populations obtained at the B3LYP/6-31G* level
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According to the MPA results, C(6)-N(11) in I and C(3)-N(2) in II have the smallest populations, which is obviously not reasonable and not in concordance with the conclusion of theoretical and experimental studies [38, 55] that N-NO2 bond is commonly weaker than C-N and C-C bonds and is prone to cleave. From the NBO analysis, N(2)-N(10) of I and N(5)-N(12) of II have the smallest populations, which is consistent with their longer lengths and is believed to be more reliable. This indicates that N(2)-N(10) of I and N(5)-N(12) of II are prone to cleave upon impact or other stimuli, and their breaking may be the initial steps in the decomposition or detonation. This is in line with the thermal decomposition mechanism of nitramine explosives such as HMX and CL-20 and seems to show that NBO analysis is more reliable than MPA, at least for these kinds of compounds. In addition, it can be seen that because of the electron-withdrawing effect of the coordination oxygen atom and the steric hindrance between O and the neighboring NO2 groups, the weakest bond changes from N(2)-N(10) in I to N(5)-N(12) in II. Compared with CL-20, the strength of the N-NO2 bonds and the stability of I and II are a little lower.

Conclusions

From the DFT studies on the title compounds, the following conclusions can be drawn:

  1. (1)

    In the stable structures of the title compounds obtained at the B3LYP/6-31G* level, the pyridine and imidazole ring are essentially but not completely planar. The nitro groups departure from the plane slightly. The N-NO2 bonds on the side of pyridine nitrogen in II have the longest bond lengths due to the steric hindrance effect between the N→O coordination bond and the NNO2 groups.

  2. (2)

    The IR spectra were computed and assigned. The strongest absorption (1240 cm-1 in I and 1270 cm-1 in II) corresponds to the symmetrical stretching vibrations of N = O in the nitro groups and out of plane wagging of C-H. The asymmetrical stretching vibration of N = O in the nitro groups is the next strongest and is located at 1650 cm-1 for I and 1660 cm-1 for II. Both absorption bands are blue-shifted by the oxidation of N. The N-N stretching vibration locates at 850 cm-1 for I and 820 cm-1 for II and is red-shifted when a coordination O atom is introduced. The peak at 1580 cm-1 for II corresponds to the symmetrical stretching vibration of N→O coordination bond.

  3. (3)

    Heat capacity, entropy, and enthalpy have been predicted and all increase quantitatively with the increasing temperature. The correlation equations have been obtained by fitting the calculated results.

  4. (4)

    Natural bond orbital analysis is more reliable than Mulliken population analysis for these kinds of compounds. The N-NO2 bonds are weaker and more fragile than the other bonds. The N-NO2 bonds on the imidazole rings on the side of pyridyl aza nitrogen become weaker than the other N-NO2 bonds after oxidation and they will rupture initially in the thermal decomposition processes. II is less stable than I and both are less stable than CL-20.

  5. (5)

    The title compounds may be novel potential candidates of HEDM according to their predicted densities (ca.2 g•cm-3), detonation velocities (over 9 km•s-1), and detonation pressures (about 40 GPa), which are all superior to HMX and only slightly inferior to CL-20. They are worth further investigations.