含能雙環(huán)HMX衍生物分子設(shè)計(jì)的密度泛函研究

趙國政， 范建敏， 楊東芳， 范榮榮， 陸 明

(1. 山西師范大學(xué) 現(xiàn)代文理學(xué)院，臨汾041000； 2. 山西師范大學(xué)化學(xué)與材料科學(xué)學(xué)院 磁性分子與磁信息材料教育部重點(diǎn)實(shí)驗(yàn)室， 臨汾041004； 3. 南京理工大學(xué) 化工學(xué)院, 南京210094)

1 Introduction

Development of high energetic density materials (HEDMs) with favorable insensitivity, good explosive performance, and environmental acceptability is one of the major challenges to explosives chemists[1,2]. The energy of HEDMs is derived from combustion of the carbon backbone, ring/cage strain, and high nitrogen content[3]. A large number of inherently energetic C-N and N-N bonds could ideally store a large amount of energy, which leads to high positive heats of formation[4]. For example, a high nitrogen-containing compound, bicyclo-HMX has fewer H atoms and larger ring strain than HMX and may be able to exhibit superior explosive performance to HMX[5]. Therefore, molecular design of energetic materials with high nitrogen content plays a very important role in designing new potential HEDMs. Optimization of bicyclo-HMX derivatives with high density and energy has been a major focus in designing and synthesizing HEDMs. In a previous study by Wang et al., density functional theory (DFT) calculations were performed to identify the relationship between the structure and performance of a series of energetic cyclic nitramines, which exhibit better detonation performance than bicyclo-HMX[6]. As such, it is very necessary to analyze molecular structures of existing explosives to better understand the structure-performance relationship.

In this work, a systematic study on the heats of formation, thermodynamic properties, detonation performance, and stabilities of bicyclo-HMX derivatives was conducted. The three bicyclo-HMX derivatives are N-(1,3,4,6-tetranitrohexahydroimidazo[4,5-d]imidazol-2(1H)-ylidene)nitramide (A), 2-(dinitromethylene)-1,3,4,6-tetranitrooctahydroimidazo[4,5-d]imidazole (B), and N-(5-(dinitromethylene)-1,3,4,6-tetranitrohexahydroimidazo[4,5-d]imidazol-2(1H)-ylidene) nitramide (C). The structures of the title compounds are listed in Fig. 1.

2 Theory and methods

Geometry optimization of bicyclo-HMX derivatives was carried out with Gaussian 09 package[7]. Previous studies have shown that DFT-B3LYP method[8,9]with 6-311G(d,p) basis set[10]is able to reproduce the accurate energies, electronic structures, and thermodynamic properties which are very close to the experimental results[11,12]. The theoretical density was obtained with an improved equation, which was proposed by Politzer et al.[13]to better reflect the effects of intermolecular interactions in the crystals.

H298= ∑Hf, P-∑Hf, R=

(1)

(2)

The Politzer approach[16]which links the heat of sublimation to molecular electrostatic potential (MEP) mapped onto isodensity surface of a molecule and was successfully applied to many energetic materials[17,18]was employed to determine heat of sublimation.

3 Results and discussion

3.1 Heat of formation

M + 5CH3NO2+ NH(CH3)2

M + 6CH3NO2+ C2H4

M + 7CH3NO2+ CH3CN

Table 1 Calculated heats of formation and parameters related with electrostatic potential

3.2 Thermodynamic properties

3.3 Detonation performance

Table 2 shows the detonation properties of bicyclo-HMX derivatives. The detonation performances of bicyclo-HMX derivatives are computed by K-J equations[20]on the basis of the theoretical crystal density (p) and condensed-phase heat of formationwhich are the important parameters to evaluate performance of explosion of energetic materials. It can be found from Table 2 that all bicyclo-HMX derivatives have good detonation properties (Q= 1417.94-1686.53 Jg-1,D= 9.13-9.44 kms-1,P= 38.86-41.20 GPa). Therefore, in the design of molecule, we could adjust detonation properties by changing the substituted group. According to our suggested energy criteria for HEDMs, i.e.,≥ 1.90 gcm-3,D≥ 9.0 kms-1, andP≈40.0 GPa, bicyclo-HMX derivatives satisfy the requirements as new HEDMs.

Fig.2 Relationships between the thermodynamic functions and temperature (T) for bicyclo-HMX derivatives

Table 2 Predicted densities and detonation properties of bicyclo-HMX derivatives

3.4 Thermal stability

Table 3 lists the energies (a.u.) of frontier molecular orbitals and the gaps (ΔELUMO-HOMO) of bicyclo-HMX derivatives at B3LYP/6-311G(d,p) level. TheΔELUMO-HOMOof molecule A (0.18298 a.u.) is the largest while molecule C is the smallest (0.15500 a.u.) which is less stable than the former. For molecules A, B, and C, it can be seen that theΔELUMO-HOMOvalues are different with different positions of the groups. It can be easily found thatΔELUMO-HOMOdecrease when =N-NO2and =C(NO2)2groups is attached to the ring. The stability here refers to the chemical or photochemical processes with electron transfer or electron leap.

Table 3 Calculated energies of HOMO (EHOMO), LUMO (ELUMO), energy gaps (ΔELUMO-HOMO) and characteristic heights (h50)

CompoundsHOMO/(a.u.)LUMO/(a.u.)ΔELUMO-HOMO/(a.u.)h50/cmA-0.31208-0.129100.1829821.39B-0.31229-0.152780.1595111.40C-0.31888-0.163880.1550011.26

Characteristic height h50that can also reflect the impact sensitivity and stability of bicyclo-HMX derivatives was estimated using equation suggested by Pospí?iletal.[21]. The values of characteristic height h50are listed in Table 3. Variations of h50for bicyclo-HMX derivatives are in range of 11.26-21.39 cm. The h50of molecule A (21.39 cm) is the largest, while molecule C is the smallest (11.26 cm) indicating that the former is more stable than the latter. When =N-NO2and =C(NO2)2groups are attached, characteristic height h50decreases. This shows that incorporating =N-NO2and =C(NO2)2groups make their stability decrease. The predicted h50values have the order of A > B > C, which is consistent with the order based onΔELUMO-HOMO.

4 Conclusions

In this work, we have studied the gas-phase and condensed-phase heats of formation, thermodynamic properties, detonation performance, and thermal stabilities for three new bicyclo-HMX derivatives by using density functional theory method. Three derivatives have significant densities (1.92-1.98 gcm-3) and comparable detonation properties (D= 9.13-9.44 km·s-1,P= 38.86-41.20 GPa). The =N-NO2and =C(NO2)2groups are helpful for improving theDandPof bicyclo-HMX derivatives, which exhibit better energetic performance. The ordering in characteristic height h50is consistent with that inΔELUMO-HOMO. Our results may provide theoretical support for further design of bicyclo-HMX derivatives.