YUAN Fang,LI Hui-li,ZHAO Guo-zheng

School of Chemistry and Material Science,Shanxi Normal University,Linfen 041000,Shanxi,China

Abstract：2,4,7,9,11,12-Hexanitro-2,4,7,9,11,12-hexaaza-tetracyclo[8.4.0.03,8.05,6]dodecane (cage-RDX) was calculated to obtain the geometric and electronic structures by the DFT-B3LYP/6-31G(d) method.Detonation performance was obtained by Kamlet-Jacobs equations on the basis of the theoretical density and heat of formation (HOF).The crystal structure was evaluated by molecular mechanics,which belongs to Pna21 space group,with cell parameters Z=4,a=14.705 ?,b=7.416 ?,c=12.055 ? and ρ= 2.214 g·cm-3.Detonation velocity (10.35 km·s-1) and detonation pressure (50.85 GPa) are higher than those of CL-20.For a high energy density compound (HEDC),based on the quantitative standard of energy and stability,cage-RDX RDX fully meets this requirement.These results provide theoretical guidance for the design of novel HEDCs.

Key words：density functional theory;cage-RDX;crystal structure;detonation performance

0 Introduction

High energy density compounds have been used widely for both military and civilian applications[1～3].To meet the requirements of future military and space applications,unremitting efforts were received by researchers of explosive chemistry,in order to obtain new energetic materials with good thermal stability,excellent detonation performance and green preparation[4～6].Therefore,the first task is to find energetic molecules with good detonation performance and stability.

Highly nitrated cage molecules constitute a new class of energetic materials that have gained great importance in recent years[7～9].These strained rings of cage compounds possess a concomitant increase in the heat of formation (ΔHf°) and a high density,which make them powerful explosives.In this class,CL-20 [2,4,6,8,10,12-hexanitrohexaazaisowurtzitane (HNIW)] is a new nitramine explosive,which has six N-NO2groups in its polycyclic structure,resulting in an increased density and heat of formation[10～12].Octanitrocubane (ONC) is another highly energetic explosive[13].The energy performance of ONC calculated at density 2.03 g/cm3give 20 % more energy output than HMX[14].Theoretical calculations not only make it possible to screen energetic molecules,but also further study the relationship between molecular structure and performance[15～18].To date,there is limited information available to cover cage-RDX.In this study,DFT and molecular mechanics (MM) methods were carried out to optimize structure and properties of cage-RDX,such as HOF and detonation performance.

1 Theoretical methods

The calculation was carried out by Gaussian 09 package at B3LYP[19]method with 6-31G (d) basis set(Gaussian 09,Gaussian Inc:Pittsburgh,PA，2013).The optimized molecular structure was characterized to be true local energy minima on potential energy surfaces without imaginary frequencies.Detonation velocity and pressure were determined by the Kamlet and Jacob equations[20].

Fig.1 Molecular structure of cage-RDX圖1 籠型-RDX的分子結(jié)構(gòu)

P=1.558NM1/2Q1/2ρ2

(1)

D=1.01(NM1/2Q1/2)1/2(1+1.30ρ)

(2)

wherePis detonation pressure in GPa,Dis detonation velocity in km·s-1,Nis the number moles of gaseous detonation products per gram of explosive,Mis the average molecular weight of the gaseous products,Qis the energy of explosion in J·g-1of explosive andρis the crystal density in g·cm-3[21].The possible polymorphs and crystal structure of cage-RDX were investigated by polymorph module of Materials Studio(Materials Studio 6.0,Accelrys,2012.)[22，23].

2 Results and discussion

2.1 Heat of formation

Tab.1 Calculated total energies of species表1 各種分子計(jì)算的總能量

The most practical parameter for experimentalists to determine the energetic properties of a chemical system is HOF.It has been reported that DFT is quite accurate for computing HOF through appropriate reactions.In this paper,the HOF of cage-RDX was calculated with the help of the following reaction:

6C(s)+3H2(g)+6O2(g)+6N2(g)=C6H6O12N12

With the calculated enthalpies of all species and experimental sublimation enthalpy of graphite,it is easy to obtain the HOF of cage-RDX.The related data are collected in Table 1.The result of 1 470.65 kJ·mol-1is larger than that of CL-20 (691.30 kJ·mol-1) and satisfies the necessary characteristic of energetic materials.

2.2 Molecular packing prediction and density

COMPASS[25，26]has been used to predict the crystal structure of cage-RDX in this paper.The B3LYP/6-31G (d) level-optimized ground-state geometry is used as the initial structure to search the polymorph.The high density polymorph is sorted out from the large number of potential crystal structures,and lattice parameters of the same are presented in Tab.2.For cage-RDX,the lowest energy is -344.19 kJ·mol-1·cell-1withPna21space group.Therefore,the title compound tends to exist in thePna21group (Fig.2) because the most stable polymorph usually possesses the least Gibbs free energy (or energy at 0 K).The corresponding lattice parameters areZ=4,a=14.705 ?,b= 7.416 ?,c=12.055 ? andρ=2.214 g·cm-3.We carefully compared the density of CL-20 predicted from the Compass force field (2.173 g·cm-3) and from the volume inside an electron density contour of 0.001 e·Bohr-3using Monte Carlo method (2.040 g·cm-3) with the experimental value (2.035 g·cm-3).For CL-20,the value predicted from the molecular structure is closer to the experimental one.Therefore,we believe 2.020 g·cm-3obtained using Monte Carlo method from the volume inside an electron density contour of 0.001 e·Bohr-3for cage-RDX is more reliable.

Fig.2 Molecular packing of cage-RDX in Pna21 space group圖2 籠型-RDX的Pna21空間群

Tab.2 Unit cell parameters of possible polymorphs of cage-RDX表2 籠型-RDX可能晶型的晶胞參數(shù)

2.3 Detonation performance

Tab.3 Detonation performance of cage-RDX and CL-20表3 籠型-RDX和CL-20的爆轟性能

Together with the density of 2.02 g/cm3obtained using Monte Carlo method from the volume inside an electron density contour of 0.001 e·Bohr-3,the detonation velocity and pressure were computed by the Kamlet and Jacob equations[28].Table 3 shows the detonation performance of cage-RDX and CL-20.In comparison with famous caged explosive CL-20,cage-RDX exhibits much better detonation performance.Therefore,the above detonation performance indicates that cage-RDX is a potential high energy explosive.comparable to nitramine explosive CL-20.Based on the quantitative standard of HEDC,i.e.,ρ≈1.90 g/cm3,D≈9.0 km/s,andP≈40.0 GPa,it is found from Table 3,that cage-RDX satisfies the requirements as HEDC.

3 Conclusions

The full geometrical optimization of cage-RDX was investigated by density functional theory with B3LYP/6-31G (d) level.The crystal structure,gas-phase HOF,and detonation properties were predicted.The results of detonation velocity and detonation pressure indicate that cage-RDX (ρ=2.02 g/cm3,D=10.35 km/s,P=50.85 GPa) outperforms CL-20,which essentially satisfies the quantitative criteria for the energy as HEDC.These results pave the way for structural design and experimental synthesis of high energetic density compounds.