Comparative Theoretical Studies of Energetic Substituted Carbon- and

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Comparative Theoretical Studies of Energetic Substituted Carbon- and Nitrogen-Bridged Difurazans Xiaowen Zhang, Weihua Zhu,* and Heming Xiao Institute for Computation in Molecular and Materials Science and Department of Chemistry, Nanjing UniVersity of Science and Technology, Nanjing 210094, China ReceiVed: September 18, 2009; ReVised Manuscript ReceiVed: NoVember 17, 2009

Density functional theory method was used to study the heats of formation (HOFs), electronic structure, energetic properties, and thermal stability for a series of bridged difurazan derivatives with different linkages and substituent groups. The results show that the -N3 group and azo bridge (-NdN-) play a very important role in increasing the HOF values of the difurazan derivatives. The effects of the substituents on the HOMO-LUMO gap are combined with those of the bridge groups. The calculated energetic properties indicate that the -ONO2, -NO2, -NF2, -NdN-, or -N(O)dN- group is an effective structural unit for enhancing the detonation performance for the derivatives. An analysis of the bond dissociation energies for several relatively weak bonds suggests that the N-O bond in the ring is the weakest one and the ring cleavage is possible to happen in thermal decomposition. On the whole, the -NH-NH-, -NdN-, or -N(O)dNgroup is an effective bridge for enhancing the thermal stability of the derivatives. Considered the detonation performance and thermal stability, five compounds may be considered as the potential candidates of highenergy density materials (HEDMs). 1. Introduction High-nitrogen heterocyclic compounds are potential and promising candidates for high-energy density materials (HEDMs) owing to their rather high density, high positive heat of formation, good oxygen balance, and good thermal stability.1–11 Among these heterocyclic systems, the furazan ring is an efficient fragment to enhance the performance of HEDMs.12,13 A large number of the substituted monofurazan derivatives,13,14 chained furazans,15,16 macrocyclic furazans,17,18 ring-fused furazans,19,20 and furazan-functionalized tetrazolate-based salts21 have been synthesized and investigated for energetic applications. Some of them have displayed potential as energetic additives for high explosives, rocket propellant formulations, and pyrotechnic ingredients. To meet the continuing demand for improved energetic materials, there is a clear need to continue to design and develop new furazan-based HEDMs. The optimization of furazan-based molecules with high density and energy is the primary step for designing and synthesizing new HEDMs. Properties are often manipulated by making structural modifications. Theoretical calculations can play a very important role for understanding the structure-property relationships and make it possible to screen candidate compounds. Therefore, they can help design better and more efficient laboratory tests. To our knowledge, besides many experimental researches about the furazan and furoxano22,23 derivatives theoretical calculations have been performed to investigate their heats of formation and detonation properties.20,22,24,25 However, there is still lacking systematic and comprehensive molecular design for difurazan-based HEDMs. Recently, Huynh et al.6 reported the synthesis and properties of novel hydrazo- and azo-bridged 1,3,5-triazines. This study has indicated that the hydrazo (-NH-NH-) and azo (-NdN-) linkages not only desensitize but also dramatically increase the * To whom correspondence should be addressed. E-mail: zhuwh@ mail.njust.edu.cn.

melting point of the polyazido products. Hiskey et al.26 studied the heats of formation and explosive properties of 4,4′-diamino3,3′-azoxyfurazan and 4,4′-diamino-3,3′-azofurazan and concluded that the internal energy of an energetic material can be greatly increased by incorporating the azo or azoxy [-NdN(O)-] linkage in the molecular framework. Joo and Shreeve27 investigated the crystal structure and physical properties of the substituted carbon-bridged tetrazoles. The results show that the nitroiminotetrazoles linked by -CH2-CH2- have very high positive heats of formation and good detonation properties. These suggestions indicate that the combination of high-nitrogen heterocycles with different bridges may be helpful for improving the performance of energetic materials. In this paper, we reported a systematic study of the heats of formation, electronic structure, energetic properties, and thermal stability of a series of bridged difurazans with different linkages (-CH2-CH2-,-CHdCH-,-NH-NH-,-NdN-,-N(O)dN-) and substituent groups (-ONO2, -NH2, -NF2, -N3, -NO2) by using density function theory (DFT). Our main purpose here is to investigate the important role of different linkages and substituents in the design of efficient high-energy density compounds. The remainder of this paper is organized as follows. A brief description of our computational method is given in Section 2. The results and discussion are presented in Section 3, followed by a summary of our conclusions in Section 4. 2. Computational Method The DFT-B3LYP method with 6-31G(d) basis set was previously used to predict the HOFs of many organic systems via isodesmic reactions.28–34 The method of isodesmic reactions has been employed very successfully to calculate HOFs using total energies obtained from ab initio calculations. The so-called isodesmic reaction processes, in which the number of each kind of formal bond is conserved, must comply with the bond

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separation reaction (BSR) rules.30 The molecule is broken down into a set of two heavy-atom molecules containing the same component bonds. However, usual bond separation reaction rules cannot be applied to the molecules with delocalized bonds and cage skeletons because of large calculated errors of HOFs. Therefore, we design isodesmic reactions in which the numbers of all kinds of bonds keep invariable to decrease the calculation errors of HOF. Because the electronic circumstances of reactants and products are very similar in isodesmic reactions, the errors of electronic correction energies can be counteracted, and then the errors of the calculated HOF can be greatly reduced. In these designed reactions, the basic structural unit of furazan skeleton keeps invariable, and the big molecules are changed into small ones too. This approach has been proved to be reliable.31,33 The isodesmic reactions used to obtain the HOFs of difurazan derivatives at 298 K are as follows:

For the isodesmic reaction, heat of reaction ∆H298 at 298 K can be calculated from the following equation:

∆H298 ) ∆Hf,p - ∆Hf,R

(2)

where ∆Hf,R and ∆Hf,P are the HOFs of reactants and products at 298 K, respectively. As the experimental HOFs of some bridge groups are unavailable, additional calculations were carried out for the atomization reaction CaHbOcNd f aC(g) + bH(g) + cO(g) + dN(g) using the G2 theory to get an accurate value of ∆Hf for bridge groups.33 And the experimental HOF of reference compound CH4 is available.43 Therefore, the HOFs of furazan derivatives can be figured out when the heat of reaction ∆H298 is known. Now the most important task is to compute ∆H298. The ∆H298 can be calculated using the following expression:

∆H298 ) ∆E298 + ∆(PV) ) ∆E0 + ∆EZPE + ∆ET + ∆nRT

(3)

where ∆E0 is the change in total energy between the products and the reactants at 0 K; ∆EZPE is the difference between the zero-point energies (ZPE) of the products and the reactants at 0 K; ∆ET is thermal correction from 0 to 298 K. The ∆(PV) value in eq 3 is the PV work term and equals ∆nRT for the reactions of ideal gas. For the isodesmic reactions in this work, ∆n ) 0, so ∆(PV) ) 0. The detonation velocity and pressure were estimated by the Kamlet-Jacobs equations35 as

j 1/2Q1/2)1/2(1 + 1.30F) D ) 1.01(NM j 1/2Q1/2 P ) 1.558F2NM

(4) (5)

where each term in eqs 4 and 5 is defined as follows: D, the detonation velocity (km · s-1); P, the detonation pressure (GPa); j , the N, the moles of detonation gases per gram explosive; M average molecular weight of these gases; Q, the heat of detonation (J · g-1); and F, the loaded density of explosives

(g · cm-3). For known explosives, their Q and F can be measured experimentally; thus their D and P can be calculated according to eqs 4 and 5. However, for some compounds, their Q and F cannot be evaluated from experimental measures. Therefore, to estimate their D and P, we first need to calculate their Q and F. For these difurazan derivatives, the theoretical density was obtained from the molecular weight divided by the average molecular volume. The volume was defined as inside a contour of 0.001 electrons/bohr3 density that was evaluated using a Monte Carlo integration. We performed 100 single-point calculations for each optimized structure to get an average volume. Q was evaluated by the HOF difference between products and explosives according to the principle of exothermic reactions. In the Kamlet-Jacobs equations, the products are supposed to be only CO2, H2O, and N2, so released energy in the decomposition reaction reaches its maximum. On the basis of the F and Q values, the corresponding D and P values can be evaluated. The theoretical density of the molecules in this work is slight greater than practical loaded density. Therefore, according to the Kamlet-Jacobs equations, the D and P values can be regarded as their upper limits. The strength of bonding, which could be evaluated by bond dissociation energy, is fundamental to understand chemical processes.36 The energy required for bond homolysis at 298 K and 1 atm corresponds to the enthalpy of reaction A-B(g) fA · (g) + B · (g), which is the bond dissociation enthalpy of the molecule A-B by definition.37 For many organic molecules, the terms “bond dissociation energy” (BDE) and “bond dissociation enthalpy” often appear interchangeably in the literature.38 Therefore, at 0 K, the homolytic bond dissociation energy can be given in terms of eq 6

BDE0(A-B) ) E0(A · ) + E0(B · ) - E0(A-B)

(6)

The bond dissociation energy with zero-point energy (ZPE) correction can be calculated by eq 7

BDE(A-B)ZPE ) BDE0(A-B) + ∆EZPE

(7)

where ∆EZPE is the difference between the ZPEs of the products and the reactants. The calculations were performed with the Gaussian 98 package39 at the B3LYP/6-31G(d) level.40,41 The optimizations were performed without any symmetry restrictions using the default convergence criteria in the program. All of the optimized structures were characterized to be true local energy minima on the potential energy surfaces without imaginary frequencies. 3. Results and Discussion 3.1. Heats of Formation. The energy of high-nitrogen compounds is derived from their very high positive HOF rather than from the combustion of the carbon backbone or the ring/ cage strain as traditional and modern energetic polynitro compounds. Therefore, the HOF is frequently taken to be indicative of the “energy content” of a energetic high-nitrogen compound. Here we investigate the effects of different linkages and substituents on the HOFs of the bridged difurazans. The molecular frameworks of a series of bridged difurazans (molecular numbering as A1-A6, B1-B6, C1-C6, D1-D6, E1-E6, F1-F4, H1-H6, and I1-I4) are displayed in Figure 1. Table 1 lists the total energies, ZPEs, and thermal corrections for 8 reference compounds in the isodesmic reactions. In the isodesmic reactions, the experimental HOFs of many reference compounds are available, while others’ are unavailable. For

Energetic Substituted C- and N-Bridged Difurazans

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Figure 1. Molecular frameworks of bridged difurazans (molecular numbering as A1-A6, B1-B6, C1-C6, D1-D6, E1-E6, F1-F4, H1-H6, and I1-I4).

example, the experimental HOFs of reference compounds CH4 is taken from ref , but some corresponding values of bridge groups are not found. So additional calculations were carried out for the atomization reaction CaHbOcNd(g) f aC(g) + bH(g) + cO(g) + dN(g) using the G2 theory to get an accurate ∆Hf values for the bridge groups. An accurate ∆Hf value for CaHbOcNd was then obtained through eq 2 as well as the available experimental HOFs for C(g), H(g), O(g), and N(g). Table 2 summarizes the total energies, ZPEs, thermal corrections, and HOFs for the bridged difurazans. Previous studies28–30 have shown that the theoretically predicted values of HOFs were in good agreement with experiments when the appropriate reference compounds in the isodesmic reaction were chosen. An efficient way of reducing errors of HOFs is to keep

the conjugated bonds or cage skeletons unbroken. This approach has been proved to be reliable.31,33 By comparison of our calculated results with available experimental and other calculated values, the HOFs of the bridged difurazans are supposed to be credible. When the substituent is -N3 or -NO2, an increase in the HOF value of its substituted difurazans (A-N3 and A-NO2) is large compared with the unsubstituted case (A-H). For the substituent -ONO2, -NH2, or -NF2, the case is quite the contrary. When the H atoms of difurazans are replaced by -N3, its HOF value is the largest one among these derivatives. It is also seen in Table 2 that the substitution of the group -N3 extremely enhances its HOF value compared to parent difurazans (A-H). The same is true of the carbon-bridged difurazans

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TABLE 1: Calculated Total Energies (E0), Zero-Point Energies (EZPE), Thermal Corrections (ET), and Heats of Formation (HOFs) for the Reference Compounds at the B3LYP/6-31G(d) Levela compd

E0

EZPE

ET

HOFc

CH4 CH3CH3 Furazan CH3CH2CH2CH3 CH3CHdCHCH3 CH3NHNHCH3 CH3NdNCH3 CH3NdN(O)CH3

-40.5185 -79.8304 -262.0515 -158.4586 -157.2274 -190.4767 -189.2751 -264.4646

0.0452 0.0752 0.0459 0.1330 0.1085 0.1103 0.0850 0.0906

10.02 11.74 13.67 18.00 17.15 17.34 16.21 15.30

-74.4 -84.68 -125.7 -11.4 92.2

HOFb

196.2

151.8 50.6

a E0 and ZPE are in au; HOF and ET are in kJ/mol. The scaling factor for ZPE is 0.98 and the scaling for ET is 0.96.42 b The values are calculated at the G2 level from the atomization reaction. c Reference 43.

(B and C) and the nitrogen-bridged difurazans (D and H). However, for E series, the case is different. The substitutions of -N3, -NF2, or -NO2 increases the HOF value of parent difurazans (E-H), while the substituent -ONO2, or -NH2 plays opposite effect. For asymmetric substitutions, F (or I) series have larger HOF values than the corresponding unsubstituted ones E-H (or H-H). Also, we note that the symmetrically N3substituted nitrogen-bridged difurazans E-N3 (or H-N3) have the largest HOF values among the symmetrically substituted series E (or H) and the asymmetrically substituted ones F (or I). These observations indicate that the -N3 group plays a very important role in increasing the HOF values of the bridged difurazans. Figure 2 presents a comparison of the HOF values for different bridged difurazans. When the bridge group is -CHdCH-, -NH-NH-, -NdN-, or -N(O)dN-, the HOFs of the bridged difurazans are higher than those of the directly linked difurazans (A-H) with the same substituents. For the bridge group -CH2-CH2-, the case is quite the contrary. This shows that incorporation of -CH2-CH2- into difurazans is unfavorable for increasing the HOF value of the directly linked difurazans (A-H). Also, we note that the substituted difurazans withtheconjugatedbridge-CHdCH-(-NdN-or-N(O)dN-) have higher HOF values than the corresponding ones with the unconjugated bridge -CH2-CH2- (-NH-NH-). This is because the two difurazans and the conjugated bridge make a big conjugated system. The substituted difurazans linked by the azo -NdN- have highest HOF values among these derivatives with the same substituents. This indicates that the azo group is an effective bridge for increasing the HOF of the bridged difurazans. 3.2. Electronic Structure. Table 3 lists the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energies and the energy gaps (∆ELUMO-HOMO) for the substituted bridged difurazans. For A, B, C, and H series, when the -NH2, or -N3 group is attached to the ring, the HOMO energy level increases, whereas the attachment of other group such as -ONO2, -NF2, or -NO2 will make the HOMO energy level decreased. The A, B, C, D, or H series with the substituent -ONO2, -N3, -NF2, or -NO2 decrease the LUMO energy level as compared with the corresponding unsubstituted difurazans, whereas these with the -NH2 group increase the LUMO energy level. This indicates that different substituents have different effects on the HOMO and LUMO energy level. It is found from Table 3 that all the unsubstituted derivatives

(C-H, D-H, E-H, and H-H) increase the HOMO energy level as compared with the unsubstituted difurazans (A-H) except for the derivative B-H. But incorporation of the substituent into the ring alters the variation trend, and furthermore, different substituents cause different effects on the HOMO energy level of the derivatives with different bridges. This shows that the substituents interact predominately with the HOMO orbital. However, for their LUMO energy level, the case is different. Incorporation of the bridge group -CH2-CH2- or -NH-NH- into difurazans increases the LUMO energy level, while the -CHdCH-, -NdN-, or -N(O)dN- bridge group plays the contrary action. Also, note that further introduction of the substituent does not bring any effects on the sequence of the LUMO energy level. This indicates that the bridge groups interact mainly with the LUMO orbital. Some of the derivatives increase the HOMO-LUMO gaps of the unsubstituted difurazans, while other ones decrease these. However, for A or B series, incorporation of the substituent into the difurazans decreases its HOMO-LUMO gap. C(-ONO2, -NF2), D(-NH2, -N3, -NF2), E(-ONO2, -N3), F(-ONO2, -NF2), H(-NF2, -NO2), and I(-ONO2, -N3, -NF2) have higher energy gaps than the corresponding unsubstituted molecule, indicating a shift toward higher frequencies in their electronic absorption spectra. But A(-ONO2, -NH2, -N3, -NF2, -NO2), B(-ONO2, -NH2, -N3, -NF2, -NO2), C(-NH2, -N3, -NO2), D(-ONO2, -NO2), E(-NH2, -NF2, -NO2), F(-ONO2, -NH2), H(-ONO2, -NH2, -N3), and I-NH2 have lower energy gaps than the corresponding unsubstituted one, reflecting a shift toward lower frequencies in their electronic absorption spectra. This shows that the effects of the substituents on the HOMO-LUMO gap are coupled to those of the bridge groups. Among these derivatives, B-H has the highest HOMO-LUMO gap, whereas H-NH2 has the smallest one. Overall, different substituted bridged difurazans present a comparison of the energetics. In addition, the -CH2-CH2bridged difurazans have higher HOMO-LUMO gaps than other bridged ones with the same substituents. Thus, it may be inferred that the CH2-CH2-bridged difurazans have the lowest reactivity among these bridged derivatives. 3.3. Energetic Properties. Detonation velocity and detonation pressure are two important performance parameters for an energetic material. The Kamlet-Jacobs eqs 4 and 5 show that F is a key factor to influence D and P. Thus, density is one of the most important physical properties for all energetic materials. Table 4 presents the calculated F, Q, D, P, and oxygen balance (OB) of the bridged difurazans together with available experimental15,47,48,51,52 and other calculated data.49,50 As is evident in Table 4, the calculated densities and detonation properties of the bridged difurazans agree well with available experimental and other theoretical values within some deviation. Maybe, these errors come from HOF of them. This is because detonation pressures and detonation velocities are calculated by HOF of gas state, not of crystal. Although the error or limitation of the calculation method leads to the predicted D and P somewhat deviate those from experiments, these results are still reliable and meaningful. Previous studies9,54 indicated that Kamlet-Jacobs formula is proper to predict the detonation properties of energetic high-nitrogen compounds. Our calculated results here further support the conclusion. The bridged difurazans with different substituent groups have different F values, for example, the largest value and the smallest one is 2.10 and 1.50 g · cm-3, respectively. All the substituted difurazans increase the F values as compared with the corresponding unsubstituted ones except for the derivatives A-NH2,



TABLE 2: Calculated Total Energies (E0), Zero-Point Energies (EZPE), Thermal Corrections (ET), and Heats of Formation (HOFs) for the Bridged Difurazans at the B3LYP/6-31G(d) Levela HOFs compd A(-) A1 A2 A3 A4 A5 A6 B(C-C) B1 B2 B3 B4 B5 B6 C(CdC) C1 C2 C3 C4 C5 C6 D(N-N) D1 D2 D3 D4 D5 D6 E(NdN) E1 E2 E3 E4 E5 E6 F(NdN) F1 F2 F3 F4 H(N(O)dN) H1 H2 H3 H4 H5 H6 I(N(O)dN) I1 I2 I3 I4 c

E0

EZPE

ET

this work

expt

others

-522.9047 -1082.2381 -633.6276 -850.0692 -1030.2473 -931.8525

0.0723 0.0831 0.1064 0.0784 0.0701 0.0768

21.14 41.27 28.58 35.59 36.77 34.81

386.42 280.62 342.82 1038.52 348.82 421.31

422.18b

412.98b

-601.5357 -1160.8790 -712.2574 -928.7133 -1108.8940 -1010.5075

0.12960 0.1410 0.1636 0.1356 0.1274 0.1341

28.74 49.03 36.47 43.31 44.52 42.42

371.56 250.27 334.80 1031.63 316.92 383.70

-600.3093 -1159.6521 -711.0216 -927.4748 -1107.6652 -1009.2769

0.1059 0.1173 0.1400 0.1120 0.1036 0.1105

27.37 47.86 35.13 42.12 43.62 41.41

548.59 358.83 522.81 1153.84 438.85 576.56

-633.561 -1192.9090 -744.2764 -960.7307 -1140.9297 -1042.5392

0.1061 0.1180 0.1408 0.1126 0.1040 0.1114

27.59 46.48 34.92 41.81 43.32 40.57

549.46 438.79 530.36 1238.01 512.04 572.90

209c

393.44c

-632.3358 -1191.6880 -743.0725 -959.5054 -1139.6864 -1041.2891

0.0809 0.0932 0.1157 0.0875 0.0787 0.0855

26.92 45.91 33.37 40.49 42.35 40.44

658.57 567.43 595.68 1361.58 662.38 742.26

-1116.4781 -892.1767 -1000.3910 -1090.4868

0.0889 0.1002 0.0862 0.0821

43.72 37.34 40.74 41.41

679.19 688.16 1060.44 707.08

-707.5178 -1266.8564 -818.2490 -1034.6812 -1214.8666 -1116.4636

0.0863 0.0978 0.1203 0.0922 0.0840 0.0905

28.25 48.52 35.78 42.96 44.15 42.67

591.21 505.87 550.17 1294.74 587.82 674.85

-1191.6482 -967.3477 -1075.5602 -1165.6578

0.0940 0.1052 0.0913 0.0871

45.76 39.13 42.71 43.59

629.40 638.17 1010.82 657.41

153.4c

536c

477.44c

703.9d

762.85e 703.1e

444b

354.11b

646.6c

638.7c 700d

a E0 and ZPE are in au; HOF and ET are in kJ · mol-1. The scaling factor for ZPE is 0.98 and the scaling for ET is 0.96.42 b Reference 15. Reference 44. d Reference 16. e Reference 45.

E-NH2, and H-NH2. When the substituent is -ONO2, -NF2, or -NO2, an increase in the F value of its substituted difurazans is fairly large compared with the corresponding unsubstituted case. The symmetrically NF2-substituted difurazans has the largest F values among the same series. For asymmetric substitutions, F (or I) series have larger F values than the corresponding unsubstituted one E-H (or H-H). When the bridge group is -NdN-, or -N(O)dN-, the F values of the bridged difurazans are higher than those of the directly linked difurazans (A) with the same substituents. For the bridge group

-CH2-CH2-, -CHdCH-, or, -NH-NH-, the case is quite the contrary. It is also found that the substituted difurazans with the conjugated bridge -CHdCH- (-NdN- or -N(O)dN-) have higher F values than the corresponding ones with the unconjugated bridge -CH2-CH2- (-NH-NH-). In addition, the substituted -N(O)dN-bridged difurazans H (or I) have higher F values than the corresponding -NdN-bridged ones E (or F). This may be due to adding one oxygen atom, which not only allows better crystal packing but also increases oxygen balance. The substituted difurazans linked by the azoxy

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Zhang et al. TABLE 3: Calculated HOMO and LUMO Energies (au) and Energy Gaps (∆ELUMO-HOMO) of the Bridged Difurazans at the B3LYP/6-31G(d) Level compd

Figure 2. Comparison of the HOFs of the bridged difurazans influenced by different linkages and substituents.

-N(O)dN- have the highest F values among these series with the same substituents. Therefore, incorporation of the -ONO2, -NF2, or -NO2 substituent or the -NdN- or -N(O)dNbridge group into difurazans is very helpful for increasing its F value. The calculated heats of detonation in Table 4 show that the substitution of the group -ONO2, -N3, -NF2, or -NO2 increases its heat of detonation value compared to the corresponding unsubstituted difurazans, whereas for the group -NH2, the instance is opposite. Different bridge groups also play different effects on the heats of detonation for the bridged difurazans. On the whole, the -NdN- or -N(O)dN- group is an effective bridge for enhancing the heat of detonation of the bridged difurazans. Oxygen balance is another one of the most important criterion for selecting potential HEDMs. It is found from Table 4 that by and large, the higher the oxygen balance is, the larger the D and P values are, and the better the performance of the bridged difurazan is. The -ONO2 or -NO2 group is a good substituent for improving oxygen balance in designing potential HEDMs. The same is true of the bridge group -N(O)dN-. However, it is clear that overmuch oxygen is not favorable for advancing explosive performance of HEDMs. The primary reason is that the overmuch oxygen will produce O2 that take away a great deal of energy. Therefore, one had better keep the value of oxygen balance around zero in designing HEDMs. The effects of the substituents and/or bridges on the densities make the bridged difurazans have different D and P values. All the substituted derivatives increase the D and P values as compared with the unsubsituted ones except for the derivatives A-NH2, E-NH2, and H-NH2. It is observed from Table 4 that the F values of A(-ONO2, -NF2, -NO2), C-NF2, D(-ONO2, -NF2), E(-ONO2, -NF2), F(-ONO2, -NF2), H(-ONO2, -NF2, -NO2), and I(-ONO2, -NF2) are very high and above 1.9 g · cm-3. Moreover, their D and P values are very high and close to or above 9.0 km · s-1 and 40.0 GPa, respectively. The substituted difurazans linked by the -NdN- or -N(O)dNgroup have higher D and P values than other derivatives with the same substituents (A, B, C, and D series). It is also found that H-NF2, the derivative bridged by -N(O)dN- with two -NF2 groups, has the largest D and P values among these derivatives. This shows that the -ONO2, -NO2, -NF2, -NdN- or -N(O)dN- group is an effective structural unit for increasing the detonation properties of the difurazan derivatives. Figure 3 displays the calculated F, D, and P for the substituted bridged difurazans together with commonly used explosives RDX (1,3,5-trnitro-1,3,5-triazinane) and HMX (1,3,5,7-tetrani-

A(-) A1 A2 A3 A4 A5 A6 B(C-C) B1 B2 B3 B4 B5 B6 C(CdC) C1 C2 C3 C4 C5 C6 D(N-N) D1 D2 D3 D4 D5 D6 E(NdN) E1 E2 E3 E4 E5 E6 F(NdN) F1 F2 F3 F4 H(N(O)dN) H1 H2 H3 H4 H5 H6 I(N(O)dN) I1 I2 I3 I4

EHOMO

ELUMO

∆ELUMO-HOMO

-0.3074 -0.3239 -0.2484 -0.2788 -0.3190 -0.3414

-0.0881 -0.1091 -0.0763 -0.0923 -0.1119 -0.1455

0.2193 0.2148 0.1721 0.1866 0.2072 0.1959

-0.3105 -0.3235 -0.2516 -0.2761 -0.3138 -0.3305

-0.0538 -0.1058 -0.0355 -0.0723 -0.0813 -0.1308

0.2567 0.2177 0.2161 0.2038 0.2325 0.1996

-0.2660 -0.2838 -0.2417 -0.2644 -0.2921 -0.2985

-0.0983 -0.1160 -0.0889 -0.1078 -0.1230 -0.1366

0.1677 0.1678 0.1528 0.1567 0.1691 0.1619

-0.2398 -0.2810 -0.2561 -0.2666 -0.2785 -0.3011

-0.0576 -0.1052 -0.0463 -0.0790 -0.0882 -0.1402

0.1822 0.1758 0.2098 0.1876 0.1903 0.1609

-0.2808 -0.2912 -0.2566 -0.2893 -0.2653 -0.3135

-0.1399 -0.1399 -0.1159 -0.1321 -0.1373 -0.1787

0.1410 0.1513 0.1407 0.1572 0.1280 0.1348

-0.3044 -0.2731 -0.2936 -0.3057

-0.1593 -0.1453 -0.1580 -0.1595

0.1450 0.1278 0.1356 0.1463

-0.2871 -0.3020 -0.2493 -0.2716 -0.3031 -0.3191

-0.1320 -0.1474 -0.1230 -0.1370 -0.1477 -0.1533

0.1550 0.1546 0.1263 0.1347 0.1554 0.1659

-0.3163 -0.2809 -0.3034 -0.3177

-0.1459 -0.1381 -0.1457 -0.1450

0.1705 0.1428 0.1577 0.1727

tro-1,3,5,7-tetrazocane). It is found that with the variation of the molecular numbering, the evolution pattern of F is very similar to that of D and P for the bridged difurazans. This shows that the detonation properties of an explosive are predominated by its density. Some of the difurazan derivatives have higher F but do lower D and P than RDX or HMX. This is because their Q lead F to have less influence on D and P. Compared with RDX, the derivatives A(-ONO2, -NF2, -NO2), D(-ONO2, -NF2, -NO2), E(-ONO2, -NF2, -NO2), F(-ONO2, -NF2), H(-ONO2, -NF2, -NO2), and I(-ONO2, -N3, -NF2,) have higher D and P than RDX. But only A(-ONO2, -NF2), D(-ONO2, -NF2), E(-ONO2, -NF2), F-NF2, H(-NF2, -NO2), and I(-ONO2, -NF2) have good detonation performance (D and P) over HMX, one of the most widely used



TABLE 4: Predicted Densities (G), Heats of Detonation (Q), Detonation Velocities (D), Detonation Pressures (P), and Oxygen Balance (OB) for the Bridged Difurazans at the B3LYP/6-31G(d) Levela compd A(-) A1 A2 A3 A4 A5 A6 B(C-C) B1 B2 B3 B4 B5 B6 C(CdC) C1 C2 C3 C4 C5 C6 D(N-N) D1 D2 D3 D4 D5 D6 E(NdN) E1 E2 E3 E4 E5 E6 F(NdN) F1 F2 F3 F4 H(N(O)dN) H1 H2 H3 H4 H5 H6 I(N(O)dN) I1 I2 I3 I4 RDX HMX

F (g · cm-3)

Q (J · g)

OB (%)j

1.66 1.96 1.65 1.75 2.08 1.92(1.85)b

1428.84 1704.88 1175.80 1555.71 1730.91 1679.14

-81.2 0 -76.2 -43.6 -40.0 -14.0

7.14 9.32 7.11 8.08 9.71 8.98

21.46 40.51 21.24 28.45 45.43 37.13

1.50 1.78 1.53 1.61 1.88 1.79

1231.34 1588.77 998.04 1460.32 1602.03 1544.55

-125.3 -33.3 -114.3 -77.4 -71.6 -50.0

6.37 8.35 6.58 7.27 8.58 8.14

16.04 30.74 17.36 21.87 33.51 29.28

1.52 1.83 1.56 1.68 1.94 1.80

1504.35 1652.92 1239.95 1547.13 1683.12 1695.76

-117.1 -28.0 -107.2 -71.5 -66.2 -44.1

6.42 8.53 6.79 7.51 8.83 8.29

16.44 32.63 18.70 23.94 36.20 30.53

1.61 1.92 1.64 (1.63)c 1.77 2.02 1.87(1.792)c

1469.77 1696.02 1224.02 1602.84 1722.97 1666.08

-76.2 -5.5 -72.7 -44.8 -41.5 -18.6

7.39 9.32 7.56 8.39 9.65 8.96

22.61 40.05 23.95 30.92 44.11 36.41

1.70 1.93 1.66(1.70)d 1.75 2.05 1.88(1.73)b

1579.66 1777.13 1316.17 1691.40 1829.70 1795.12

-67.5 0.0 -65.3 -38.7 -35.8 -12.5

7.72 9.41 7.50 (7.42)d 8.37 9.84 9.08[9.14]f

25.55 40.92 23.74(26.2)d 30.59 46.33 37.47[37.09]f

1.90 1.78 1.82 1.97

1806.99 1607.72 1752.16 1423.93

-5.9 -35.4 -25.4 -24.4

9.27 8.41 8.76 9.50

39.40 31.12 34.33 42.27

1.75 1.94 1.72(1.764)g 1.80 2.10 1.93[1.94]f

1610.71 1635.20 1387.33 1706.51 1829.45 1803.17

-52.8 5.3 -52.8 -30.3 -28.2 -5.9

8.07 9.26 7.91[8.06]f 8.65 10.08 9.35[9.44]f

28.44 39.75 27.03[28.1]f 33.21 49.23 40.31[41.30]f

1.95 1.85(1.86)h 1.88 1.99 1.78i 1.88i

1828.56 1016.12 1778.77 1839.01 1597.39 1633.88

0 -26.4 -17.9 -17.3 -21.6 -21.6

9.53 8.81[9.4]e 9.09 9.66 8.88i 9.28i

42.22 34.95[44.1]e 37.61 43.84 34.75i 39.21i

D (km · s-1)

P (GPa)

a

The data in square brackets are the calculated values and those in parentheses are experimental values. b Reference 15. c Reference 47. Reference 48. e Reference 49. f Reference 50. g Reference 51. h Reference 52. i Reference 25. j Oxygen balance (%) for CaHbOcNd: 1600 × (c - 2a-b/2)/Mw; Mw ) molecular weight of the titled compounds.

d

energetic ingredient in various high performance explosives and propellant formulations. Although A-NO2,15 E-NH2,48 E-NO2,15 H-NH2,51 and I-NH252 have been successfully synthesized, some detonation properties are still lack. In addition, the syntheses of other energetic compounds have not been reported yet. Thus, further investigations are still needed. 3.4. Thermal Stability. Bond dissociation energy (BDE) provides useful information for understanding the stability of energetic compounds. Generally, the smaller the energy for

breaking a bond is, the weaker the bond is, and the easier the bond becomes a trigger bond; that is to say, the corresponding compound is more unstable, and its sensitivity is larger. To evaluate the stability of the bridged difurazans by bond dissociation energies (BDEs), we investigated the BDE values for several relatively weak bonds at the B3LYP/6-31G(d) and B3LYP/6-311+G (2df,p) levels. The BDEs of the weakest bonds for the bridged difurazans along with those of RDX and HMX are listed in Table 5, while these of other relatively weak bonds

610


Zhang et al.

Figure 3. Density, detonation velocity, and detonation pressure of the bridged difurazans.

TABLE 5: Bond Dissociation Energies (BDE, kJ · mol-1) and Bond Order (BO) of the Weakest Bonds for the Bridged Difurazans at the B3LYP/6-31G(d) and B3LYP/ 6-311+G(2df,p) Levels (N-O)ring B3LYP/6-31G(d) compd A1 A2 A3 A4 A5 A6 B1 B2 B3 B4 B5 B6 C1 C2 C3 C4 C5 C6 D1 D2 D3 D4 D5 D6 E1 E2 E3 E4 E5 E6 F1 F2 F3 F4 H1 H2 H3 H4 H5 H6 I1 I2 I3 I4

BDE 204.62 196.76 215.26 185.34 178.92 155.52 236.14 162.33 169.12 175.95 158.57 148.26 213.58 144.76 178.26 158.44 169.72 155.75 223.16 196.28 185.15 197.24 143.08 180.02 211.59 185.99 209.35 185.08 165.49 159.08 144.04 157.80 155.50 153.29 198.73 180.96 188.53 177.72 171.73 154.57 123.45 138.00 135.41 119.06

BO 0.1282 0.1037 0.1145 0.1094 0.0963 0.0992 0.1307 0.1092 0.1181 0.1165 0.1037 0.1077 0.1305 0.1100 0.1171 0.1071 0.1123 0.1034 0.1395 0.1165 0.1208 0.1205 0.1097 0.1107 0.1181 0.0979 0.1112 0.1078 0.0958 0.0999 0.1001 0.0997 0.1008 0.1002 0.1146 0.0794 0.0924 0.0830 0.0763 0.0702 0.0928 0.1058 0.1011 0.1043

B3LYP/6-311+G(2df,p) BDE 201.97 195.62 211.39 189.51 180.82 168.51 222.19 165.17 172.88 176.49 157.60 148.95 214.52 147.94 176.88 156.84 166.52 156.71 221.59 196.98 187.72 198.79 146.76 178.59 210.11 182.72 206.17 187.88 166.84 160.07 146.97 160.73 153.57 158.50 197.62 184.46 190.76 177.21 169.99 156.42 126.58 136.94 140.02 121.66

BO 0.1303 0.1033 0.1150 0.1132 0.0988 0.0965 0.1326 0.0959 0.1121 0.1039 0.1109 0.1209 0.1362 0.1049 0.1216 0.1133 0.1192 0.1116 0.1421 0.1245 0.1297 0.1331 0.1278 0.1228 0.1295 0.1032 0.1128 0.1046 0.0853 0.0965 0.0989 0.0988 0.1005 0.1030 0.1206 0.0713 0.0836 0.0826 0.0764 0.0704 0.0932 0.1064 0.1017 0.1051

are presented in Table S of the Supporting Information for brevity. The BDEs for all the N-O bonds in two parent ring for each molecule were calculated. Only the smallest BDE value of N-O bond among them is listed in Table 5. The results show that the BDE values of different bonds at the two levels present the same variation trend, and furthermore the differences between them are very small. According to the calculated BDE values, it is found that the N-O bonds in the rings have smaller BDE values than other bonds for the difurazan derivatives, but different N-O bond has slightly different BDE due to incorporating different linkage groups and substituents into the furazan rings. The calculated BDE can be used to measure the relative order of thermal stability for energetic materials.42,55 Therefore, it can be inferred that the trigger linkage in the bridged difurazans appears to be N-O cleavage, while other bonds are relatively strong and resistant to rupture. All the substituted difurazans have smaller BDE values than the corresponding unsubstituted ones except for the derivative A-NH2. Different bridge groups also play different effects on BDE for the bridged difurazans. Compared with the directly linked difurazans, some of the bridged ones have higher BDE, while the others do smaller BDE due to the substitution of different substituents. None of the bridge groups produce dominant influence on BDE. This shows that the effects of the bridge groups on BDE are combined with those of the substituents. On the whole, the -NH-NH-, -NdN- or -N(O)dN- group is an effective bridge for enhancing BDE of the bridged difurazans. Compared with an important modern explosives RDX and HMX, most of the bridged difurazans have higher BDE for the weakest bond. This indicates that most of them have high thermal stability, in agreement with previous experimental reports.1,6 Bond order is a measure of the overall bond strength between two atoms. A high value of the bond order indicates a covalent bond, while a low value shows an ionic nature. Table 5 also presents the bond orders of the weakest bonds for the bridged difurazans, while these of other weak bonds are also presented in Table S of the Supporting Information. It is found that the bond orders of the N-O bonds in the rings are much smaller than those of the C-R (R1/R2) bonds and the bonds in the bridges for all the derivatives. This indicates that the N-O bond in the ring is the weakest one and the ring cleavage is possible to happen in thermal decomposition. Also, note that all the substituted difurazans have smaller bond orders of the N-O bonds than the corresponding unsubtituted ones. The same is true of the C-R (R1/R2) bonds and the bonds in the bridges. This shows that the substitution decreases the strength of these relatively weak bonds of the corresponding unsubsituted difurazans. For the weakest bond N-O in the ring, incorporation of the bridge group -CH2-CH2-, -CHdCH-, or -NH-NHinto the directly linked difurazans slightly increases their bond orders, while for the -NdN-, or -N(O)dN- bridge group, the case is quite the contrary. Overall, the effects of different bridges on the bond orders are very small. Additionally, the NdN-bridged difurazans (E) have higher bond orders than the corresponding NdN(O)-bridged ones (H). This is mainly since the former with symmetric structures can delocalize the π-electron cloud density of the system and the latter with asymmetric structures are unfavorable for the electronic delocalization. It is interesting to note that the N-O bond in the ring of A-ONO2 has higher BDE than that of A-N3, whereas the former has smaller bond order than the latter. The same is true of A-NF2 and A-NO2. This indicates that the variation trend


Figure 4. Average dissociation energies of the weakest bond for the bridged difurazans at the B3LYP/6-31G(d) and 6-311+G (2df,p) levels.

of BDE is inconsistent with that of the bond order for the N-O bond in the ring of A series under the influence of different subsituents. Similar situation is also found to be in other series. The initial step should be via ring cleavage in thermal decompositions. Therefore, to judge the thermal stability of the bridged difurazans is not by the bond order simply, but it is necessary to depend on the BDE. As is evident in Table 5, the E (H) derivatives have higher BDE than F (I). By analyzing the structure of the compounds, it is easy to find that the difurazan derivatives E or H have symmetric structures, while the F or I are asymmetric. This symmetry can delocalize the π electron cloud density of the system and so make the BDE of the compound increased. This shows that the symmetric substitution of the substituent could strengthen the thermal stability. As is well-known, a good nitrogen-rich HEDM candidate not only has excellent detonation properties but also could exist stably. Figure 4 presents average bond dissociation energies of the weakest bonds for the bridged furazans together at the two levels with RDX and HMX. It is found that most of the substituted furazans have higher BDE than RDX53 except for B-NO2, C-ONO2, D-NF2, F-NF2, and I(-ONO2, -NH2, -N3, -NF2). But only A(-H, -ONO2, -NH2, -N3, -NF2), B(-H, -NH2, -N3), C(-H, -NH2, -NF2), D(-H, -ONO2, -NH2, -N3, -NO2), E(-H, -ONO2, -NH2, -N3), and H(-H, -ONO2, -NH2, -N3) have higher BDE than HMX. On the basis of the BDE for the initial steps in the thermal decompositions, it may be inferred that A(-H, -ONO2, -NH2, -N3, -NF2), B(-H, -NH2, -N3), C(-H, -NH2, -NF2), D(-H, -ONO2, -NH2, -N3, -NO2), E(-H, -ONO2, -NH2, -N3), and H(-H, -ONO2, -NH2, -N3) have good thermal stability over HMX and are more insensitive to thermal and impact. On the above suggestions, it may be concluded that only A-ONO2, A-NF2, D-ONO2, E-ONO2, and H-NF2 have good detonation performance (D and P) and thermal stability (BDE) over RDX and HMX. Therefore, A-ONO2, A-NF2, D-ONO2, E-ONO2, and H-NF2 may be considered as the potential candidates of HEDMs with less sensitivity and higher performance. 4. Conclusions In this work, we have studied the heats of formation (HOFs), electronic structure, energetic properties, and thermal stability for a series of bridged difurazan derivatives with different linkages and substituent groups by using the DFT-B3LYP method. The results show that the -N3 group and azo bridge (-NdN-) play a very important role in increasing the HOF values of the difurazan derivatives. The substituents interact predominately with the HOMO orbital, and the bridge groups

J. Phys. Chem. A, Vol. 114, No. 1, 2010 611 interact mainly with the LUMO orbital. The effects of the substituents on the HOMO-LUMO gap are combined with those of the bridge groups. The calculated detonation velocities and detonation pressures indicate that the -ONO2, -NO2, -NF2, -NdN-, or -N(O)dNgroup is an effective structural unit for enhancing the detonation performance for the derivatives. An analysis of the bond dissociation energies for several relatively weak bonds suggests that the N-O bond in the ring is the weakest one and the ring cleavage is possible to happen in thermal decomposition. Incorporation of the substituents into the difurazans decrease the BDE values of parent ones except for the derivative A-NH2. On the whole, the -NH-NH-, -NdN-, or -N(O)dNgroup is an effective bridge for enhancing the thermal stability of the derivatives. Considered the detonation performance and thermal stability, A-ONO2, A-NF2, D-ONO2, E-ONO2, and H-NF2 may be considered as the potential candidates of HEDMs with less sensitivity and higher performance. These results provide basic information for the molecular design of novel HEDMs. Acknowledgment. This work was supported by the NSAF Foundation of National Natural Science Foundation of China and China Academy of Engineering Physics (Grant 10876013), the Specialized Research Fund for the Doctoral Program of Higher Education (200802881043), and the Project-sponsored by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry. Supporting Information Available: Bond dissociation energies and bond orders of several relatively weak bonds for the bridged difurazans at the B3LYP/6-31G(d) and B3LYP/6311+G(2df,p) levels. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Benson, F. R. The High Nitrogen Compounds; Wiley-Interscience: New York, NY, 1984. (2) Chavez, D. E.; Hiskey, M. A.; Gilardi, R. D. Angew. Chem., Int. Ed. 2000, 39, 1791. (3) Fried, L. E.; Manaa, M. R.; Pagoria, P. F.; Simpson, R. L. Annu. ReV. Mater. Res. 2001, 31, 291. (4) Kerth, J.; Lobbecke, S. Propellants, Explos., Pyrotech. 2002, 27, 111. (5) Neutz, J.; Grosshardt, O.; Schaufele, S.; Schuppler, H.; Schweikert, W. Propellants, Explos., Pyrotech. 2003, 28, 181. (6) Huynh, M. H. V.; Hiskey, M. A.; Hartline, E. L.; Montoya, D. P.; Gilardi, R. D. Angew. Chem., Int. Ed. 2004, 43, 4924. (7) Huynh, M. H. V.; Hiskey, M. A.; Chavez, D. E.; Naud, D. L.; Gilardi, R. D. J. Am. Chem. Soc. 2005, 127, 12537. (8) Schmidt, M. W.; Gordon, M. S.; Boatz, J. A. J. Phys. Chem. A 2005, 109, 7285. (9) Singh, R. P.; Verma, R. D.; Meshri, D. T.; Shreeve, J. M. Angew. Chem., Int. Ed. 2006, 45, 3584. (10) Jones, C. B.; Haiges, R.; Schroer, T.; Christe, K. O. Angew. Chem., Int. Ed. 2006, 45, 4981. (11) Smiglak, M.; Metlen, A.; Rogers, R. D. Acc. Chem. Res. 2007, 40, 1182. (12) Hiskey, M.; Goldman, N. Energ. Mater. 1998, 16, 119. (13) Zelenin, A. K.; Trudell, M. L. J. Heterocycl. Chem. 1998, 35, 151. (14) Sheremetev, A. B.; Aleksandrova, N. S. Russ. Chem. Bull. 2005, 54, 1715. (15) Sheremetev, A. B.; Kulagina, V. O.; Aleksandrova, N. S.; Dmitriev, D. E.; Strelenko, Y. A.; Lebedev, V. P.; Matyushin, Y. N. Propellants, Explos., Pyrotech. 1998, 23, 142. (16) Shaposhnikov, S. D.; Korobov, N. V.; Sergievskii, A. V.; Pirogov, S. V.; Mel’nikova, S. F.; Tselinskii, I. V. Russ. J. Org. Chem. 2002, 38, 1351. (17) Averkiev, B. B.; Timofeeva, T. V.; Sheremetev, A. B.; Shatunova, E. V.; Antipin, M. Y. Acta Crystallogr., Sect. C 2004, 60, o520. (18) Sergievskii, A. V.; Romanova, T. V.; Mel’nikova, S. F.; Yselinskii, I. V. Russ. J. Org. Chem. 2005, 41, 261.

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