Scientific paper Desensitization of TNAZ via Molecular Structure Modification and Explosive Properties - A DFT Study Lemi Türker* and Serhat Varis Middle East Technical University, Department of Chemistry, 06800, Ankara, Turkey * Corresponding author: E-mail: lturker@metu.edu.tr; Tel: +90 312 2103244, Fax: +90 312 2103200 Received: 07-12-2011 Abstract TNAZ (1,3,3-trinitroazetidine) is a highly nitrated four membered nitrogen heterocyclic ring with greater performance when compared to melt castable explosive, TNT (trinitrotoluene). Desensitization of explosives is a significant area in military use. One current method is to use additives and coatings for explosives, as in the case of RDX. Another tactic would be to attempt small molecular level chemical changes in the explosive that bring the expected decrease in sensitivity without noteworthy loss in performance. TNAZ has three nitro groups. We thought that conversion of the nitro groups to nitroso and amine groups may decrease the sensitivity. We have correlated the bond dissociation energies with sensitivity and h50 values obtained from Keshavarz relations. We have also investigated chemical hardness and Mulli-ken electronegativities employing the frontier molecular orbitals. Furthermore, the explosive properties, i.e. detonation velocity (D), and detonation pressure (P) have been questioned by using both Kamlet-Jacobs equations and Keshavarz relations. Detonation products and power index values have also been calculated. We have proved that molecular modification is an operative method in desensitization of TNAZ. Keywords: TNAZ, Desensitization, Structural Molecular Modification, Kamlet-Jacobs equation 1. Introduction Highly nitrated small ring heterocycles and car-bocycles are interesting energetic materials due to their increased performance originating from the additional energy release (manifested as a higher heat of formation) upon opening of the strained ring system during decomposition. Nowadays, the most widely studied energetic small-ring compound is 1, 3, 3-trinitroazetidine, TNAZ.1 It is a highly nitrated four membered nitrogen heterocyclic ring with improved performance in comparison to conventional melt castable explosive trinitrotoluene. The additional contribution of energy is expected from the strained ring system.2-7 There are more than 16 methods reported for the synthesis of 1, 3, 3-trinitroazetidine.8 TNAZ, a high performance, melt castable explosive, has been proposed as potential replacement for TNT9. The low melting point of TNAZ (101 oC) enables processing of formulations on modified production lines. Its performance is approximately 30% greater than TNT. It shows excellent thermal stability (>180 oC).10 TNAZ has many added advantages over known explosives. It is a highly energetic material, more powerful than RDX, and is less vulnerable than most other nitrami-nes.1112 Unlike HMX, TNAZ is soluble in molten TNT, and is compatible with aluminum, steel, brass and glass.13-15 Desensitization of explosives is of great value in reducing their sensitivity in military use. One approach that is being tried toward these objectives is to use additives and coatings for explosives in which surfaces may play an important role. Many the examples exist in the literature, especially on RDX.16 Another approach would be to attempt some molecular level chemical changes in the explosive that bring the expected decrease in sensitivity without significant loss in power. TNAZ has three NO2 groups. We thought that on converting the -NO2 groups to -NO or -NH2 groups (Figure 1), one might decrease the sensitivity as well as brisance values. Furthermore, an understanding of the trend in energetic properties in going from TNAZ to azetidine derivatives might reveal factors which can be used in altering the sensitivity of explosives, in general, via structural modification. Desensitization makes explosives much safer compared to their parents by preventing some accidental explosions triggered by various factors such as thermal and/or mechanical shock, static electric discharging, etc. In the present study, some theoretical studies have been performed for TNAZ itself and eleven different aze-tidine derivatives. 2. Theoretical Methods The preliminary geometry optimizations resulting in energy minima were completed employing MM2 followed by semi-empirical PM3 self-consistent fields molecular orbital (SCF-MO) methods17 at the restricted level.18,19 Afterwards, geometry optimizations were done within the framework of Density Functional Theory (DFT, Figure 1. The Structures of TNAZ (1) and some azetidine derivati- B3LYP)20 21 at the restricted level22 of 6-31G(d,p) basis set. The exchange term of B3LYP contains hybrid Har-tree-Fock and local spin density (LSD) exchange functions with Becke's gradient correlation to LSD exchange.21,22 The correlation term of B3LYP consists of Vosko, Wilk, Nusair (VWN3) local correlation functional23 and Lee, Yang, Parr (LYP) correlation correction functional.24 Vibrational analyses and the calculation of total electronic energies were performed using B3LYP/ 6-31G(d,p) type calculations for closed-shell systems. The frontier molecular orbital energies were obtained by HF/6-31G(d,p)//B3LYP/6-31G(d,p) method. The normal mode analysis for each compound yielded no imaginary frequencies which indicates each compound had at least a local minimum on the potential energy surface. The total electronic energies were corrected for zero point vibratio-nal energies (ZPE). Gas phase heat of formations of all the molecules were calculated by a semi-empirical approach (PM3) over DFT (B3LYP/6-31G(d,p)) optimized geometries. Additionally the geometry optimizations and the single point calculations of all the structures were performed at UB3LYP/6-31G(d,p) theoretical level for bond dissociation energy (BDE) calculations. Note that in bond dissociation process open-shell systems are generated by the elimination of R radical via homolytic bond dissociation (radical dissociation process). The basis set superposition error (BSSE) analysis for bond dissociations were carried out with the counterpoise method, introduced by Boys and Bernardi25, at the same level of theory. All the computations, except for BSSE, were performed using Spartan 06 software package.26 BSSE analyses were performed at the same theoretical levels (UB3LYP/6-31G(d,p)) by Gaussian 03 software package. The normal mode analysis for each fragment resulted in no imaginary frequencies. 3. Results and Discussion 3. 1. The Geometries All the structures presently considered have been thought to be the potential candidates of explosives (Figure 1). The geometry optimizations of the structures in Figure 1 were done at the B3LYP/6-31G(d,p) level. The bond lengths for the geometry optimized structures are presented in Table 1. The numbering in Table 1 is consistent with the numbering manner in Figure 2. The corresponding experimental X-ray diffraction values of TNAZ27 are also shown in Table 1. The compatibility of the experimental and theoretical values of the bond lengths for TNAZ and the absence of imaginary frequencies in the potential energy diagrams are indications of the successful geometry optimization of the molecules. This compatibility also guarantees that bond lengths of other azetidine derivatives are close to the real values. Note that there are no experimental data for the azetidine derivatives to the best of our knowledge. Figure 2. The numbering manner of TNAZ and azetidine derivati- 5 different isomer groups on the basis of substituent groups. Note that 2, 3a, 3b (having 2 nitro and 1 nitroso groups); 4a, 4b, 5 (having 1 nitro and 2 nitroso groups); 6, 7a, 7b (2 nitro and 1 amino bearing isomeric group); 8, 9 (having 1 nitro and 2 amino groups); and 10a, 10b, 11a, 11b, 12a, 12b (possessing 1 nitro, 1 amino and 1 nitroso group) are isomers. It can be inferred from Table 2 that 2, 5, 7b, 8 and 11a seem to be the most stable in their corresponding isomer groups. Since total electronic energies of 3a, 4a, 10a, 11a, 7b and 12b are less than 3b, 4b, 10b, 11b, 7a and 12a (see Table 2). We continued the calculations with these less energetic molecules. On the whole, a comparison between the experimental and theoretical bond lengths shows that the calculated results are slightly larger than the experimental values. For example, the observed crystal structure of TNAZ has shorter N-NO2 bonds by approximately 0.04 Á than the calculated values, and the experimental C-NO2 bonds are shorter than the calculated results by about 0.02 Á. These minor inconsistencies are mainly due to the solid-state effect, i.e., intermolecular interactions. Such interactions are not represented in the DFT calculations.28 3. 2. Relative Total Energies In Table 2, the corrected absolute and relative total energies of the geometry optimized compounds calculated at the theoretical level of B3LYP/6-31G(d,p) are shown. When Table 2 is considered, it is obvious that compounds 3a, 4a, 7b, 11a and 12b are more stable than their stereoisomers 3b, 4b, 7a, 11b and 12a. The structures 10a and 10b are equal in energy. (See Figure-1 for structures). It is essential to compare the energies of the isome-ric structures in the evaluation of the stabilities. There are Table 2. The calculated (and corrected) absolute and relative total energies of TNAZ and azetidine derivatives at (DFT) B3LYP/ 6-31G(d,p) theoretical level. Compound Etotalkj/m°l Erel TNAZ (1) —2G65237 G 2 —1867847 19739G 3a -18678G1 197436 3b -1867799 197438 7b -167368G 391557 7a -1673669 391568 6 -167357G 391667 5 -167G411 394826 4a -167G4G9 394828 4b -167G351 394886 11a -1476294 588943 11b -1476257 58898G 10a -1476226 589G11 10b -1476226 589G11 12b -1476131 5891G6 12a -1476128 5891G9 8 -1282G65 783172 9 -1282GG3 783234 Table 1. The bond lengths (A) of the geometry optimized TNAZ and azetidine derivatives calculated at the theoretical level of (DFT) B3LYP/6-31G(d.p) -o— Bond Lengths in (A) TNAZa i 2 3a 4a 5 6 7b s 9 iOa iia Hb Cl -Ni 1.5G1 1.523 1.524 1.538 1.523 1.5G7 1.519 1.547 1.447 1.573 1.529 1.568 1.5G8 Nl Xla 1.21G 1.224 1.224 1.198 1.197 1.2G5 1.224 1.227 1.G19 1.226 1.2G7 1.226 1.2G1 Nl Xlb 1.212 1.219 1.219 - - - 1.221 1.227 1.G19 1.228 - 1.225 - Cl -N3 1.512 1.513 1.513 1.497 1.492 1.5G9 1.517 1.421 1.458 1.412 1.424 1.41G 1.5GG N- -x3a 1.212 1.223 1.223 1.226 1.227 1.2G4 1.223 1.G16 1.G19 1.G16 1.G18 1.G16 1.227 N- "X3b 1.212 1.222 1.222 1.225 1.226 - 1.224 1.G16 1.G19 1.G16 1.G18 1.G16 1.227 Ni -N4 1.356 1.397 1.347 1.396 1.343 1.394 1.464 1.389 1.381 1.468 1.385 1.337 1.464 N4 X4a 1.221 1.225 1.221 1.225 1.223 1.228 1.G23 1.227 1.229 1.G24 1.228 1.226 1.G23 N4 X4b 1.224 1.225 - 1.226 - 1.225 1.G23 1.227 1.23G 1.G23 1.228 - 1.G23 Ci -Ci 1.538 1.543 1.545 1.532 1.548 1.566 1.533 1.547 1.561 1.544 1.559 1.559 1.538 C3 -Cl 1.534 1.542 1.545 1.551 1.547 1.534 1.533 1.545 1.572 1.544 1.561 1.556 1.539 Ci -Ni 1.472 1.481 1.475 1.483 1.474 1.475 1.487 1.479 1.477 1.486 1.474 1.469 1.484 C3 -Ni 1.473 1.481 1.477 1.478 1.477 1.482 1.487 1.48G 1.475 1.487 1.474 1.472 1.486 a Experimental values at 298 K reported in ref.27 All molecules possess Cj point group. Only the most stable isomers are included. 3. 3. Bond Dissociation Energies (BDE) In the present study, in order to compare the C-NO2 and N-NO2 bond strengths of the compounds, homolytic bond dissociation energy (BDE) calculations for the removal of nitrogen dioxide moiety from the structures were performed at UB3LYP/6-31G(d,p) level of theory. The expressions for the homolysis of R-NO2 bond and for calculating its homolytic BDE are shown as follows: R-NO2(g) ^ R(g) + NO2(g) (1) BDE(R-NO2) = [Er + ENO2] - E(R-NO2) (2) where R-NO2 stands for the neutral molecule and R. and NO2. for the corresponding product radicals after the bond dissociation; BDE(R-NO2) is the bond dissociation energy of the bond R-NO2; E(R-NO2), ER, and ENO2 are the zero-point energy corrected total energies of the parent compound and the corresponding radicals, respectively.29-31 Furthermore, the basis set superposition error (BSSE) analyses were carried out. The sensitivity behavior of an energetic material under different heat, impact, friction conditions may vary. In the present study, the "sensitivity" term denotes the "impact sensitivity" of a considered energetic material. Impact sensitivities of energetic compounds can be determined experimentally by physical tests, especially drop height test. Moreover, there are theoretical approaches for the computational determination of impact sensitivity. Murray et al.32 have indicated that there is a relationship between the BDEs of the N-NO2 and C-NO2 trigger linkages and the electrostatic potentials on the molecular surfaces of some energetic molecules. There are various valuable studies in the literature29'33-36 on the homolytic BDE of the nitro compounds such as nitroaromatic and nitramine molecules, which have revealed that there is a parallel correlation between the BDE for the weakest R-NO2 bond scission in the molecule and its sensitivity. The usual trend is that the larger the homolytic BDE value for scission of R-NO2 or C-NO2 bonds are, the lower the sensitivity is. Keshavarz et al has suggested valuable empirical methods for prediction of impact sensitivity of explosives.37-41 Among these methods, we have chosen ref42 for the impact sensitivity prediction of TNAZ and other molecules. h50 (impact drop height at which there is 50% probability (cm)) values have been associated with impact sensitivity. The higher the h50 value, the less sensitive the explosive. For a CaHbNcOd type polynitro aliphatic explosive, h50 is given as log h50 = (81.40a+16.11b-19.08c + 1.089d)/molecular weight (3) Desensitization of explosives is a hot topic in military use. Our approach in the current study is to attempt small structural changes in the explosive that bring the expected decrease in sensitivity without significant loss in power. TNAZ has three -NO2 groups. We thought that on converting the NO2 groups to -NO or -NH2 groups, one might decrease the sensitivity. To visualize the effect, we attributed the lowest sensitivity to the highest N-NO2 and C-NO2 BDEs. Furthermore, an understanding of the trend of energetic properties in going from TNAZ to azetidine derivatives might reveal the factors which can be used in altering the sensitivity of explosives, in general, via structural modification. Table 3 indicates BDE values. The consistency of our BDE values and the literature data Table 3. The homolytic bond dissociation energies (BDE) of C-NO2 and N-NO2 bonds of TNAZ and azetidine derivatives calculated at (DFT) UB3LYP/6-31G(d.p) theoretical level and h50 values calculated according to Keshavarz relations42 C(2) N(2)02 BDE (kJ/mol) C(2)-N(3)02 N(i)-N(4)02 Keshavarz h50 (cm) TNAZ (1) 165.23 (167)* 165.23 160.22 (162.8)* 18 2 163.85 163.81 - 22 3a - 62.29 163.1 4a 62.85 - - 30 5 - - 167.02 6 166.48 166.48 - 46 7b 186.1 - 155.82 8 - - 181.36 184 9 211.82 - - 10a - - 173.14 68 11a 198.31 - - 12b 231.65 * Data in parenthesis are the literature values taken from ref. for BDE of C-NO2 bond of TNAZ and ref.44 for BDE of N-NO2 bond of TNAZ. Numbers in parenthesis below the element symbols indicate the positions. Only the most stable isomers are considered. (available for some of the compounds)43'44 increases the reliability of the method employed in the present article. We have designated the smallest BDE of the molecules and compared them with those of other molecules and considered the h50 values obtained by Keshavarz relations. When the nitro (NO2) group on atom of TNAZ is replaced with nitroso (NO) group (compound 2), the difference between the smallest BDEs becomes 3.59 kJ/mol. This extra energy resulted in desensitization of TNAZ. This desensitization is obvious from the h50 values. The value increases from 18 cm to 22 cm. However, the conversion of nitro (NO2) group on C2 atom of TNAZ in the same manner (compound 3a), drops the BDE dramatically to 62.29 kJ/mol. The molecule becomes more sensitive. We thought that this drop is due to the instability of isomer (compound 3a) when compared with the isomers in its group (2 nitro and 1 nitroso groups having isomer group). When both nitro groups on C2 of TNAZ are replaced with nitroso groups (compound 5), the difference between the smallest BDEs becomes 6.80 kJ/mol. Also, the increase of h50 value from 18 to 30 cm supports the idea of de-sensitization. However, conversion of TNAZ into compound 4a results in sensitization of TNAZ. This is again due to the instability of compound 4a in its isomer group (1 nitro and 2 nitroso groups bearing isomer group). Conversion of the nitro group on the N1 of TNAZ into amino group (NH2) group (compound 6) results in a difference of 6.26 kJ/mol between the smallest BDEs. Also, this desensitization is clear from the increase of h50 values from 18 cm to 46 cm. Conversion of nitro group on C4 atom into amino group (compound 7b) does not decrease the BDE dramatically. This conversion is not useful for desensitization. Alteration of both nitro groups on C2 with amino groups (compound 8) and conversion of one of the nitro group on C2 and other nitro group on N1 with amino groups increases BDE tremendously. Thus, this type molecular structural modification seems to be beneficial for desensitization purpose. Similarly, the increase of h50 value from 18 to 184 supports desensitization phenomena. Stereochemically variable introduction of one nitroso and one amino groups into TNAZ accomplishes compounds 10a, 11a and 12b (each one having one nitro, one nitroso and one amino groups). All the conversions lead to a remarkable rise in BDEs, accordingly an effective decrease in sensitivity is expected theoretically. Such type of variation of functional groups of TNAZ is very advantageous for depressing sensitivity as seen from the increase of h50 values from 18 cm to 68. In conclusion, introduction of an amino group into TNAZ desensitizes more as compared to the introduction of nitroso group. Additionally, replacement of two of the nitro groups with nitroso groups produces the same effect with the replacement of one nitro group with an amino group. 3. 4. The Frontier Molecular Orbitals Mulliken electro negativities (xM) and chemical hardness (n) are significant assets in mirroring chemical reactivity of compounds. The xM and n values are calculated according to formulas given: Xm = (I + A)/2 n = (i - A)/2 (4) (5) where I and A are the ionization potential and electron affinity, respectively.45 Note that I = -eHOMO and A = -eLUMO within the rationality of the Koopmans' theorem.46 The HOMO, LUMO, Ae energies (Ae = eLUMO - eHOMO), Mulliken electro negativities (%M) and chemical hardnesses (n) of TNAZ and other azetidine derivatives calculated at HF/6-31G(d'P)//B3LYP/6-31G(d'P) theoretical level are shown in Table 4. Hartree-Fock is preferred over DFT in the frontier molecular orbital calculations due to the absence of Hartree-Fock type orbital concept in DFT.47 TNAZ (1) is the most electronegative of all; therefore it is less susceptible to oxidation when compared to others. The xM trend of the compounds shows partial parallelism with the total electronic energies. Generally, the most stable isomers in the corresponding isomer groups are more electronegative than the other group members, except for 3 and 10a. The chemical hardness (n) value of a compound expresses the kinetic stability of the corresponding com-pound48-58 and it is acknowledged that the harder compounds show higher kinetic stability.48 The chemical hardness values of the questioned compounds are between 6 and 7b. TNAZ, the thermodynamically most stable of all, shows also good kinetic stability. The highest value belongs to compound 8. It is the kinetically most stable one; whereas it shows very poor thermodynamic stability. 3. 5. Explosive Properties Explosive outcomes of energetic materials can be evaluated by the determination of the explosive properties, namely detonation velocity (D) and detonation pressure (P). The empirical Kamlet-Jacobs59-64 equations are employed for the calculations of these properties as follows: D = 1.01 (N Mave1/2 Q1/2 )1/2 (1 + 130 p) (6) P = 1.558 p2 N Mave1/2 Q1/2 (7) where each term in equations 6 and 7 is defined as follows: D, detonation velocity (km/s); P, detonation pressure (GPa); p, density of a compound (g/cm3); N, Table 4. The HOMO, LUMO, Ae energies (Ae = eLUMO - eHOMO), Mulliken electronegativities (xM) and chemical hardnesses (n) values of TNAZ and azetidine derivatives calculated at HF/6-31G(d.p)//B3LYP/6-31G(d.p) theoretical level. ehomo (ev) elumo (ev) AE Xm n TNAZ(1) -13.03 0.99 14.02 6.02 7.01 2 -11.95 1.13 13.08 5.41 6.54 3a -12.35 0.81 13.16 5.77 6.58 4a -11.65 1.68 13.33 4.99 6.67 5 -11.98 1.06 13.04 5.46 6.52 6 -10.54 1.67 12.21 4.44 6.11 7b -12.15 2.00 14.15 5.08 7.08 8 -11.22 3.17 14.39 4.03 7.20 9 -9.78 2.70 12.48 3.54 6.24 10a -11.11 2.10 13.21 4.51 6.61 11a -11.16 2.20 13.36 4.48 6.68 12b -10.29 1.84 12.18 4.23 6.07 moles of gaseous detonation products per gram of explosive; Mave, average molecular weight of gaseous products; Q, chemical energy of detonation (kJ/g). The parameters N, Mave, and Q are calculated according to the chemical composition of each explosive as listed in Table 5.28 Here, the parameters N, Mave, and Q were calculated according to the chemical composition of each explosive as listed in the second column of Table 5. (AH°f(c)) of compounds (Table 6). Keshavarz has related condensed phase heat of formation of an energetic com-pound73 to its molecular structure. For a CaHbNcOd type nitramine, AHf(c) (kJ/mol) is given as, AHof(c) = 29.68a - 31.85ft + 144.2c - 88.84d - 88.84«OH- 39.14«N-NO2 - 45.62«C=O+ (8) 256.3«° - 380.5«=CNN + 30.20 nO-NO2 Table 5. Stoichiometric relations for the calculations of the N, Mave and Q parameters of CaHbOcNd type explosives. Stoichiometric Relations Parameter N M„.„ Qx10 1-3 c £ 2a + b/2 (b + 2c + 2d)/4M 4M/(b + 2c + 2d) (28.9b + 94.05a + 0.239aH°f)/M 2a + b/2 > c £ b/2 (b + 2c + 2d)/4M (56d + 88c - 8b)/(b + 2c + 2d) [28.9b + 94.05(c/2 - b/4) + 0.239aH°f]/M b/2 > c (b + d)/2M (2b + 28d + 32c)/(b + d) (57.8c + 0.239aH°f)/M In Table 5, M is the molecular weight of the compound (in g/mol); AHof is the gas phase standard heat of formation of the compound (in kJ/mol). Earlier studies65-77 have reported that the gas phase standard heat of formation (AHof(g) / 6-31G(d,p)) geometry optimized TNAZ and other azetidine derivatives to calculate the gas phase heat of formations in gas phase. The density of each compound is defined as the molecular weight divided by the molar volume. The molar volume was calculated using a Monte Carlo integration technique implemented in the Gaussian 03 software package.68 Q values show % oxygen balance of the compounds in the study. Molecular volume and density results are given with standard deviation in order to show the accuracy of the method. The predicted densities and detonation properties of TNAZ and other azetidine derivatives are listed in Table 6. It also includes experimental and theoretical performance values of TNT69, rdx286770-72 and HMX28'71'72 taken from the literature. We have also calculated detonation velocity and pressure employing condensed phase heat of formation where nOH nN-NO2, nC=O and «o_NO2 are the number of specified functional groups, nf is equal to 0 and 1 for existence of hydrogen in molecule and hydrogen free compound, respectively. n=CNN is the number of structural moiety =C-NN in the energetic compound. Keshavarz has also suggested very simple methods for the investigation of detonation velocity(D)74, detonation pressure (P)75 and detonation temperature (Tdet).76 The detonation velocity for both CaHbNcOd type and CaHbNcOdAle type explosive is given as, D = 1.64 + 3.65po - 0.135a + 0.117c + (9) 0.0391d - 0.295n_NRR - 0.620nA; - 1.41^3 salt where D is expressed in km/s; po is the density in (g/cm3), nNRR' is the number of specific group -NH2, NH4+ and five member ring with three (or four) nitrogens in any explosive as well as five (or six) member ring in cage nitramines. nAl is equal to the number of moles of aluminum except that its value can be changed according to some conditions.74 « w « ■gaii w m ^ 3 » £ O H m Z ^ W „ -Ï QqS O w O Is — H — 0 m ^ B CM m ,—. ^ 0 O (km/s o> a ^ T3 = 5 O 6 S o O o o t- 00 CO CO 00 a\ I/o I/O I/o o\ IN IN o\ o\ IN IN o o o 00 ,—1 ,—1 CO CO I/o I/O o o o I/o I/o I/o I/o I/O I/O I/o CO 00 IN o 00 VO o CO CO co o I/o c^ c^ P^ O) 00 iN ,—H cK VO 00 I/o CO CO —H ,—H ,—H CO CO IN IN IN IN IN iN iN iN o vo IN O CO 00 IN ^ CO ït CO 00 CD p^ I/O CO 00 00 00 00 00 00 p^ p^ V!D p^ p^ p^ ^ 00 I/o ^o o p~ CO o o o OO O) CO p^ 00 P^ p^ 00 p- IN ^ cK p^ 00 CD ■'t ■'t CO CO IN IN IN IN IN IN IN IN iN IN in vo t- IN I/O a\ CO P- VO VO I/o CO CD i—i 1—1 CO p- P~ p- 00 00 00 00 00 00 00 p^ p^ p^ P^ p^ t- I/o o o I/o IN I/o 00 O iN 00 r^ c^ oo iN c^ CD CO ,—H 00 CD 00 cK cK CD I/O I/o C^ CO CO CO IN CO IN IN IN iN iN iN (N CO o CO IN IN I/o CO CO iN iN i/o i/o c? C? O) p^ IN IN CO 00 P^ 00 T-H p- p^ 00 00 00 00 00 00 p^ p^ p^ P^ p^ P^ ■'t ■'t c^ cK CO 00 CO 00 ^ t- OO i/o ,—1 i/o a\ i/o i/o VO ,—1 ^ i/o 00 i/o 00 CD VO p^ p^ vi^ i/^ 1/^ V!^ O) 00 p^ iN ,—; i/o ,—: ,—: ,—: ,—; ,—: ,—: ,—: ,—: ,—: ^^ VID 00 00 C^ cK CO 00 00 i/o vo 00 CO ,—i p~ ,—i CO iN 00 ,—1 00 C? iN VO O) r^ c^ c^ V!^ c^ \o p^ 00 00 cK 00 ,—H CO 00 cK p^ c^ c^ 00 ,—H —H ^^ ,—H o •—( o o o\ o\ o\ o\ o\ a\ o\ o\ o\ iN ^—( *—( CO 00 vo IN i/o i/o ^o IN p- o 00 o p~ iN iN CO VO o iN O) CD p^ c^ p^ ■^t c^ VO i/o CD i/o i/o CO 0¿ CO CO oo CD 00 ,—H ^^ ■'t p^ CO ,—1 CO o ,—1 00 o\ CO 00 o VO IN i/o t- s—( t- t- p- ••o i/o o ,—i i/o ■'t VO CO ,—1 ,—1 00 o 00 00 IN VO 00 IN iN ^ 00 VO cM o IN CO CD C^ c^ 00 00 CO 00 i/o CO oo cK CD oo cK 00 00 p^ oo CO •—( o\ i/o 00 ,—1 00 o\ CO VO o o o\ CO 1 ,—1 ,—1 ,—1 IN ,—1 iN iN i/o VO vo I/o IN ^ o i/o ^o IN ,—1 ,—1 VO o ,—1 o o co IN c^ 1/^ 00 p^ P^ 1/^ O) I/o cK iN VO oo ,—H CO i/o i/o cK 00 c^ rJ 00 CD (N IN 00 o VO o\ p~ IN ,—1 p~ o 00 i/o i/O VO p~ IN IN IN iN iN iN t- t- t- O o 00 00 p~ p~ i/O i/o i/O 00 cM cM CD CD CO CO c^ P^ p^ P^ c^ VID VÍD VO O CD cK cK VO VO i/O i/o i/O oo ,—H "T IN 1 IN 1 T f o\ 1 o\ 1 VO 1 VO 1 VO 1 p~ 1 iN 1 iN I sí (S o (S H X X z C3 C3 -O -O iN Zi Q s H IN CO I/o p- 00 a\ H K Similarly, Keshavarz has proposed detonation pressure75 for both CaHbNcOd type and CaHbNcOdAle type explosive, P = -2.335 + 10.586po2 - 1.239a - 0.183ft + 0.650c + 0.540d -2.471 n_Nm - 6.308 nAl (10) where P is expressed in GPa, po is the density in (g/cm3), n-NHx is the number of -NH2, NH4+ or five (or six) member ring in cage nitramines; nAl is a function of the number of moles of Al which can be determined according to equations in ref75. Detonation temperature (Tdet) is another important parameter in the investigation of explosives. Keshavarz et. al. has projected a simple method76 to assess the detonation temperature using molecular structure and gas phase heat of formation AHf(g). For a CaHbNcOd type non-aromatic explosive, detonation temperature is given, Tde/1000 = 149.0 - 1513.9 a' -196.5ft' - 2066.1c' - 2346.2 d' + 1.2 AH'f(g) (11) where Tdetis expressed in Kelvin, ab', c', d' and AH'f(g) are a, b, c, d and gas phase heat of formation of explosive divided by molecular weight of explosive,7 respectively. The detonation velocity and pressure values (calculated using AHof (g) and Kamlet-Jacobs) for TNAZ are in accordance with the literature data.72,77 When Table 6 is considered, it is obvious that the performance of TNAZ lies between well-known explosives HMX and RDX and is better in usage than its alternate, TNT. The performances of TNAZ and other azetidine derivatives are in the following manner (See Figure 3): TNAZ (1) >2> 3a> 5> 7b> 4a> 6> 12b> 10a> 11a> 9> 8> TNT. The results show that the more nitro groups the compounds have, the better the explosive properties are. TNAZ has the highest detonation properties as we expected. Replacement of nitro groups with nitroso groups (on going from TNAZ to compounds 2, 3, 4a and 5) slightly a Gas phase standard heat of formation values obtained from the PM3 single point calculations65-67 over B3LYP/6-31G(d,p) geometry optimized structures. b Condensed phase heat of formation values obtained from Kesha-varz relation73 c Average molar volumes from 100-single point calculations at the B3LYP/6-31G(d,p) level.28 d Detonation velocity and pressure results obtained from Kam-let-Jacobs equations using gas phase heat of formation data. e Detonation velocity and pressure results obtained from Kamlet-Ja-cobs equations using condensed phase heat of formation data. f Detonation velocity and pressure results obtained from Keshavarz empirical relations.74-76 Data in parenthesis are the experimental values taken from ref.77 for AH°f (g) of TNAZ, ref.78 for density of TNAZ, ref.79 for detonation velocity of TNAZ, ref.80 for detonation pressure of TNAZ, ref.69 for TNT, refs.67 70-72 for RDX and refs.71-72 for HMX. Figure 3. Detonation velocity and pressure calculated according to Kamlet-Jacobs equations using gas phase and condensed phase heat of formation and according to Keshavarz relations. decreases explosive properties. Whereas, amino group replacements (from TNAZ to compounds 6, 7b, 8 and 9) decreases detonation velocity and pressure more. The compounds 10a, 11a and 12b have one nitro, one nitroso and one amino group. These isomers (10a, 11a and 12b) are better in performance and the most insensitive isomer groups in the present study. As seen from Figure 3, detonation velocity and pressure values calculated employing AH°f(g) and AH°f(c) are quite analogous. Whereas detonation values calculated using Keshavarz relations are somehow lower, however they follow the same trend with the results of Kamlet-Jacobs. The Keshavarz detonation relations provide timesaving calculations with quite satisfactory results. The detonation temperature is another substantial parameter in the examination of explosives. Detonation reaction of an explosive is enormously fast and the heat produced by detonation increases the temperature of gases, which lead them to expand and work on surroundings.76 The detonation temperature of TNAZ and other azetidine derivatives are in the following manner 4a = 5 (C3H4N4O4) >2 = 3 (C3H4N4O5)> 10a = 11a = 12b (€^403) > TNAZ (C3H4N4O6)>6 = 7b ^H^O^ = 9(C3H8N402). As seen from the sequence, as the number of oxygen and hydrogen atoms increases, detonation temperature decreases. 3. 5. 1. Detonation Products The detonation of a CaHbOcNd type explosive will result in the formation of smaller molecules, i.e., CO2, CO, H20, etc. In order to clarify the decomposition products, a set of rules was developed by Kistiakowsky and Wilson.81 Table 7 shows the number of moles of detona- Table 7. Gaseous decomposition products of TNAZ and other azetidine derivatives using the Kistia-kowsky and Wilson Rules Number of moles of detonation products Total Formula N2 H2O CO CO2 H2 Csolid TNAZ(1) C 3H4N4O6 2 2 2 1 - - 7 2 C3H4N4O5 2 2 3 7 3a C3H4N4O5 4a C3H4N4O4 5 3444 C3H4N4O4 2 2 2 - - 1 7 6 C3HóN4Oó 7b 3ó4ó C3H6N404 2 3 1 - - 2 S 8 C3HSN4O2 9 3 8 4 2 C3H8N4O2 2 2 - - 2 3 9 10a C3H0N4O3 11a C3H0N4O3 2 3 - - - 3 S 12b C3H0N4O3 Picric Acid CóH3N3O7 3/2 3/2 11/2 - - 1/2 9 TNT CANA 3/2 5/2 7/2 - - 7/2 11 RDX C3H0N0O0 3 3 3 - - - 9 HMX C4H8N808 4 4 4 - - - 12 tion products of the compounds questioned in the present study. When total amount of gas produced upon detonation is considered, the compounds 8 and 9 seem to be the most gas releasing ones. These compounds produce as much gas as well known explosives Picric Acid and RDX. The next group of compounds producing less gas upon detonation contain 5, 6, 10a, 11a and 12b. Since TNAZ, 2 and 3a do not produce solid carbon, they produce the most amount of gas upon detonation. The most hazardous detonation product is carbon monoxide (CO). It is a colorless, odorless poisonous gas that is extremely harmful to human health. Compounds 2 and 3 produce 3 moles of carbon monoxide upon detonation. TNAZ, compounds 4 and 5 produce 2 moles when compounds 6 and 7 only produce 1 mole of carbon monoxide. TNAZ is the only compound that produces CO2 upon detonation. Compounds 8, 9, 10, 11 and 12 seem to be the most environment friendly when detonation products of other azetidine derivatives are considered. TNAZ and other derivatives produce less CO when compared to those of Picric Acid, TNT, RDX and HMX. It is appropriate to consider TNAZ as an environment friendly explosive in terms of detonation products. 3. 5. 2. Explosive Power and Power Index Heat and gases are released in an explosive reaction. The volume of gas produced will provide information on the amount of work done by the explosive. Standard conditions must be established in order to measure the volume of generated gas, since the volume of gas varies according to the temperature. The standard conditions (273 K, 1atm) also enable one to make comparisons between different explosives. Division of the value of total volume of gas produced upon detonation by the molecular weight gi- ves an idea of how much gas is released per gram of explosive. The heat of explosion Q can be calculated as expressed in section 3.5. The volume and Q values can be combined to give the value for the explosive power82 as shown in the following equation: Explosive power = QV (8) The value for the explosive power is then compared with the explosive power of a standard explosive (picric acid) to obtain power index, as shown in the following equation: Power index = [QV/ Q(picric acid)V (picric acid)] x 100 (9) Table 8 shows the power index values of TNAZ, azetidine derivatives, Picric Acid, TNT, RDX and HMX and the deviation of values relative to TNAZ (API). The power index values of TNAZ and other azetidine derivatives are between 118 - 163% and in the following manner: 12b> 10a> 11a> 9> 6> 5> 7b> 4a> 8> 3a> TNT> 2> HMX> RDX> TNAZ (1)> Picric Acid. The results show that TNAZ is as favorable as RDX and HMX in terms of power index. The compounds 10a, 11a and 12b having one nitro, one nitroso and one amino group have the highest power index value of all. 4. Conclusion Presently, theoretical studies have been performed on TNAZ itself and eleven different azetidine derivatives. The corrected absolute and relative total energies of the geometry optimized structures have been calculated at the theoretical level of B3LYP/6-31G(d,p). We have Table 8. The power index values of TNAZ, azetidine derivatives, Picric Acid, TNT, RDX and HMX Compound Q (kJ/g) V(dm3/g) QxV Power Index % API TNAZ (1) 1740.43 0.82 1421.35 118 0 2 1715.06 0.89 1527.96 126 8 3a 1733.22 0.89 1544.14 128 10 4a 1707.95 0.98 1673.80 139 21 5 1748.05 0.98 1713.09 142 24 6 1613.76 1.11 1785.09 148 30 7b 1543.32 1.11 1707.18 141 23 8 1084.77 1.53 1656.75 137 19 9 1193.90 1.53 1823.42 151 33 10a 1530.48 1.23 1878.50 155 37 11a 1488.49 1.23 1826.97 151 33 12b 1601.07 1.23 1965.15 163 45 Picric Acid 1372.86 0.88 1208.07 100 -18 TNT 1417.54 1.09 1538.69 127 9 RDX 1598.39 0.91 1450.86 120 2 HMX 1634.89 0.91 1484.66 123 5 correlated the bond dissociation energies with sensitivity. TNAZ has three NO2 groups. We have proved that on converting the nitro groups to nitroso and amino groups, it is possible to decrease the sensitivity without significant loss in power. The introduction of an amino group into TNAZ desensitizes the molecule more when compared to the introduction of nitroso group. Besides, replacement of two of the nitro groups with nitroso groups makes the same effect with the replacement of one nitro group with an amino group. It is obvious that as the number of amino group increases, BDE values also increases, consequently sensitivity decreases, however explosive property might be lost. As for explosive effects, replacement of nitro groups with nitroso groups (on going from TNAZ to compounds 2-5) slightly decreases explosive properties. Whereas, amino group replacements (from TNAZ to compounds 6, 7b, 8 and 9) decrease detonation velocity and pressure more. Compounds 8-12 seem to be the most environment friendly when detonation products of all azetidine derivatives are considered. Note that the compounds 10a, 11a and 12b have one nitro, one nitroso and one amino group. These isomers not only have the highest power index values but also are optimum structures in performance and the most insensitive isomer group in the present study. TNAZ is as favorable as RDX and HMX in terms of power index. All the compounds investigated showed better explosive properties than TNT. They are all potential candidates for insensitive high explosives. They are all alternative to TNT whenever lower sensitivity is required. We have proved that molecular modification is a functioning method in both desensitization of TNAZ and reduction of its explosive effects. 5. References 1. P. F. Pagoria, G. S. Lee, R. A. Mitchell, R. D Schmidt, Ther-mochim. Acta. 2002, 384, 187-204. 2. T. G. Archibald, R. Gilardi, K. Baum, C. J. George, J. Org. 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Proučevali smo tudi vpliv kemijske trdote in Mullikenove elektronegativnosti na eksplozivne lastnosti. Z uporabo Kamlet-Jacobsove enačbe smo reziskovali tudi balističen lastnosti, kot so hitrost detonacije (D) in detanacoisjki tlak (P). Napovedali smo produkte detonacije in indeks moči. Dokazali smo, da z modifikacijo molekule lahko bistveno vplivamo na eksplozivno občutljivost TNAZ.