Estimating the Densities of Benzene-Derived Explosives Using Atomic Volumes

Journal of Molecular Modeling (2018) 24: 50 https://doi.org/10.1007/s00894-018-3588-9 ORIGINAL PAPER Estimating the densities of benzene-derived explosives using atomic volumes Vikas D. Ghule1 & Ayushi Nirwan1 & Alka Devi1 Received: 7 November 2017 /Accepted: 8 January 2018 /Published online: 9 February 2018 # Springer-Verlag GmbH Germany, part of Springer Nature 2018 Abstract The application of average atomic volumes to predict the crystal densities of benzene-derived energetic compounds of general formula CaHbNcOd is presented, along with the reliability of this method. The densities of 119 neutral nitrobenzenes, energetic salts, and cocrystals with diverse compositions were estimated and compared with experimental data. Of the 74 nitrobenzenes for which direct comparisons could be made, the % error in the estimated density was within 0–3% for 54 compounds, 3–5% for 12 compounds, and 5–8% for the remaining 8 compounds. Among 45 energetic salts and cocrystals, the % error in the estimated density was within 0–3% for 25 compounds, 3–5% for 13 compounds, and 5–7.4% for 7 compounds. The absolute error surpassed 0.05 g/cm3 for 27 of the 119 compounds (22%). The largest errors occurred for compounds containing fused rings and for compounds with three –NH2 or –OH groups. Overall, the present approach for estimating the densities of benzene- derived explosives with different functional groups was found to be reliable. Keywords Density . Atomic volume . Explosive . Group additivity method . Energetic salts Introduction providing that the density and heat of formation values fed into the formula are reliable. The synthesis or hypothetical design of new explosive com- The purpose of the work reported in the present paper was to pounds requires the evaluation of various molecular and energet- develop a simple and straightforward correlation for predicting ic properties in order to select promising molecules. Superior the densities of benzene-derived explosives. Various methods performance is always the decisive factor in high-explosive ap- of estimating the densities of different classes of explosives plications, and a high density is crucial to maximizing the deto- based on group additivity and quantum chemistry software nation performance of an explosive. The relationship between have been reported. Among these, the group additivity ap- density and explosive power is highlighted by an empirical for- proach is one of the most straightforward, as it involves simply mula devised by Kamlet and Jacobs [1] to estimate detonation summing the volumes of the atoms or groups in the molecule parameters. Indeed, this formula indicates that the detonation [2–13]. While group additivity or volume-based approaches performance is much more strongly influenced by the density have the benefits of being inexpensive and easy to use, they of the explosive than its heat of formation. It is known that the are known to give the same densities for isomers and poly- formula can be used to evaluate the detonation properties of morphs. On the other hand, methods based on quantum chem- CHNOexplosivestowithintheexperimentalmeasurementerror, istry software require computationally expensive calculations [14–24]. All of these methods can give reasonably predictive modelsforenergeticcompoundsandtaketheconformationand Electronic supplementary material The online version of this article interactions into account in the crystal packing efficiency. (https://doi.org/10.1007/s00894-018-3588-9) contains supplementary Benzene-derived explosives are prominent in the literature on material, which is available to authorized users. energetic materials due to their high densities, low sensitivities, and high thermal stabilities. Inspired by the work of Hofmann * Vikas D. Ghule [email protected] [11], in the present study, we used the average atomic volume to predict the densities of explosives containing one or more ben- 1 Department of Chemistry, National Institute of Technology zene rings, and included a correction for the amino groups in the Kurukshetra, Kurukshetra, Haryana 136119, India compound to further improve the density estimation. 50 Page 2 of 18 J Mol Model (2018) 24: 50 Results and discussion To demonstrate the reliability of Eqs. 2 and 3, the densities of 119 benzene-derived explosives were predicted and com- In recent years, several methods for predicting crystal density pared with corresponding experimental data. The predicted have been reported that divide explosives into different classes densities and percentage errors relative to the experimental and apply various descriptors. The success of a density pre- data are given in Tables 2 and 3. Table 2 shows that the den- diction approach depends on its ability to estimate inter- and sities predicted for nitrobenzenes (entries 1–6) had % errors of intramolecular interactions, steric hindrance, conjugation, and less than 2.18% (0.04 g/cm3). For the OH-substituted nitro- ring systems, as well as to account for the effects of benzenes (entries 7–12, 22), the maximum % error was esti- 3 explosophores such as NO2,NH2,OH,N3,ONO2,and mated to be 3.65% (0.06 g/cm ), while the % error for 2,4,6- NHNO2 groups. The crystal density of a neutral or ionic com- trinitrobenzene-1,3,5-triol (entry 27) was 4.41%, which may pound can be estimated from its molecular volume (VM)and be attributed to the complexity of the interactions involving its molecular mass (MW) via three OH groups. Nitrobenzenes containing a CH3 moiety (entries 13–16) or an NH2 group (entries 17–20) showed max- MW imum % errors of 3.26% (0.05 g/cm3) and 3.33% (0.06 g/ Density ðÞ¼ρ : ð1Þ 3 V M cm ), respectively. The predicted density of TATB (entry 21) showed a maximum deviation of 7.82%, which may be due to It has been reported that the volumes of the atoms compris- its complex inter- and intramolecular H-bonding. Entries 24– ing the explosive compound can be used to calculate its den- 26 and 28–34 contain various bulky groups on the benzene sity. Indeed, Hofmann [11] reported that the average atomic ring, and the presence of an ONO2, CN, NHNH2, NHNO2, volumes of various elements as well as thermal expansion can N3, or guanidine group resulted in a maximum error of 6.3%. be used to predict the density of an explosive as follows: The compounds with two benzene rings in their structures (entries 35–45, 73, and 74) showed a maximum error of 5.08%. Nitrobenzotriazoles (entries 49–72) with a CH , ðÞ¼ρ MWexplosive Â : ; ð Þ 3 Density 0 00164 2 NH ,orOCH group showed maximum deviations of up to ðÞaVC þ bVH þ cVN þ dVO 2 3 6%. The densities calculated in the present work were compared with previous results reported by Rice et al. [17]and where a, b, c,andd are the numbers of carbon, hydrogen, Politzer et al. [21], which were computed using an electrostat- nitrogen, and oxygen atoms in a molecule of the explosive, ic potential approach. The predicted values are in good agree- respectively. V , V , V ,andV are the volumes of the cor- C H N O ment with the experimental and reported results (see Table S1 responding atoms, which are summarized in Table 1. Density in the BElectronic supplementary material,^ ESM). estimation for compounds with strong H-bonding or with Considering the complexities of the inter- and intramolecular strong van der Waals or electrostatic interactions is more com- interactions involved in density prediction, the present ap- plex and challenging. While various corrections to group ad- proach appears to be reliable for neutral benzene-derived ditivity methods have been suggested to account for H- explosives. bonding between amino and oxygen-containing groups, the The predicted densities for salts and cocrystals are summa- resulting methods underestimate the density [8, 9, 13]. We rized in Table 3. TNT, picric acid, and trinitrobenzene have have observed that the presence of two or more NH2 or + been widely used in the preparation of cocrystals owing to NH groups in the molecule of an explosive compound in- 3 their excellent thermal stabilities and reasonable energetic creases its density. Hence, along with the atomic volumes, the + properties. Therefore, most of the salts and cocrystals studied contributions from NH and/or NH groups should also be 2 3 in this work contained these compounds. For the picric acid accounted for, leading to the following optimized expression: salts and cocrystals (entries 75, 79–81, 84–95, 101–103, and MW 105 in Table 3), the % error was less than 5% except for the ðÞ¼ρ explosive Â : : ð Þ ′ Density ðÞaV þ bV þ cV þ dV 0 00175 3 1,1 -methylenebis(imidazolium) (entry 79) and 1,2,4- C H N O triazolium (entry 89) salts. Further, among the TNT- containing cocrystals (entries 104, 106, 109, and 111–119 in Table 3), the anthracene and phenylenediamine cocrystals Table 1 The atomic showed % errors of 7.09 and 6.8%, respectively. All other Element Atomic volume (nm3) volumes of C, H, N, and salts and cocrystals presented errors of less than 5% in their Oat298K[11] C 0.01387 estimated densities. As can be seen in Table S2 of the ESM, H 0.00508 the densities predicted using Eq. 3 for compounds containing + N0.0118 two or more NH2 or NH3 groups in their molecular structures O0.01139 displayed excellent agreement with the corresponding experimental values, in contrast to the densities computed via Eq. 2. JMolModel(2018)24:50 Page 3 of 18 50 Table 2 Predicted densities for neutral benzene-derived explosives Expt. Calculated MW Compd. Name Structure MF Density Density (g/mol) (g/cm3) (g/cm3) NO 2 NO 2 1.56 1 1,2-Dinitrobenzene

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