III. Fused Heterocyclic Energetic Compounds

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Comprehensive End-to-End Design of Novel High Energy Density Materials: III. Fused Heterocyclic Energetic Compounds Roman Tsyshevsky, Aleksandr S. Smirnov, and Maija M. Kuklja J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b00863 • Publication Date (Web): 08 Mar 2019 Downloaded from http://pubs.acs.org on March 9, 2019

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The Journal of Physical Chemistry

Comprehensive End-to-End Design of Novel High Energy Density Materials: III.

Fused Heterocyclic Energetic Compounds

Roman Tsyshevsky1, Aleksandr S. Smirnov2, and Maija M. Kuklja1,* 1Materials

Science and Engineering Department, University of Maryland College Park, College Park, MD 20742

2Bakhirev

Scientific Research Institute of Mechanical Engineering, 11a Sverdlov St., Dzerzhinsk, Nizhny Novgorod Region, Russia, 606002 Abstract

In contrast to synthesis and experimental characterization that are usually expensive and timeconsuming, a coupled combination of ab initio and group additive theoretical methods represents a powerful alternative to computationally design and characterize new materials with targeted properties. Heterocyclic energetic materials are considered attractive candidates to replace conventional high explosives, such as PETN, RDX, HMX and TNT. Heterocycles enable an intriguing opportunity for combinatorial design of new classes of energetic materials with targeted performance and sensitivity properties and offer ways for an accurate analysis of structureproperty correlations of the materials. By using a computational strategy that links methods of quantum chemistry and semi-empirical statistical analysis, we designed, modeled and characterized a series of novel linear and fused explosive compounds. Proposed materials with best combinations of performance and sensitivity parameters can be now considered as potential candidates for synthesis and experimental characterization.

*

Author to whom correspondence should be addressed, e-mail: [email protected] and [email protected]

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1

Introduction

With the demand for new and improved materials endlessly growing, experimental discovery is largely bound by a trial-and-error approach, high costs and time-consuming sophisticated synthesis1. The flourishing era of computational materials science offers an appealing alternative - computational materials design. It is usually based on bridging computational quantummechanical–thermodynamic methods, data mining through large databases, and some validation checks. Although the computational high-throughput approach1,2,3,4 is considered successful and even rather mature for some classes of inorganic materials5,6, it is still far from being a universal toolbox for materials discovery. The large class of molecular energetic materials was barely touched upon the modern computational materials design methods, perhaps, because of complex functionalities of these materials or coupled behaviors. Despite tremendous advances in synthesis7,8,9,10,11,12,13 and the fact that ultimately desired functionalities are well defined — high energy content, high density, high performance, low toxicity, low sensitivity, reliable stability, and so on14,15,16— the materials developed with traditional serendipitous methods are unlikely to directly yield the desired properties since the structures underpinning them, much less the correlations between structures, properties, and functions, are not well understood. Illustratively, many new energetic materials were produced over the years only to be rejected because they turned out to be so dangerously sensitive that it was problematic to use and, sometimes, even to characterize them17. The lack of understanding of how the structure and chemical composition of the material govern its performance and sensitivity, the most important characteristics of energetic compounds, hampers both design of new formulations and the development of new technologies. We recently proposed a comprehensive strategy18,19 for design of energetic materials and illustrated how new targeted high energy density materials with desired properties can be obtained. Using this approach, we suggested the potential structure, predicted a set of properties, synthesized, and characterized LLM-200, the compound with performance and stability superior to those of benchmark RDX (and even CL-20) and recently discovered promising energetic heterocyclic materials18,20. We further showed19 how this methodology can be used for a systematic analysis of property-structure correlations in a series of linear oxadiazole based energetic materials constructed by varying the number and consequence of particular atoms in the


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hetero rings, the arrangement of the rings in the molecule and, the attachment of different functional groups. Our studies18,19 convincingly illustrated advantages of multiscale-modeling, linking quantum-chemistry, analytical theory, and statistical analysis21, as a powerful tool for a prediction of new materials and economical high-throughput search engine to select which candidate structures are worthy of experimental synthetic efforts. This research aimed at a further refinement of our computational materials design strategy. We report here a systematic study that helps to reveal and optimize structure-property-function relationships in linear isomers and fused heterocyclic energetic materials. We briefly summarize results of our previous studies of linear oxadiazole based energetic materials, introduce new isomers, and discuss new directions for combinatorial design of new classes of high energy density materials with improved structure-stability-performance characteristics. We show that an arrangement of heterocyclic rings in fused molecules offers opportunities for obtaining insensitive energetic materials with high performance. The proposed materials are predicted to exhibit properties superior to all known energetic materials.

2

Methods

We computationally design and characterize new high energy density materials by means of a complex multilevel approach,19 which involves first principles calculations, analytical theory, and empirical statistical analysis. First principles modeling (illustrated in Scheme 1) is used to explore molecular and electronic structures of the materials, calculate thermodynamic parameters (enthalpy, entropy, and Gibbs free energy), study mechanisms of thermal decomposition and estimate Arrhenius parameters of chemical reactions. The Scheme 1 is color-coded and shows how various methods are coupled and used to obtain characteristic materials parameters. It also indicates that several parameters can be obtained from different methods (e.g., formation enthalpy and thermodynamics is delivered by both quantum-chemical methods and by MAC). Such integrated approach allows for multilayered validation and additional checks. In our research, density functional theory (DFT)22,23 with the M0624 functional and valence split double-zeta 6-31+G(2df,p) basis set, as implemented in the Gaussian 09 code25, were employed to study molecular structures, formation enthalpies, and chemical stability of the designed heterocyclic energetic molecules. Our previous study26



demonstrated that a combination of M06 functional with the 6-31+G(2df,p) basis set is suitable for calculations of formation enthalpies of nitro compounds and for modeling their thermal decomposition pathways. The formation enthalpies of heterocyclic compounds in the gas phase were calculated using an atomization approach.27,28,29 Thermal stability of molecules has been investigated by modeling most feasible decomposition reactions. The corresponding reaction rates for decomposition pathways with a well-defined structure of the transition state were calculated with the transition state theory (TST)30. Reaction pathways were investigated by conducting intrinsic reaction coordinate computations using the Hessian-based Predictor-Corrector integrator algorithm31,32 for each transition state. The homolysis of X-NO2 (X=C, N, O) bond, the most important decomposition reaction in nitro compounds, belongs to the class of so called barrierless reactions, which do not have a well-defined transition state structure on their minimum energy profile and, hence, the conventional TST is not applicable for evaluation of kinetic parameters. Therefore, variational transition state theory (VTST)33 was employed to calculate reaction rates and pre-exponential factors of C-NO2 bond cleavage reactions34,35,36. Decomposition mechanisms of newly designed linear and fused heterocyclic compounds are summarized in Supporting Information (SI). Coordinates of all studied molecules, transition state and products are also collected in SI. The method of atomic contributions (MAC)21 can be used for calculating thermodynamic parameters and density of the material based on its molecular structure (Scheme 1). In this study, we used MAC to calculate density of the materials, whereas formation enthalpies were obtained from DFT calculations. Formation enthalpies, calculated using either quantum chemistry methods or MAC approach, and densities of the materials, obtained with MAC, are then used in a regression statistical analysis21 (Scheme 1) to estimate basic explosive characteristics of the materials including detonation velocity (D, km/s), detonation pressure (P, GPa), critical pressure of detonation initiation (Pcr, GPa), calorimetric heat of explosion Qc (kcal/kg), and a relative acceleration ability (η). The latter is also known as a relative propelling ability, which serves as a realistic measure of lethality (and power) of the material placed in a device and is quantified relative to the acceleration ability of an etalon material, in our case RDX, in the geometry of a face-plate pushed from the end of the explosive charge.


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Scheme 1. Schematic of the multilevel modeling to design and characterize high energy density materials prior to their actual synthesis.

3 3.1

Results

Linear oxadiazole based compounds Properties of organic energetic materials are largely defined by the structure of the constituent

molecules. To computationally design new energetic compounds and optimize their properties, we use oxadiazole rings (Figure 1a) as the molecular building blocks and explore the structureproperty relationships of obtained materials through an analysis of a tied set of stability and performance parameters for each proposed compound.



Figure 1. The structures of a) oxadiazole fragments and functional groups as building blocks involved in constructing energetic materials b) LLM-200, c) PHE-1, d) PHE-2, e) PHE-3, f) PHE-4 and g) PHE-5.

We started with linear chains of rings bound into molecules to form solids18,19,20. For example, LLM-20018 (Figure 1b) compound comprised of two central 1,2,4-oxadiazole rings and two outer 1,2,5-oxadiazole rings has performance and stability superior to those of benchmark RDX. Our study showed that the cleavage of outer 1,2,5-oxadiazole rings requires a relatively low activation energy (48.8 kcal/mol) and dominates in the decomposition of LLM-200 at a wide temperature range. We found that breaking of the central 1,2,4-oxadiazole rings of LLM-200 required a noticeably higher activation energy (55-65 kcal/mol) than the cleavage of the outer rings18. The discovered difference in thermal stability of different types of oxadiazole rings inspired us to search for performance-stability correlations in nitro compounds by varying oxadiazole rings (Figure 1a). The resulting structures are depicted in Figure 1 b-g. We note that PHE-1, PHE-2, and


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PHE-3 were first described earlier19. Here we complete the set with two new relevant isomers, PHE-4 and PHE-5, in an attempt to further explore whether performance can be increased and sensitivity - decreased by combining the molecular rings in a targeted manner. We found that PHE-1 (Figure 1 c), which is built with the molecules consisting only from 1,3,4-oxadiazole rings, demonstrates overall better thermal stability than LLM-200 (Figure 2) with a slow CONO isomerization reaction (Ea = 50.2 kcal/mol and log(A, s-1)=13.3) being the most favorable primary decomposition step. Relatively high critical pressure of detonation initiation (Pcr=2.28 GPa) points to improved impact sensitivity of the PHE-1 material. At the same time, PHE-1 has a lower formation enthalpy (than LLM-200) and lower relative propelling ability (than LLM-200), which makes performance of PHE-1 inferior to that of LLM-200. Replacing the 1,3,4-oxadiazole rings with the 1,2,4-oxadiazole rings does not lead to any significant improvement in performance and stability, as PHE-2 compound (Figure 1d) demonstrates thermal and impact sensitivity close to that of LLM-200 (Table 1, Figure 2) and performance parameters (ρ=1.85 g/cc, ΔHf0298=127.3 kcal/mol, D=8.34 km/s and =94.1%, Table 1) inferior to LLM-200. Thermal decomposition of the PHE-2 is dominated by an elimination of CN2O2 molecule via a cleavage of 1,2,4-oxadiazole ring with calculated Arrhenius parameters of Ea = 49.7 kcal/mol and log(A, s-1)=15.0. The CONO isomerization reaction in PHE-2 though has a lower activation barrier (47.3 kcal/mol) and proceeds at slightly lower rates than an elimination of CN2O2 due to the lower pre-exponential factor (log(A, s-1)=13.2). Taking into consideration that PHE-2 has lower thermal and impact stability than PHE-1, but at the same time, demonstrates a higher formation enthalpy, we built a new molecule through a combination of 1,2,4- and two outer 1,3,4-oxadiazole rings. Thus, the PHE-3 molecule, depicted in Figure 1e, has two central 1,2,4- and two outer 1,3,4-oxadiazole rings. Indeed, its thermal stability is close to that of PHE-1 (Table 1). At the same time, sensitivity and performance of PHE3 were found slightly better than of PHE-2 but inferior to those of PHE-1.



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Table 1. Safety, performance, and sensitivity parameters of energetic materials Testing parameter

RDX O

Structure

H2C -

O

N

+

O

N

LLM-200

PHE-1

PHE-2

PHE-3

PHE-4

PHE-5

-

N N

+

O

N

CH2 N

CH2

N

+

O

N O N

O N O

-

N

N

O

O

O

N

O N

O

N

+

N

O

+

N

O

N

N

-

O

N

O O

N

O

N

+

N O

-

O

N

N

O N

N

-

N O

O

N

+

N

+

N

O O

N

O

N

N

-

+

N

N O

-

O

-

O

Chemical Formula C3H6N6O6 C8N10O8 ρ, g/cc 1.816a 1.940b d 19.0 ; 0 45.8e; ΔHf 298, kcal/mol 182.3g f 47.1 Oxygen balance, % -21.6 -35.2 45.1 Ea, (kcal/mol) h 48.8 (30-40) i 18 log(A, s-1) h 15.0 (12-16) i D, km/sj 8.93k 8.78k P, GPaj 36.7k 37k j k Pcr, GPa 1.86 1.47k Qc, kcal/kgj 1428k 1400k 100k 102.1k  % rel RDXj

C8N10O8 2.03c

C8N10O8 1.85c

C8N10O8 1.94c

C8N10O8 1.85c

C8N10O8 2.03

98.2g

127.3g

112.8g

124.4g

109.7g

-35.2

-35.2

-35.2

-35.2

-35.2

50.2

49.7

50.7

51.8

51.6

13.3

15.0

13.4

13.1

13.2

8.76 37 2.28 1240 100.3

8.34 31 1.49 1270 94.1

8.54 34 1.84 1260 97.1

8.31 31 1.56 1250 93.2

8.75 37 2.27 1240 100.2

a From

Ref.10 From Ref.18 c Calculated in this study using MAC approach d Experimental formation enthalpy of solid RDX is taken from Ref. 37,38 e Experimental formation enthalpy of gas phase RDX is taken from Ref.37,39 f Calculated using G3MP2B3 method formation enthalpy of gas phase molecule taken from Ref.18 g Formation enthalpies were calculated in this study using M06/6-31+G(2df,p) method h Activation barriers and pre-exponential factors of gas phase decomposition reactions were calculated using M06/6-31+G(2df,p) method (See SI for more details) i Experimental data for RDX decomposition was taken from Ref.40 j Explosive parameters were calculated in this study using statistical analysis k Calculated explosive parameters taken from Ref.18 . b


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Figure 2. Reaction rates of the predominant low temperature decomposition channels of the PHE-1, PHE-2, PHE-5 and LLM-200 molecules are shown in comparison with RDX.

The difference in thermal stability of LLM-200, PHE-1 and PHE-2 can be explained by means of an analysis of molecular geometry structures and partial charges on atoms. The calculated bond lengths and interatomic distances of the most reactive outer oxadiazole rings of LLM-200, PHE-1 and PHE-2 molecules as well as calculated Mulliken atomic charges are collected in Figure 3 a-c. The calculated geometry parameters of the molecules, Mulliken charges and surface maps of electrostatic potentials are also shown in Supporting Information. In the 1,2,5-oxadiazole ring of LLM-200 (Figure 3a), negative charges are localized on nitrogen and oxygen atoms of the ring, whereas positive charges are localized on carbon atoms. As a result of the electrostatic repulsion between positively charged carbon atoms and repulsion between negatively charged oxygen and nitrogen atoms, the cleavage of the outer 1,2,5-oxadiazole ring in LLM-200 requires a lower energy (48.8 kcal/mol) than the cleavage of the 1,3,4-oxadiazole ring (58.4 kcal/mol) of PHE-1 (Figure 3b) and 1,2,4-oxadiazole ring (50.1 kcal/mol) of PHE-2 (Figure 3c). In 1,3,4- and 1,2,4-oxadiazole rings, negatively charged oxygen or one of the negatively charged nitrogen atoms are placed between positively charged carbon atoms. Coulomb attraction between positively and negatively charged atoms makes the 1,3,4- and 1,2,4-oxadiazole



rings more stable than the 1,2,5-oxadiazole ring. The cleavage of 1,3,4-oxadiazole ring in PHE-3 (58.1 kcal/mol) has the activation energy close to PHE-1. A further inspection of the geometry structures of outer rings and atomic charges reveals yet another interesting trend. According to our calculations, the large positive charge (~0.9 e) is localized on C2 carbon atoms of the 1,3,4- and 1,2,4-oxadiazole rings of PHE-1 and PHE-2 molecules (Figures 3 b and c). The C2 atom of 1,2,5-oxadiazole of LLM-200 (Figure 3a) has a significantly lower positive charge (0.47 e). Such a charge distribution strongly affects the activation barrier of the CONO isomerization reaction in these isomers. In the transition state structures of the CONO isomerization (Figure 3 d-f), the NO2 group is rotated by ~90° about the C-N bond relative to the plane of the ring. The C-NO2 bonds at the transition states are elongated by 0.09-0.12 Å, whereas valence angles C2-N3-O3 are decreased by ~47° from ~115° in the equilibrium structures of these three isomers to ~68° in corresponding transition states. This is due to the electrostatic attraction occurring between negatively charged O3 atoms of the nitro group and positively charged C2 atoms of the ring. The calculated positive charges localized on C2 atoms of PHE-1 (1.01 e) and PHE-2 (1.10 e) are noticeably higher than the corresponding charges in LLM-200 (0.61 e). As O3 oxygen atoms have close negative charges (~0.4 e) regardless of the structure of isomers, the stronger electrostatic attraction occurs between C2 and O3 atoms at the transition state structure of the CONO isomerization reactions of PHE-1 and PHE-2 than of LLM200. As a result, the calculated activation barrier of the CONO isomerization in PHE-1 (50.2 kcal/mol) and PHE-2 (47.3 kcal/mol) is ~3-5 kcal/mol lower than in LLM-200 (52.9 kcal/mol) (See SI for more details).


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Figure 3. The bond distances (obtained with M06/6-31+g(2df,p) method) and Mulliken atomic charges (calculated using MP2/6-31+G(d,p)//M06/6-31+g(2df,p)) of outer oxadiazole fragments of: a) LLM-200, b) PHE-1, and c) PHE-2. The bond distances and Mulliken atomic charges of the transition state structures of the CONO isomerization in: d) LLM-200, e) PHE-1, f) PHE-2

Taking into consideration the structure-stability correlations observed for the former four oxadiazole-based molecules, we decided to design and model two more isomers PHE-4 and PHE-5 and compare their stability and performance parameters with other oxadiazole-based molecules. Building PHE-4 from four 1,2,4-oxadiazole rings, similarly to PHE-2 (Figure 1f and Figure 4a), we look to increase thermal stability of the material. That is why unlike PHE-2, the outer rings of PHE-4 are connected to the central rings in such a way that the nitro group is linked to carbon with two neighbor nitrogen atoms rather than to carbon connected to oxygen and nitrogen atoms. In PHE-4, smaller electrostatic repulsion between negatively charged oxygen atoms of nitro group and ring atoms is expected as much lower negative charge is on N2 nitrogen in PHE4 (Figure 4a) than on O1 oxygen of PHE-2 (Figure 3c). Thus, the CONO isomerization in PHE-4 requires 4.5 kcal/mol higher energy (51.8 kcal/mol) than in PHE-2 (47.3) as electrostatic attraction between



C2 and O3 atoms at the transition state structure is smaller in PHE-4 due to a smaller positive charge (0.82 e, Figure 4b) on the C2 atom. In addition, the cleavage of the outer oxadiazole ring in PHE-4 requires ~70 kcal/mol versus ~50 kcal/mol in PHE-2 (See SI for more details). Clearly, such deliberate changes in the structure of outer rings of PHE-4 lead to the improved thermal stability (Ea=51.8 kcal/mol, log(A, s-1)=13.1) and impact sensitivity (Pcr=1.56 GPa) relative to PHE-2. The formation enthalpy of PHE-4 (124.4 kcal/mol) is close to that of PHE2 and is noticeably higher than the formation enthalpies of PHE-1 and PHE-3 molecules containing 1,2,4- and 1,3,4-oxadiazole rings. However, despite relatively attractive low thermal and impact sensitivity, PHE-4 has the worst performance between studied here oxadiazole based molecules as can be judged by relatively low density (1.85 g/cc), detonation velocity (D=8.31 km/s), and propelling ability (=93.2%).

Figure 4. a) The bond distances and Mulliken atomic charges of outer oxadiazole fragment of PHE-4 and b) of the transition state structure of CONO isomerization of PHE-4

The PHE-5 molecule (Figure 1g) was obtained from PHE-4 by replacing the two central 1,2,4-oxadiazole rings with the 1,3,4-oxadiazole rings. We expect that the compound containing such a combination of the oxadiazole rings will be more thermally stable than PHE-1 and PHE-3, molecules of which contain outer 1,3,4-oxadiazole rings. At the same time, PHE-5 is anticipated to demonstrate performance and mechanical stability higher than compounds containing only 1,2,4-oxadiazole rings (PHE-2 and PHE-4). Indeed, our calculations show that PHE-5 exhibits the


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highest density (2.03 g/cc) and thermal stability (Ea=51.6 kcal/mol, log(A, s-1)=13.2) among all explored here oxadiazole materials. The calculated reaction rates (Figure 2) suggest that the decomposition of PHE-5 will proceed at noticeable lower rates than the decomposition of LLM200, PHE-2 and by far of benchmark RDX. At the same time, relatively high critical pressure of detonation initiation (2.27 GPa) suggests that PHE-5 should have one of the highest impact stabilities, significantly higher than that of LLM-200. In addition, relatively high propelling ability (=100.2%) and detonation velocity (D=8.75 km/s) point towards attractive performance of the material. The only drawback of PHE-5 is its relatively low formation enthalpy (109.7 kcal/mol). Conclusions of our analysis of structure-property correlations in LLM series compounds18,19,20,41,42 signify linear oxadiazole-based energetic materials as appealing potential candidates to be used as explosives, propellants, and cast-melt ingredients in composites because of their high performance and low sensitivity. Both explosive characteristics of LLM series are much better than conventional high explosive materials exhibit. Besides, the chemical compositions and molecular structures, which are built through variations of oxadiazole rings, create an exciting opportunity for an in-depth multifaceted analysis of structure-property-function correlations important for intelligent design of materials with pursued properties. We showed that LLM-200 compound comprised from two central 1,2,4- and two outer 1,2,5-oxadiazole rings had an attractive performance and stability parameters despite relatively low thermal stability determined by somewhat low activation energy required for the cleavage of outer 1,2,5-oxadiazole rings. A replacement of the outer 1,2,5-oxadiazole rings in LLM-200 with the more stable 1,2,4-oxadiazole rings (PHE-2 and PHE-4 molecules) tends to improve thermal and impact stability of the materials, but also leads to a decreased overall performance (with respect to LLM-200). Materials comprised of 1,2,4- and 1,3,4-oxadiazole rings (PHE-3 and PHE-4) were predicted to demonstrate an attractive combination of performance and sensitivity parameters. Our modeling suggests that a combination of oxadiazole rings allows us to create a material with the best set of performance and stability parameters. Despite all advantages of the oxadiazole-based compounds and the fact that their stability and performance, indeed, can be tuned, our study concludes that the improvements are bound by certain limits. In other words, it is impossible to create a new material with significantly improved parameters by variation of oxadiazole rings within the linear molecule. A further logical step in enhancing explosive characteristics, i.e. higher performance and lower sensitivity, in heterocycles



would be to probe a fused energetic molecule26 in which a stable (rigid) molecular core is functionalized with appropriate rings (or even combinations of rings). Therefore, we further design and analyze fused heterocyclic molecules.

3.2

Building principles of the fused heterocyclic materials We have recently proposed the structure of a promising energetic fused heterocyclic

molecule DNBTT26 with the central tetrazine and two outer triazole rings. When building DNBTT, we formulated the following main guiding principles:  To ensure high energy content the energetic molecule should be comprised of several nitrogen and/or oxygen fused hetero rings. Indeed, the calculated formation enthalpy of DNBTT (177.1 kcal/mol)26 is only 5 kcal/mol lower than that of LLM-200 and significantly (50-80 kcal/mol) higher than formation enthalpies of relevant PHE series molecules (Table 1). 

To yield high thermal stability the nitro group has to be attached to a carbon atom, as the

C-NO2 bond has the higher dissociation energy than the O-NO2 and N-NO2 bonds. The calculated C-NO2 bond dissociation energy in DNBTT (69.9 kcal/mol)26 is consistent with theoretical and experimental estimates previously reported for different classes of C-nitro compounds (60-70 kcal/mol)43,44,45,46,47,48 49,50,51. We also note that the cleavage of C-NO2 in DNBTT requires a higher energy (by ~5-8 kcal/mol) than the activation of this channel in the oxadiazole-based molecules BNFF-1 (63.1 kcal/mol)41, ANFF-1 (61.5 kcal/mol)41, BNFF (62.3 kcal/mol)42 and LLM-200 (64.1 kcal/mol)18,19  The molecular structure should serve to additionally stabilize heterocyclic rings to prevent their dissociation as the primary decomposition step. One of the main reasons to make the structure with fused rings was an attempt to enhance thermal stability of LLM-series compounds built from 1,2,5-oxadiazole rings. Our DFT modeling showed that the slow CONO isomerization reaction (Ea~55 kcal/mol and log(A, s-1)~13.5)26 and the subsequent NO loss dominates in the decomposition of DNBTT at wide temperature range. This makes DNBTT a more stable material than LLM-series compounds (including BNFF, BNFF-1, ANFF-1 and LLM-200), decomposition of which is governed by breaking of outer 1,2,5-oxadiazole rings with a relatively lower activation barrier (48-50 kcal/mol) and higher pre-exponential factor (log(A, s-1)~15)18,41,42.


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To investigate how the number and type of hetero rings in the fused molecule will affect performance and stability of the compound, we augmented the list of guidelines with additional specific details of the structural arrangement, illustrated in Figure 5: 

The central pyrazine ring is used as a core framework for building fused compounds. Similarly to other aromatic rings, the pyrazine ring can take place in reactions of cycloaddition and potentially allows one to attach up to three outer hetero rings. In addition, the pyrazine has a rather high formation enthalpy (46.5 vs 19.8 kcal/mol)52,53,54, this is higher than, for example, the formation enthalpy of the benzene. o The 1,2,5-oxadiazole ring is used as one of the outer rings to increase energy content of the molecules; o The molecular core is functionalized with the pyrazole and/or triazole rings and nitro and/or amino groups (see Fig. 5).

The resulting structures of the six proposed molecules are depicted in Figure 6 a-f. Nomenclature names of the compounds, corresponding abbreviations and the structure description are collected in Table 2. We expect these fused heterocyclic compounds to have performance superior to oxadiazole-based molecules due to their nitrogen and oxygen rich structures. In addition, fused compounds should demonstrate relatively high thermal and impact stability due to their rigid fused structures.



Figure 5. Building blocks of the fused heterocyclic molecules.


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Figure 6. The proposed molecular structures of fused heterocyclic energetic materials (Abbreviations of nomenclature names of the compounds are shown in blue)



Page 18 of 33

Table 2. The molecular structures of fused heterocyclic molecules

Structure

Name

f-PN

f-PNA

a

Building blocks Number of Outer groups fragments -NO2 -NH2

Chemical formula

Nomenclature name

C8N10O9

6,7,8,9-tetranitro[1,2,5]oxadiazolo[3,4e]dipyrazolo[1,5-a:5’,1’c]pyrazine (TNODPP)a

pyrazole rings

4

0

C8H4N10O5

7,9-dinitro[1,2,5]oxadiazolo[3,4e]dipyrazolo[1,5-a:5’,1’c]pyrazine-6,8-diamine (DNODPPDA)

pyrazole rings

2

2

triazolerings

2

0

triazolerings

2

0

Pyrazole and triazole rings

3

0

Pyrazole and triazole rings

2

1

f-TN-1

C6N10O5

f-TN-2

C6N10O5

f-PTN

C7N10O7

f-PTNA

C7H2N10O5

6,9-dinitro[1,2,5]oxadiazolo[3,4e]bis([1,2,4]triazolo)[1,5a:5’,1’-c]pyrazine (DNOBTP-1) 5,10-dinitro[1,2,5]oxadiazolo[3,4e]bis([1,2,4]triazolo)[4,3a:3’,4’-c]pyrazine (DNOBTP-2) 6,7,10-trinitro[1,2,5]oxadiazolo[3,4e]pyrazolo[1,5a][1,2,4]triazolo[3,4c]pyrazine (TNOPTP) 6,10,-dinitro[1,2,5]oxadiazolo[3,4e]pyrazolo[1,5a][1,2,4]triazolo[3,4c]pyrazine-7-amine (TNOPTPA)

Abbreviations of nomenclature names of compounds are depicted in parentheses


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3.3

Fused heterocycles with pyrazole rings The fused heterocyclic f-PN molecule with the 1,2,5-oxadiazolo-pyrazin framework

functionalized with two pyrazole rings (Figure 6a) has four nitro groups attached to carbon atoms of pyrazole rings. The molecule has a planar structure with two central nitro groups rotated by ~90° out of the ring’s plane due to repulsion between negatively charged oxygen atoms of nitro groups (Figure 7a). f-PN is characterized by the high density (1.98 g/cc) and formation enthalpy (186 kcal/mol), which are slightly higher than those of LLM-200. In addition, f-PN has higher detonation velocity (9.01 km/s) and propelling ability (106.9 %). Excellent performance parameters of f-PN, superior to LLM-200, are accompanied by low thermal sensitivity despite of the electrostatic repulsion between oxygen atoms of nitro groups. The homolytic cleavage of CNO2 bond being the most favorable decomposition channel requires 62.3 kcal/mol, which is ~15 kcal/mol higher than that of LLM-200 (Table 3). The CONO isomerization of f-PN, although requires 50.8 kcal/mol, becomes a predominant decomposition channel at low temperatures due to a relatively low pre-exponential factor log(A, s-1) = 13.5. The only minor drawback of f-PN is its relatively low stability to impact sensitivity as can be seen from a comparison of Pcr values. The next compound, f-PNA (Figure 6b), which is obtained by a replacement of two nitro groups with amino groups in f-PN, shows the significantly improved thermal and mechanical stability due to electrostatic attraction (Figure 7b) between hydrogen atoms of amino and oxygen atoms of nitro groups. We note that several earlier reports showed correlations between a distribution of the electrostatic potential in the molecule and impact sensitivity of the relevant material (see for example, ref.55,56,57 and reference therein). According to these studies, the impact sensitivity of CHNO explosives depends on the degree of internal charge imbalance within the molecule. It appeared that the charge imbalances that affect sensitivity are associated with localized regions of a positive charge build-up over covalent bonds within the molecular frame. It was shown, that sensitivity of aromatic compounds generally increases as the electrostatic potential over the inner portion of the molecule becomes more positive. Following the same logic, we conclude that f-PNA material should demonstrate relatively low impact sensitivity due to relatively even distribution of electrostatic potential (see Figure 7b) and the absence of areas with the increased positive



electrostatic potential. On the other hand, much positive surface potential in the central part of fPN molecule relates to considerably higher sensitivity of the material. Thus, the decomposition of f-PNA is triggered by a slow CONO isomerization with the activation energy of 61.1 kcal/mol and pre-exponential factor of log(A, s-1) = 14. The homolytic loss of the NO2 group requires 73-79 kcal/mol and dominates decomposition of f-PNA at high temperatures. A high value of Pcr (7.2 GPa), six times higher than Pcr of f-PN, points toward extremely low impact sensitivity of the material. As usual, however, the replacement of nitro groups with amino groups leads to a reduction of the formation enthalpy, density and propelling ability. Consistently, similar trends were observed in the LLM series molecules18 upon the replacement of one of the nitro groups with an amino group. Among certain advantages of having the pyrazole rings in the composition of the fused heterocyclic molecules is an ability to tune performance and stability of the compound through varying functional groups. For example, adding four nitro groups in f-PN serves to significantly improve performance of the material relative to LLM-200 and PHE series compounds. The replacement of two nitro groups with amino groups tends to maximize overall stability (especially mechanical) of the f-PNA compound. Attractive high densities and formation enthalpies of f-PN and f-PNA compounds as compared to LLM series compounds18,19 including LLM-200 are also noted.


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Figure 7. The electrostatic potential distribution (mapped using MP2/6-31+G(d,p)//M06/631+g(2df,p) method) and Mulliken atomic charges (in parentheses) of a) f-PN and b) f-PNA molecules. The calculated bond distances are shown in Angstroms.

3.4

Fused heterocycles with triazole rings In f-TN-1 and f-TN-2 molecules (Figure 6 c and d, Table 2), two outer pyrazole rings are

replaced with two triazole rings. Two nitro groups are connected to carbon atoms of the triazole rings. Both molecules have planar structures. f-TN-1 is a more stable isomer and lies 22.7 kcal/mol lower in energy than f-TN-2. Therefore, we assume that synthesis of f-TN-1 will deliver higher yield than of f-TN-2. f-TN-1 demonstrates higher density (1.97 g/cc) than f-TN-2 (1.71 g/cc), while f-TN-2 has a higher formation enthalpy (212 kcal/mol). The calculated formation enthalpies of both f-TN-1 and f-TN-2 are noticeably higher than that of LLM-200 (182.3 kcal/mol). In addition, f-TN-1 and f-TN-2 compounds exhibit higher thermal stability than LLM-200 due to higher



activation barrier (~52 kcal/mol vs 48.8 kcal/mol) and lower pre-exponential factor of the predominant decomposition mechanism, the CONO isomerization reaction. A comparison of Pcr values suggests that f-TN-1 is less sensitive to a mechanical impact than f-TN-2 as well as f-PN and LLM-200. The relatively low sensitivity of f-TN-1 is combined with an attractive high performance, as its detonation velocity (8.86 km/s) and propelling ability (102.8 %) are higher than these of LLM-200 (8.78 km/s and 102.1%). f-TN-2 is inferior to LLM-200 in terms of performance and sensitivity to a mechanical impact. A comparison of f-PN and f-TN-1 shows that the replacement of pyrazole rings with triazole rings increases the formation enthalpy of the material (Table 3). f-TN-1 with two outer triazole rings has also higher Pcr than its counterpart f-PN with two pyrazole rings, which advocates for its lower impact sensitivity. In addition, f-TN-1 demonstrates higher thermal stability than f-PN. 3.5

Fused heterocycles with a combination of pyrazole and triazole rings To complete design and characterization of fused nitro compounds, we built fused heterocyclic

molecules containing both pyrazole and triazole rings. The first molecule, f-PTN (Figure 6 e), has three nitro groups attached to carbon atoms of the rings. It has performance parameters, formation enthalpy (199.5 kcal/mol), density (1.98 g/cc) detonation velocity (9 km/s) and propelling ability (106.7 %), superior to those of LLM-200. f-PTN also demonstrates improved thermal stability and impact sensitivity relative to LLM-200 as can be seen from Arrhenius parameters (Ea=50.6 kcal/mol and log(A, s-1)=13) of thermal decomposition and critical pressure of detonation initiation (Pcr=1.51), collected in Table 3. The f-PTNA molecule is made from f-PTN by replacing one of the nitro groups with an amino group (Figure 6f, Table 2). As a result, f-PTNA has lower performance than f-PTN, which is reflected in lower formation enthalpy (181.7 kcal/mol), density (1.95 g/cc), detonation velocity (8.54 km/s) and propelling ability (99.3%). At the same time, f-PTNA has lower thermal and impact sensitivity as it is seen from relatively high activation energy (52.7 kcal/mol), low pre-exponential factor (log(A, s-1)=13) and high critical pressure of detonation initiation (4.18 GPa). A combination of pyrazole and triazole rings in f-PTN tends to increase enthalpy of formation of the compound relative to molecules containing either two pyrazole (f-PN) or two triazole (f-TN1) rings. Impact sensitivity of the f-PTN is to be lower than that of f-PN but higher than of f-TN-1 judging by Pcr values. According to our calculations, f-PTN exhibits thermal stability close to f-


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TN-1, whereas performance parameters (, D, Qc) of the material containing both pyrazole and triazole rings is analogous to f-PN compound containing two pyrazole rings and four nitro groups. Therefore, we conclude that a combination of both pyrazole and triazole rings in f-PTN allows us to produce a compound with high performance comparable to that of pyrazole-based f-PN material and attractively high thermal and impact stability close to that of f-TN-1 – a molecule containing two triazole rings. A comparison of amino compounds shows that f-PTNA – a compound containing both pyrazole and triazole rings, has higher density, formation enthalpy detonation velocity and propelling ability than pyrazole-based f-PNA. At the same time, thermal stability and impact sensitivity of f-PTNA are inferior to f-PNA as it can be seen from reaction kinetics and Pcr values collected in Table 3 and reaction rates depicted in Figure 8.



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Table 3. Safety, performance, and sensitivity parameters of fused energetic materials Testing LLM-200 parameter Chemical C8N10O8 Formula ρ, g/cc a 1.940b 0 ΔHf 298, 182.3 kcal/molc Oxygen -35.2 balance, % Ea, 48.8 (kcal/mol)d log(A, s-1)d 15 e D, km/s 8.78f P, GPae 37 e Pcr, GPa 1.47f Qc, kcal/kge 1400f  % rel 102.1f RDXe

f-PN

f-PNA

f-TN-1

C8N10O9 C8H4N10O5 C6N10O5

f-TN-2

f-PTN

f-PTNA

C6N10O5

C7N10O7

C7H2N10O5

1.98

1.93

1.97

1.71

1.98

1.95

186.7

154.4

190.3

212.2

199.5

181.7

-29.5

-38.1

-65.6

-65.6

-36.0

-52.3

62.3

61.1

51.9

51.4

50.6

52.7

18 9.01 39 1.19 1471

13.8 8.24 36 7.22 1091

13 8.86 38 2.30 1332

13 8.20 29 1.24 1372

13 9.00 39 1.51 1437

13 8.54 38 4.18 1027

106.9

95.6

102.8

92.7

106.7

99.3

a Calculated

in this study using MAC approach From Ref.18 c Enthalpies of formation calculated in this study using M06/6-31+G(2df,p) method d Activation barriers and pre-exponential factors of gas phase decomposition reactions were calculated using M06/6-31+G(2df,p) method (See SI for more details) e Explosive parameters were calculated in this study using statistical analysis f Calculated explosive parameters taken from Ref.18 b

Figure 8. Reaction rates of the predominant low temperature decomposition channels of the various fused heterocyclic molecules are shown in comparison with LLM-200 and PHE-5.


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4

Discussion

In contrast to synthesis and experimental characterization that are usually expensive and time-consuming, a coupled combination of ab initio and group additive theoretical methods represents a powerful alternative for computational design and characterization of new high explosive materials with targeted properties. Heterocyclic energetic materials are considered as attractive potential candidates for a replacement for conventional high density energy materials, such as PETN, RDX, HMX and TNT. Heterocycles also enable an intriguing opportunity for a careful, methodical exploration of the structure-property correlations and new ways for tuning performance and stability of the material through a variation of atoms within hetero rings, a consequence of the rings within the molecule, and a number and type of the different functional groups (e.g., -NO2 and -NH2). We began our study by modeling linear oxadiazole energetic molecules, which were built using 1,2,5-, 1,2,4- and 1,3,4-oxadiazole rings as Lego building blocks18,19. We showed how performance and stability of the material can be tuned through variations of these rings. Thus, LLM-200 with two outer 1,2,5-oxadiazole rings connected to two central 1,2,4-oxadiazole rings demonstrates performance and stability superior to benchmark RDX (Table 1), though thermal stability of the LLM-200 molecule was found to be inferior to other C-nitro explosive molecules, such as FOX-7 and TATB, due to a low activation energy required for breaking the outer 1,2,5oxadiazole rings. To investigate potential ways for improving stability of the LLM-200 compound, we created several molecules by varying 1,2,4- and 1,3,4-oxadiazole rings and calculated their performance and stability parameters. We found that replacing the outer 1,2,5-oxadiazole rings in LLM-200 with more stable 1,2,4-oxadiazole rings (PHE-4 molecule, Figure 1) tends to improve thermal stability and impact sensitivity of the material, but at the same time, leads to a decreased overall performance of PHE-4 (relative to LLM-200) due to its lower density, formation enthalpy, detonation velocity and propelling ability. On the other hand, the material containing both 1,2,4and 1,3,4-oxadiazole rings (PHE-5, Figure 1) is less sensitive to thermal and mechanical impact than LLM-200 as can be deduced from the calculated Arrhenius parameters and critical pressure of detonation initiation (Table 1). The relatively high density, detonation velocity and propelling ability indicate high performance of PHE-5 (Figure 9).



Acknowledging all the advantages of the oxadiazole-based compounds, our study concluded that their stability and performance can be tuned only within a certain range, whereas significant improvements of explosive parameters can hardly be achieved by considering only linear molecules and combinatorics of oxadiazole rings. A new class of materials is needed to address the challenge. Motivated by our gained understanding of a series of linear isomers and discovered structure-property-function correlations, we moved to explore further design of promising fused energetic materials. We showed that attaching of the pyrazole and triazole rings to the molecular core framework built from the central pyrazine ring and one outer oxadiazole ring is an efficient way to compose candidate explosive materials with desired improved properties. For example, properties of the pyrazole-based f-PN and f-PNA compounds can be tuned by varying the number of nitro and amino groups. Thus, f-PN compound with four nitro groups has the highest performance among the studied fused and linear molecules (Tables 1 and 3, Figure 9). On the other hand, a replacement of two nitro groups with amino groups in f-PNA allows us to significantly improve thermal and mechanical stability of the material while losing in performance (Figure 9). The formation enthalpy of f-PN, its thermal and impact sensitivity can be improved by the replacement of pyrazole rings with triazole rings. The resulting f-TN-1 compound has a higher Pcr and lower rate of decomposition than f-PN. We further showed that f-PTN, a compound, the molecular structure of which has a combination of pyrazole and triazole rings, demonstrates high performance, close to f-PN compound, containing two pyrazole rings and four nitro groups. In addition, f-PTN has high thermal stability (Table 3, Figure 8), similar to f-TN-1, - a compound with two triazole rings, - and impact sensitivity higher than f-PN but lower than that of f-TN-1. We also note that f-PTN has the highest formation enthalpy among studied materials with the only exception of f-TN-2. Figure 9 illustrates structure-stability-performance relationships of various classes of heterocyclic compounds. For example, linear oxadiazole based compounds PHE-5 and PHE-3 have critical pressure of detonation initiation higher than that of LLM-200, but lower formation enthalpies and propelling abilities. f-PNA and f-PTNA compounds have high values of critical pressure of detonation initiation but demonstrate relative low propelling ability. Figure 9 also shows that f-PTN and f-TN-1 have overall performance and stability superior to LLM-200. f-PTN demonstrates higher performance than LLM-200 due to higher values of formation enthalpy and


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propelling ability, but at the same has lower pressure of detonation initiation and, hence, lower impact sensitivity.

5

Conclusions

We designed, modeled and characterized a series of the potential linear and fused heterocyclic explosive compounds by means of methods of quantum chemistry coupled with a semi-empirical statistical analysis. On one hand, heterocyclic energetic compounds provide an intriguing opportunity for combinatorial design of new classes of energetic materials with targeted performance and sensitivity properties. On the other hand, a combination of different heterocyclic rings and functional groups within linear and fused molecules offers ways for an accurate analysis of structure-property correlations of the materials, which is the key for rational design of new materials. Proposed compounds with best combinations of performance and sensitivity parameters can be considered as potential candidates for synthesis and experimental characterization.

Figure 9. Mapping new heterocyclic explosives. Designed materials are compared to benchmark etalon RDX. Blue arrows show the direction for improved materials characteristics.



Supporting Information Supporting Information Available: Structures of molecules, atomic coordinates of transitions states and products for each decomposition reaction, calculated Mulliken charges, and plots of electrostatic potential are provided. This material is available free of charge via the Internet at http://pubs.acs.org. ACKNOWLEDGMENTS This research is supported in part by ONR (Grant N00014-16-1-2069) and NSF. We used DOE NERSC resources (Contract DE-AC02-05CH11231) and University of Maryland supercomputing resources (http://hpcc.umd.edu). The authors are grateful to Dr. P. Pagoria and his team for comments on the manuscript and for his invaluable advice on feasibility of synthesis of the proposed compounds. MMK is grateful to the Office of the Director of National Science Foundation for support under the IRD program. Any appearance of findings, conclusions, or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of NSF and other funding agencies.


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III. Fused Heterocyclic Energetic Compounds

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