In this paper, we present an approach for prediction of the solid-state enthalpy of formation, which is focused (but not limited to) the nitrogen-rich energetic materials, both ionic and molecular. The approach is based on a series of enthalpy of formation predictions, whose results are then used as input descriptors for regression analysis using artificial neural networks (ANN). Training (104 compounds), testing (300 compounds) and validation of the developed ANN was performed for experimental values only. These ANN use 6-7 input descriptors and demonstrate a high accuracy providing mean absolute errors (MAE) being about 10 kcal/mol. The median absolute error (MedAE), which is more relevant to our relatively small dataset, reach the value of 6.6 kcal/mol. The values of these errors for the training dataset are similar indicating the absence of overfitting. On the basis of the obtained ten ANN models, the solid-state enthalpies of formation for 31 cyclo-pentazolate salts are checked and a common agreement with the literature values (calculated data only) is obtained. However, a general trend to overestimation of the reported values is observed. All 10 ANN models demonstrate lower values of enthalpies of formation for cyclo-pentazolate salts for about 40-50 kcal/mol.

In this paper, we present three computational approaches for accurately predicting the crystalline densities of cyclo-pentazolate salts based on three level chemical descriptions, encompassing both metal (Li, Na, K, Mg, Ba, Al, Cu, Ag, Zn, Co, Fe, Mn, and Pb) and organic cations, based on the most comprehensive list of experimentally available crystals (69 examples). The level 1 description involves force-field-based crystal structure prediction. Level 2 employs semi-empirical PM7 calculations of vacuum-isolated crystal bases. Level 3 focuses on empirical formula analysis. Each approach generates a unique set of descriptors used to develop corresponding empirical models through machine learning techniques. The results demonstrate excellent predictive performance for cyclo-pentazolate salts across a wide range of compositions, from simple binary ionic pairs (Cat+An-) to complex multi-ionic structures containing neutral molecular additives. The mean absolute percentage errors (MAPEs) across all models range from 3% to 5%. Prediction at level 3 requires no quantum-chemical or molecular-mechanics calculations, making it applicable to high throughput predictions of any potential cyclo-pentazolate salts without significant structural voids, such as nanocages or nanopores. For novel salts with unusual ionic and/or molecular components, validation using levels 1 and 2, which are based on robust independent methodologies, is recommended.

In this paper, we report the first example of impact sensitivity prediction based on the genetic function approximation (GFA) as a regression method. The prediction is applicable for a wide variety of chemical families, which include nitro compounds, peroxides, nitrogen-rich salts, heterocycles, etc. Within this work, we have obtained 7 empirical models (with 27-32 basis functions), which all provide 0.80≤R2≤0.83 and 7.2 J≤RMSE≤7.8 J (for 450 training set compounds) and 0.64≤R2≤0.70 and 11.2 J≤RMSE≤12.4 J (for 170 test set compounds). The models were developed using Friedman Lack-of-Fit as a scoring function, which allows avoiding an overfitting. All the models have simple descriptors as basis functions and include linear splines. Furthermore, the applied descriptors do not require expensive calculation procedures, namely, non-empirical quantum-chemical calculations, complex iterative procedures, real space electron density analysis, etc. Most descriptors are based on structural and topological analysis and a part of them require very cheap semi-empirical PM6 calculations. The prediction takes a few minutes as an average, and most of the time is for the structure preparation and manual calculation of the descriptor "Increment", which is based on our recent incremental theory.

Chemodynamic therapy (CDT) is a highly targeted approach to treat cancer since it converts hydrogen peroxide into harmful hydroxyl radicals (OH·) through Fenton or Fenton-like reactions. However, the systemic toxicity of metal-based CDT agents has limited their clinical applications. Herein, a metal-free CDT agent: 2,4,6-tri(4-pyridyl)-1,3,5-triazine (TPT)/ [closo-B12 H12 ]2- (TPT@ B12 H12 ) is reported. Compared to the traditional metal-based CDT agents, TPT@B12 H12 is free of metal avoiding cumulative toxicity during long-term therapy. Density functional theory (DFT) calculation revealed that TPT@B12 H12 decreased the activation barrier more than 3.5 times being a more effective catalyst than the Fe2+ ion (the Fenton reaction), which decreases the barrier about twice. Mechanismly, the theory calculation indicated that both [B12 H12 ]-· and [TPT-H]2+ have the capacity to decompose hydrogen into 1 O2 , OH·, and O2 -· . With electron paramagnetic resonance and fluorescent probes, it is confirmed that TPT@B12 H12 increases the levels of 1 O2 , OH·, and O2 -· . More importantly, TPT@B12 H12 effectively suppress the melanoma growth both in vitro and in vivo through 1 O2 , OH·, and O2 -· generation. This study specifically highlights the great clinical translational potential of TPT@B12 H12 as a CDT reagent.

In this paper, we report the first attempt to quantify impact sensitivity using the second-order incremental approach based on the structural features of explosives. It has been found that impact height (h50) can be expressed via a multiplicative incremental exponential form, in which the exponents are characteristic coefficients of structural increments multiplied by their numbers in the molecule. The method was developed on a large array of experimental data (450 molecules and salts) of different energetic materials, namely, nitro compounds, peroxides, nitrogen-rich salts, heterocycles, etc., while testing of the model was performed for 170 compounds. The results demonstrate a noticeable correlation with the experimental h50 values. Thus, the corresponding R2 and RMSE for the training and test sets are 0.56 (12.5 J) and 0.63 (18.8 J), respectively. In this work, we use 53 individual structural increments, but their number can be extended, and the corresponding coefficients can be refined; this allows for increasing the prediction accuracy on-the-fly. The calculation algorithm is discussed, and the corresponding examples are presented. The performed machine-based regression analysis using genetic function approximation, multiple linear regression, and artificial neural network has proven the reasonability and informativity of the proposed incremental theory. Thus, the developed approach significantly extends our understanding of the impact sensitivity phenomenon and translates it into the category of one that can be calculated by a pocket calculator.

The first attempt to use genetic function approximation (GFA) for prediction of aquatic toxicity of soluble energetic materials is reported in this paper. The prediction is based on the estimation of the luminescent bacteria Aliivibrio fischeri inhibition in water according to the recently reported experimental results. Thus, two quantitative structure-activity relationship (QSAR) models for 15 min and 30 min exposure were obtained, which include five and six essential descriptors, respectively. Most of them are so-called "fast descriptors " assuming there is no need for quantum-chemical calculations. The rest descriptors are obtained in terms of semi-empirical approach allowing the prediction to be rapidly complete. The developed QSAR models provide relatively high correlation coefficients, namely, R-2 = 0.81 and 0.82 for 15 min and 30 min datasets, respectively. The experimental datasets included a number of values, which were presented ambiguously (< or > than certain values). Thus, these have not been included (13 for 15 min and 10 for 30 min datasets) in the training sets and used them as the corresponding test sets. As a result, the developed models accurately indicate what exactly the higher and lower values should be applied instead of ones presented with ambiguity. Thus, the results may be useful for predicting the aquatic toxicity of new nitrogen-rich energetic materials, both molecular and ionic, bearing nitro, nitramino, azido groups and other commonly used explosophores.

In this paper, we present a theoretical study of structure and UV-vis spectra of 11 colored complexes of nucleophiles with nitroaromatic energetic materials. Two different schemes were found to be the most suitable for absorption spectra simulation. In the case of covalently bound Meisenheimer complexes, the time-dependent density functional theory (TD-DFT) approach with the TPSS functional was the most accurate. Meanwhile, for intermolecular charge-transfer complexes, the closest spectral pattern was provided by the time-dependent Hartree-Fock (TD-HF) scheme with modified exchange contribution (40%). It has been found that the binding type is determined predominantly by the steric factors and less by the electronic effects of the nucleophile, which was approved by the quantum theory of atoms in molecules (QTAIM) analysis of the formed bond types and nucleophilicity index calculations. For the charge-transfer complex, an appropriate configuration with the intermolecular separation between the local electrophilic and nucleophilic sites (the C1···N distance) of about 3.1 Å, was revealed using both classical molecular dynamics simulations and geometry optimizations in polar continuum. Absorption energies and intensities of the electronic transitions are generally well-reproduced in all 11 cases and demonstrate a local π–π* excitation in the covalently-bound complexes and pure charge transfer in intermolecular system. The applied computational methods allow reproducing of the sample colors with a high degree of similarity, which may find their application for modeling of new reagents with other expected colorimetric characteristics.

Melting point is one of the most important characteristics for molecular engineering of energetic materials. Therefore, methods for prediction of this physical property are essential to the field. In this paper, we have developed two models for prediction of melting point of energetic molecular crystals. The first one uses two parameters (lattice energy and crystal density) and grounds on the correlation of 200 compounds. The second model does not use any calculated quantities (only tabulated data) and is based on 1500 compounds. The first model needs separate calibrations for specific families of compounds; for nitroaromatic compounds, aliphatic nitro- and nitrato compounds and peroxides it provides R2 = 0.82–0.85 and RMSE ≥ 21–54 °C, respectively. Meanwhile, Model 2 is a more universal, but less accurate approach and it was tested for 747 energetic materials of different families providing R2 = 0.62 and RMSE ≥ 64 °C. This makes Model 2 a simple and convenient tool for a fast crude estimation of melting point of a desired energetic molecular crystal using a pocket calculator. Since Model 2 does not need quantum-chemical calculations, it can be effectively applied for any arbitrary composition. In the present work, however, we have considered compounds with a restricted number of constituting elements: C–H–N–O–S–F–Cl–Br–I. Nevertheless, extension of Model 2 is a simple procedure, which assumes estimation of so-called effective densities for other elements via regression analysis of experimentally available data on melting points.

This chapter concerns with response of solid-state properties of energetic materials to the applied mechanical energy (ME) as an initiation factor of impact sensitivity (IS). Particularly, the processes of mechanically and thermally induced electron transfer (ET) as well as phonon-to-valence vibration energy transfer are in the focus of this review. Thus, a number of crystal properties, like band gap compressibility, crystal morphology, bulk modulus, phonons, and other are discussed in terms of IS phenomenon. Described models of IS are applied for aromatic, aliphatic, and heterocyclic nitro and nitrato compounds, metal azides, bistetrazole-based and aryl diazonium energetic salts (ESs). Finally, an attempt is made to compare applicability of features of isolated molecules with properties of its crystalline phases and to highlight their advantages and drawbacks.

In this paper, we report a quantitative structure-property relationship (QSPR) model development for friction sensitivity prediction of nitramine energetic materials. The model is obtained by means of a sophisticated method, namely, genetic function approximation and consists of 10 descriptors. As a training set, we have applied 80 nitramine energetic materials of a few families, both molecular and salt-like. The corresponding test set included 30 compounds. As a result, we have obtained a good correlation with R2 = 0.90. Only two descriptors, the heat of formation and quadrupole components, need semi-empirical quantum-chemical calculations, while the rest ones are so-called “fast descriptors” meaning the relatively short time of the prediction. Using the obtained QSPR model along with our recent method for fast crude estimation of the detonation properties based on empirical formulas we have modified a few energetic salts in order to obtain materials with better friction sensitivity and detonation performance. This was mainly done by changing the constituting ions: thus, 10 nitramine energetic materials with improved characteristics were proposed.

A revision of the mechanism of mechanical-to-vibrational energy transfer in crystals of energetic materials undergone impact loading is proposed. The new approach takes into account previous inaccuracies of normalization of the number of couplings between phonon overtones and conformational vibrational fundamentals ( c), which is critical for comparison of molecules that differ greatly in the number of atoms. Moreover, it introduces two very important damping factors, namely a and b . The a factor allows differentiation of the phonon overtones by their coupling strength; the lower the overtone interacts, the stronger the coupling is. Meanwhile, the b factor is aimed to distinguish the coupling strength itself. This factor is the denominator in the exponent of a Gaussian-type function and determines the rate at which the coupling strength decays with the rise of difference between the interacting phonon overtones and conformational vibrational fundamentals. After a careful regression analysis of cagainst impact sensitivities ( h 50 ) of 30 common nitroexplosives, we have determined the numerical values of these damping factors as a = 2.5 and b = 40 cm-1. The proposed approach is extrapolated on the vibrational spectra of 21 crystalline energetic materials with Z' >= 1 and a general applicability along with limitations of the method are discussed for the family of nitroexplosives and nitrogen-rich (cyclo-pentazolate and 5,5 '-bitetrazole) energetic salts as an example.

A simple and fast procedure for estimation of the effect of chemical functionalization on the change in detonation properties of energetic materials is reported. The procedure consists of two levels. Computations at Level 1 can be performed with a pocket calculator. At Level 2, quantum-chemical calculations are needed, but these include only three computational tasks: vacuum-isolated molecule relaxation (PBE/DND) → crystal structure prediction (COMPASSII) → crystal cell relaxation (PBE/DND). Thus, we have analyzed transformation of both aromatic and aliphatic amines into the corresponding nitramines and diazo compounds. The calculations at Level 1 indicated that both crystal density (dc) and solid-state enthalpy of formation (ΔHf) are always positive and increase detonation properties, while the calculations at Level 2 revealed the amines that are the most sensitive to such chemical transformation.

A theoretical study of the effect of amines-to-pentazoles transformation on the detonation performance is reported in this paper. A quantitative description of the latter is performed for the general case according to our recently developed compositional criterion evaluation algorithm. It is shown that increments of crystal density and enthalpy of formation are both positive meaning a higher detonation performance of the resulting pentazoles. Since the known arylpentazoles are thermally unstable compounds, a simple descriptor of the thermal stability was revealed (R2 = 0.98), which allowed modeling of new pentazoles with expected thermal stability up to 77 °C. Five the most thermally stable structures were then analyzed using high-level first-principles calculations, which provided negative values of the detonation energy for all ionic compounds; this may allow proposing them as safe gas-forming agents. Meanwhile, the relative gain in detonation energy caused by the studied reaction is always positive and can reach 600%. Thus, we have shown that amines-to-pentazoles transformation is an effective tool for enhancing detonation properties when the resulting compound satisfies the thermal stability criterion. Also, we have demonstrated that aromatic/heterocyclic pentazoles may be considered as self-sufficient materials without further modifications by detachment of the aromatic ring.

In this paper, we report a theoretical study of the change in detonation efficiency of energetic amines undergone diazoamination reaction. For this purpose, we selected 17 aminoaromatic and aminoheterocyclic energetic materials, both widely known and newly synthesized, and ranked all possible triazenes derived from them according to our recently developed compositional criterion evaluation algorithm. Then, top ten structures were calculated using quantum-chemical methods to obtain more accurate estimates of their detonation properties, which were calculated using the Kamlet-Jacobs equations. To ensure that input parameters, namely, crystal density (dc) and enthalpy of formation (Delta Hf) are correct, we have benchmarked a number of experimentally known triazenes as well as other structurally similar compounds. As a result, we have obtain good regression coefficients, R 2 = 0.91 (for dc) and R 2 = 0.96 (for Delta H f ). Applying the same quantum-chemical methods for structural building blocks (constituents of triazenes) we have found that diazoamination always increases detonation performance (2-15% for detonation velocity and 0-32% for pressure). Thus, transformation of aminoaromatic and aminoheterocyclic energetic materials into triazenes is a convenient method for enhancement of their detonation properties.

In this paper, we have analyzed the possibility of various neutral and anionic forms of both cyclic and acyclic N-4 species to be recovered to ambient conditions using state-of-the-art computational techniques. Phonon dispersion and mechanical properties calculations as well as ab initio molecular dynamics simulations revealed that syn-tetranitrogen units are kinetically stable only in the form of N-4(4-) anion. Meanwhile, salts of cyclic N-4 (c-N-4, tetrazete) with alkali, alkaline earth metals, and aluminum appeared to be dramatically stable at ambient conditions for a wide range of oxidation states of c-N-4(x-) from x = 1-3. Varying both metal and stoichiometry, one can obtain salts with a wide range of properties: band gap (1-5 eV), bulk modulus (36-196 GPa), enthalpy of formation (from -21 to 660 kJ mol(-1)), and so forth. Thus, crystal structure prediction and comprehensive characterization, which included bonding nature, stability criteria, spectral properties along with thermodynamic and energetic characteristics of c-N-4 and its salts (Na2N8, Li2N4, MgN4, and AlN4) as well as calcium salt of syn-N-4(4-) (Ca2N4) are performed in this work. The obtained results significantly expand our understanding of the possible forms of nitrogen existence in nature, which, if synthesized, can find a number of interesting applications.

An interesting effect was observed when studying explosive and non-explosive crystalline ionic materials at high pressures. A wide benchmark set of 76 crystals of different families was studied using the state-of-the-art methods at ambient pressure and in extremes (at 20, 50 and 100 GPa). It was found that hydrostatic compression leads to an electron transfer from the anion to the cation, which was carried out with different efficiencies for explosive and non-explosive salts. The measure of this electron transfer is reflected in the Hirshfeld charges (q) on cations, which decreased with the rise of pressure. Non-explosive materials are generally resistant to this effect, while explosives are much more susceptible. Thus, at 100 GPa, all the studied energetic salts demonstrate qcat < +0.1e, while for the non-explosive salts qcat > +0.1e. This value can be considered as a conditional boundary between explosive and non-explosive salts. The observed effect is in accord with the Szigeti's dielectric theory as well as with the electrophilicity/electronegativity equalization principle. In the present paper, we develop a mechanism of the explosive decomposition based on the assumption about formation of a radical pair as a result of the following reaction: . The study of such radicals revealed their intrinsic instability, which generally reflects either in a dissociative structure or in the presence of strongly weakened trigger bonds.

In this paper, we report a comprehensive analytical study of the factors influencing the detonation properties of C-H-N-O explosives. Besides the commonly applied parameters, namely, solid-state enthalpy of formation (AN) and crystal density (d(c)), for which simple zeroth-order additive models based on the atomic increments are developed in this work, we also consider compositional factor being an intrinsic characteristic of each single empirical formula. Using a wide number of reference molecules (320 for Delta H-f and 360 for d(c)), we have developed empirical equations, which provide rather good correlation coefficients R-2 = 0.90 and 0.80 for Delta H-f and d(c) respectively. Knowing these two equations and empirical formula, one can predict the detonation properties of a C-H-N-O explosive using a pocket calculator. Of course, such an approach, which completely neglects chemical structure, can be applied mainly for structurally similar compounds. However, having significant differences between the predicted detonation properties of two compositions, the account of their exact structures cannot reorder the predicted values. Thus, this paper can be used as a simple guide for molecular engineering and explosive structure enhancement. For this purpose, we provide a list of all compositions with the predicted properties up to C30H30N30O30 in the Supporting Information. To demonstrate how it works, we have applied the developed approach along with quantum-chemical calculations to model chemical structures outperforming epsilon-hexanitrohexaazaisowurtzitane (the most powerful explosive) in detonation performance.