Gurney velocity (uG) and cylinder wall velocity (vs) of energetic materials are calculated using the semi-empirical Cγ method, an analytical model previously developed for CHNO high explosives and presently extended to additional elements and to explosives at low loading density. The results are compared to recent procedures based on thermochemical simulations. Regarding uG, both approaches perform similarly well for organic high explosives, with an average relative error close to 2.6%. However, Cγ underestimates uG for tritonal, an explosive with 20-40 wt% aluminium powder. Regarding vs, a newly introduced empirical equation is shown to perform better than the Gurney model, although not as well as a recent correlation involving the detonation energy derived from thermochemical simulations, which are still required to predict cylinder wall velocities with optimal accuracy. With regard to the application of present models to the design of new materials, Cγ is not recommended for metal-containing compounds. However, for the high-thoughput design of organic high explosives, it is an invaluable tool allowing fast and reproducible calculations of Gurney energies with state-of-the-art accuracy. A very simple, hackable Python script is provided for this purpose as supplementary information.

Despite the value of molecular packing (MP) calculations in modeling the properties of organic crystals, its widespread adoption is hindered by the absence of a simple tool broadly accessible to non-specialists, and by the lack of reliability inherent to transferable force fields. To fill these gaps, we describe a versatile workflow, leveraging recent progress in the application of machine learning to the parameterization of interatomic potentials. It is provided as a Python script based only on free academic software running on any Linux system. A key ingredient to this workflow is a recent neural network pretrained to predict bespoke force field parameters for any organic compound on the basis of its molecular diagram. The resulting graph-based force field (GB-FF) is fed into the Tinker simulation engine and applied to crystal structures generated using the USPEX crystal structure prediction package. This low-cost workflow is found to outperform current state-of-the-art procedures based on heavily parameterized force fields, thus demonstrating the value of machine-learned bespoke potential parameters.

The evaluation of the formation enthalpies of energetic salts is hampered by the inability of current procedures to provide reliable lattice enthalpies, partly due to the lack of reference benchmark values. In this context, we report the synthesis and characterization of twenty-one energetic salts, eight of which had never been described before. In addition to density and thermal stability, special care is devoted to the accurate measurement of formation enthalpy. By subtracting experimental formation enthalpies of the salts from the ab initio formation enthalpies of their constitutive ions, benchmark lattice enthalpies are obtained. On the basis of the resulting dataset, some limitations of the widely used volume-based thermodynamics (VBT) approach are highlighted, and a more physically sound alternative that does not involve any fitting parameter is put forward. The latter should be improvable through a more detailed description of the ions and possibly the introduction of a dose of empiricism that will be made possible by the future extension of the present database to include selected literature data and further measurements.

The last few years have seen a steep rise in the use of data-driven methods in different scientific fields historically relying on theoretical or empirical approaches. Chemistry is at the forefront of this paradigm shift due to the longstanding use of computational tools involved in the calculation of molecular structures and properties. In this paper, we showcase examples from the literature as well as work in progress in our lab in order to give a brief overview on how these methods can benefit the energetic materials community. A deep learning approach is compared to "traditional" QSPR and semi-empirical approaches for molecular property prediction, and specificities inherent to energetic materials are discussed. Deep generative models for the design of new energetic materials are also presented. We conclude by giving our view on the most promising strategies for future in silico generation of new energetic materials satisfying the performance/sensitivity trade-off.

Due to the lack of well-established procedures to estimate the lower flammability limit (LFL) of arbitrary fuel-air mixtures, we report therein a simple method derived from a relationship introduced over 80 years ago for C–H–O molecules and presently extended to molecules containing C–H–N–O–F–Cl–Br–I–Si–P–S elements. The LFL was usually found to represent a constant fraction α≃1/2 of the stoichiometric concentration of fuel, except for halogen compounds for which α increases with the fraction of halogen atoms in the fuel molecules. Interestingly, this extremely simple scheme, which could be then easily integrated into any molecule design workflow, indicates that LFL values are mainly determined by the element count on the fuel structure, in sharp contrast with the premises underlying quantitative structure–property relationship (QSPR) and group contribution (GC) approaches.

New procedures to estimate the impact sensitivity of energetic materials are derived from an earlier semiempirical model correlating the drop weight impact height h50 to the rate constant k for the propagation of the decomposition process, assumed to be the limiting step. The new models are obtained by removing step by step the empiricism in the evaluation of k. We end up with a full ab initio expression for this constant in terms of theoretical activation energies and prefactors. The resulting model casts doubt on a previously introduced assumption regarding the temperature at the reaction front. Moreover, it questions possible interpretations of semiempirical estimates. A systematic comparison against alternative methods shows that although somewhat less accurate than its earlier semiempirical version, this ab initio model shows a predictive value similar to heavily parameterized approaches. The results imply that the decomposition kinetics accounts for at least 50% of the variation in the logarithms of drop height data.

Total electronic energies and frequencies predicted using the deep learning models ANI-1x and ANI-1ccx are converted to gas-phase formation enthalpies Δf H0 using an atom equivalent (AE) scheme for a database of CHNO compounds. As expected from the accuracy of those models in predicting reference DFT frequencies and DLPNO-CCSD(T)/CBS energies, this procedure usually outperforms DFT-based AE schemes. However, for some compounds, including energetic molecules, significant deviations from experiment are observed, larger than obtained using DFT procedures. A close examination of the GDB-11 database from which the training data was drawn reveals that many structures of interest in the energetic materials community are excluded from this extensive compilation primarily focused on drug discovery and designed with stability constraints in mind. This points to the urgent need to set up a comparable database including energetic species of interest for the design of energetic materials such as propellants or explosives.

Assessing the value of new compounds as components of energetic materials requires the determination of a significant amount of data, including sensitivities to various stimuli. Unfortunately, the dependence of these properties on molecular structure is still poorly understood. In view of estimating their values for putative high energy molecules, standard quantitative structure-property relationship (QSPR) methodologies are widely used. In doing so, a special focus is put on standard descriptors and formalisms. To foster further progress through consideration of alternative approaches, this article emphasizes how the Python language and associated libraries make it straightforward to implement arbitrary models, including schemes a la Keshavarz based on the occurrences of highly specific molecular fragments as well as the non-linear expressions naturally arising from physics-based approaches to sensitivities. Two previously published models are implemented for illustrative purposes. The first one is a simple fragment-based equation for electric spark sensitivity of nitroarenes. The second one is a model for impact sensitivity of general molecular energetic materials. In each case a Python implementation is provided as supporting information and may be used as is or serve as a template to implement alternative schemes.

The octanol-air partition coefficient (KOA) is useful to assess the fate of organic chemicals in the environment. Very recently, an interesting comparison of current methods to predict this property (Chemosphere 148 (2016) 118–125) highlighted a newly introduced Quantitative Structure−Property Relationship (QSPR), as a group-contribution (GC) method and a quantum chemical solvation model were reported to yield significantly less accurate results. Based on the observation that the so-called GC method investigated in this earlier study was inconsistent with the temperature dependence of KOA, the previously recommended QSPR is presently compared to the geometrical fragment (GF) additivity scheme. In addition to providing some improvement in terms of accuracy, this fragment-based procedure exhibits many advantages in terms of simplicity, interpretability, applicability and availability.

In view of developing a procedure to predict the dielectric constant (εr) of pure liquids from molecular structure, a thorough analysis of prominent factors affecting this property is carried out. The results suggest that the orientational dipolar parameter gμ2 involved in the Kirkwood-Fröhlich theory may be estimated as a sum of additive contributions (gμ2)i associated with suitably defined polar fragments i. Associated with third-party models for the molar volume Vm and the refractive index nD, this provides a practical route to predicting εr for new compounds. Advantages over previous methods include: simplicity, as the present model relies on fragment-additivity and does not require 3D structures; sound physical bases; demonstrated applicability to polar liquids with εr values up to 200; predictive ability extensively demonstrated against large datasets (for a total of 1220 compounds) covering a broad structural diversity, resulting in values of the root mean square deviation/average percent error as low as 3.7/10% for data sets focused on simple organic compounds as considered in previous studies, although the inclusion of many alcohols in the data set leads to poorer statistics (5.0/32%) due to the lack of specific parameters for hydroxyl groups in distinct environments. The approach should be of special interest in the current search for new aprotic electrolytes aimed at improving the performances of electrochemical energy storage systems. Although its reliance on many fitting parameters restricts its domain of applicability, the present implementation is recommended over current procedures whenever possible. A Python script is provided to allow its straightforward application.

An atom pair contribution (APC) model aimed at predicting the gas-phase formation enthalpy (ΔfH°) of molecules is reported. In contrast to bond contribution (BC) or group contribution (GC) methods, it relies on increments associated with pairs of bonded and geminal atoms along with 15 structural corrections. Another distinctive feature of the present APC method is the large amount of experimental and high-level theoretical data specially compiled in this work to fit and validate the model (2671 entries). Unlike GC methods, the present APC model has wide applicability with the number of adjustable parameters limited to 68. Although it requires only a structural formula as input and involves only back-of-the-envelope calculations, it is more reliable than state-of-the-art quantitative structure-property relationship methods, popular semiempirical Hamiltonians, and even low-level density functional theory approaches based on gradient-corrected functionals. It is therefore a valuable tool for fast screening applications or whenever chemical accuracy is not necessary.

In view of its success in predicting sublimation enthalpies of molecular crystals near triple point conditions [Ind. Eng. Chem. Res. 2012, 51, 2814], the geometrical fragment (GF) approach is presently used to estimate standard values Delta H-sub(0) adjusted to the reference temperature of 298.15 K. The resulting GF(0) scheme is fitted against theoretically confirmed Delta H-sub(0) data for 185 high nitrogen compounds and validated using organic compounds not used in the fitting process. It is subsequently used to predict the solid-state formation enthalpy Delta H-f(0)(cr) of 40 energetic materials, combined with either correlated ab initio methods or simple models to estimate the gas-phase contribution. The combination of GF(0) with ab initio data yields Delta H-f(0)(cr) values with state-of-the-art accuracy. Combined with the simple atom pair contribution model, this procedure predicts Delta H-f(0)(cr) with better accuracy and stronger physical grounds than alternative low-cost methods.

The microscopic behavior of vapors of nitroaromatic compounds (NAC) interacting with the surface of sensitive materials is studied using molecular dynamic simulations, in view of contributing to the development of sensors capable of detecting trace amounts of these explosives in the atmosphere. More specifically, we consider two NAC target, namely trinitrotoluene (TNT) and 2,4-dinitrotoluene (2,4-DNT), along with three kinds of silica surfaces: standard silica with hydroxyl groups at its surface (Silica-OH), ethoxylated (Silica- OEt/OH) and methylated (Silica- Me-2/OH) silica. The latter surface is of practical interest for sensing applications. These systems are simulated under various humidity conditions, ranging from a dry to a rainy weather environment. The simulations are carried out at high temperature and extrapolated to ambient temperature according to a previously established procedure. The results show that both water and NAC adsorb rapidly onto silica surfaces by avoiding the carbons of the ethoxy or methyl groups. Under dry conditions, TNT, and to a lesser extent 2,4-DNT, lie parallel to the silica surface. Interestingly, despite their close structural similarity, these two molecules exhibit strikingly different responses to humidity regarding their orientation with respect to the Silica- Me-2/OH surface. Indeed, on going from dry to wet conditions, the alignment of TNT becomes more random, whereas the parallelism of 2,4-DNT molecules becomes more pronounced.

Understanding the impact of atmospheric aerosols on the global radiative balance requires knowing the refractive index (RI) of their components. Currently available methods to estimate this property from molecular structure are mostly empirical and exhibit significant errors (<10%). This work reports a more physically sound model leading to predictions within +/- 5% from experiment. The root mean square relative error is <1% for general organic compounds, and <2% for oxygen-rich compounds of special interest in aerosol chemistry. In this approach, the RI is obtained from the Lorentz-Lorenz equation. The molar volume and polarizability required as input are obtained from the addition of a so-called geometrical fragment (GF) associated with every non-hydrogen atom in the molecule. The value of this GF method to the study of ambient aerosol is demonstrated through extensive validation and application to compounds that may be present in aerosol droplets. In so doing, insight is provided into the origin of significant errors previously noted using earlier methods. Moreover, it is demonstrated that reference values of the refractive index reported in widely used compilations should be considered with caution. Finally, a Python script is provided as supplementary information for easy use of the present model to estimate molar volume and refractive index for any molecule.