Development of a group contribution method to predict the enthalpy of formation of energetic azoles

Coetzee, Megan

Development of a group contribution method to predict the enthalpy of formation of energetic azoles

Thesis / Dissertation

2026

Publisher

University of Cape Town

Department

Department of Chemistry

Faculty

Faculty of Science

Abstract

Energetic materials (EMs) are a class of high-nitrogen content material that stores a large amount of chemical energy released upon external stimuli (e.g., friction, thermal shock, or electrostatic discharge). Azoles, which are five-membered heterocyclic aromatic com- pounds containing a nitrogen atom and at least one other heteroatom, are an ideal source of EMs. The enthalpy of formation (∆fH) is a critical thermodynamic quantity that is required to estimate the detonation performance of EMs (e.g., detonation pressure and velocity). Because physical measurements of ∆fH require time and resources, group con- tribution methods (GCMs) provide an alternative that is quick and cost-effective. A GCM is built on the principle that a property of a molecule can be estimated using the sum of individual contributions associated with its smaller structural units, or groups. The enthalpy of formation of a cyclic compound can be obtained by summing the corre- sponding group additive values (GAV) determined from the acyclic reference molecules and adding a correction accounting for the ring strain (RS). This ring-strain correction (RSC) is generally positive and is calculated from the difference between the known value of ∆fH of the cyclic compound and the sum of the acyclic GAVs. However, if ∆fH of an aromatic compound is calculated in the same way, the resulting correction must account for both the RS and the aromatic stabilisation energy (ASE), where this sum is typically negative. Alternatively, an aromatic compound may also be built directly as a sum over GAVs that have been determined using aromatic reference molecules. The former model has been applied to pyrrole derivatives only, and to the best of our knowledge, although the latter model has been applied to azines, it has not been attempted for azoles. In this work, GCMs based on both approaches were developed using ab initio quantum mechanical (QM) calculations due to the limited availability of physical measurements of ∆fH of azoles. The uncertainty arising primarily from the systematic error or bias associated with the G4(MP2)-6X composite method was first quantified using 47 neutral CHN-containing molecules. Reference ∆fH values for these molecules were obtained from Active Thermochemical Tables (ATcT). A correction of +1.11 kJ mol−1 resulted, while the standard uncertainty associated with this correction is 3.04 kJ mol−1, leading to a 95 % confidence interval of 6.08 kJ mol−1 for the calculated values. Subsequently, a database of 72 acyclic molecules and multiple linear regression (MLR) was used to determine 42 Benson-type GAVs, which were then applied to estimate ∆fH of ten unsubstituted azoles, including pyrrole, two diazoles, four triazoles, two tetrazoles, and pentazole. The sum of RS and ASE was determined as the difference between the calculated ∆fH values and the sum of the acyclic GAVs, providing a GCM based on the strain-centred approach. To extend the work to energetic azoles, the aromatic group approach was then applied and a set of 33 GAVs was obtained using MLR of a database of the calculated ∆fH values of 60 energetic azoles. In addition to unsubstituted azoles, these azoles were also functionalised with a methyl group and explosophoric functional groups such as amine, azide, nitro, and nitramide. The resulting GCM showed a mean absolute error (MAE) of 3.22 kJ mol−1 and maximum error of 10.95 kJ mol−1 for the enthalpy of formation across all functionalised and unfunctionalised azoles.

Keywords

Energetic materials

group additive values

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