Predictive methods for the heat of decomposition of reactive chemicals: From CHETAH, QSPR, and quantum chemical calculations to deep learning

3.1. Commercially available rapid and simplified predictive approaches

CHETAH is a sophisticated chemical thermodynamics and energy release (hazard) evaluation tool developed by the E27.07 Committee of the American Society for Testing and Materials (ASTM) [31]. Initially launched in 1974 and updated to its eleventh iteration in 2020, CHETAH’s primary function is to predict energy release hazards and assess the potential explosiveness risks of chemical substances or mixtures by providing thermodynamic data. For instance, in the case of the classic explosive 2,4,6-trinitrotoluene (TNT), CHETAH’s process for predicting enthalpy of formation and maximum heat of decomposition is schematically outlined in Figure 2. At its core, CHETAH employs the Benson group contribution method to estimate the enthalpy of formation of compounds, which is then used to calculate decomposition enthalpy, reaction heat, entropy, and other thermodynamic parameters. The Benson group contribution method, developed by S. W. Benson, is a semi-empirical technique that estimates the enthalpy of formation by decomposing a compound into fundamental molecular fragments (or groups) and using the known thermochemical data of these groups to surmise the overall enthalpy of formation [32]. In the prediction process for the heat of decomposition, CHETAH employs a method known as “maximum heat of decomposition” [33], which assumes that all energy released during the thermal decomposition of reactive chemicals originates intrinsically from the compound itself, with decomposition products limited to those possible formations allowed by the inherent atomic composition. Consequently, the program performs a database search for products to maximize heat of decomposition, typically selecting small, stable molecules such as water, methane, graphite, and carbon dioxide as plausible decomposition products. Although this calculation approach may not be entirely accurate from a thermodynamic perspective, since it omits the entropy component and does not perform a free energy minimization procedure, it remains the most efficient and widely applicable method available today. Despite its limitations, CHETAH is widely utilized and recognized in chemical hazard assessment and energy release prediction due to its simplicity, speed, and relatively high applicability.

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Figure 2.

A schematic diagram of the process for maximum heat of decomposition in CHETAH.

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To further explore the prediction of thermodynamic properties of chemical reactions, particularly regarding the thermal hazard evaluation of primary reactions (those anticipated during the manufacturing process) and secondary reactions (undesired sequential or side reactions), Theodor Grewer et al. [11] utilized CHETAH to estimate the reaction heats of main reactions (e.g., polymerization, diazotization, and hydrogenation reactions) alongside the heats of decomposition of secondary reactions (e.g., decomposition reactions). By comparing the thermodynamic data predicted by CHETAH with reaction heats and decomposition enthalpies obtained through experimental methods, research findings indicated a strong correlation between predicted and experimental values, highlighting the significant utility of CHETAH in assessing the thermal hazards of chemical reactions.

Additionally, Pasturenzi et al. [14] employed the CHETAH program to construct a risk database encompassing the heats of decomposition and Energy Release Potentials (ERP) of 342 commonly encountered chemicals, thereafter comparing predicted results with experimental data to verify the accuracy of the program’s predictions. Selected comparisons of predicted and experimental results are presented in Table 3, illustrating that CHETAH, as an initial screening tool, offers considerable practicality in evaluating the ERPs of compounds. Although CHETAH generally overestimates the actual heat of decomposition, its prediction reliability remains robust for most functional groups. However, for certain functional groups, such as epoxides, the predicted heats of decomposition accuracy is lower, primarily due to the Benson group contribution method’s incomplete coverage of all possible groups and its disregard for molecular spatial structure, resulting in increased prediction errors in enthalpy of formation. Overall, while CHETAH is an effective tool for assessing chemical thermochemical stability, it requires supplementation with experimental data for further validation and refinement, particularly when dealing with specific functional groups.

3.2. Limitations of the CHETAH program in predicting heat of decomposition

While CHETAH has found widespread application in the domain of heat of decomposition prediction, it continues to confront challenges necessitating enhancement.

4.1. High-precision computational methods for energy calculation

Quantum chemical computations represent an advanced computational approach grounded in the principles of quantum mechanics, capable of investigating molecular and atomic behaviors. These computations specifically aim to predict molecular structures, energies, reaction pathways, and a range of other physical and chemical properties by solving the Schrödinger equation [36,37]. As illustrated in Figure 3, quantum chemical computational methods encompass four principal categories: Hartree-Fock (HF) methods, semi-empirical methods, density functional theory (DFT) methods, and higher-level ab initio methods, such as MP2 and CCSD [38]. Among these, DFT methods have emerged as one of the most widely implemented and successful computational strategies in contemporary quantum chemistry, primarily due to their remarkable computational efficiency and chemical accuracy, particularly when applied to large-scale molecular systems. The core philosophy of DFT stems from the Hohenberg-Kohn theorem, which posits that all ground state properties of an atom or molecule are uniquely determined by its electron density. Leveraging this theorem, DFT method finds an optimal balance between chemical precision and computational cost, becoming an indispensable foundational tool in modern material science and molecular chemistry modeling [39-41].

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Figure 3.

Current quantum chemical methods. HF: Hartree-Fork, ROHF: Restricted Open shell Hartree-Fork, UHF: Unrestricted Hartree-Fork, MIDO/3: Modified Intermediate Neglect of Differential Overlap (Version 3), AM1: Austin Model 1, PM3: Parameterized Model 3, B3LYP: Becke, 3-parameter, Lee-Yang-Parr, LDA: Local Density Approximation, GGA: Generalized Gradient Approximation, CI: Configuration Interaction, CC: Coupled Cluster, MPn: Møller-Plesset Perturbation Theory (n-th order), CCSD: Coupled Cluster Singles and Doubles, CCSD(T): CCSD with Perturbative Triples.

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In the context of current scientific research and technological applications, quantum chemical computations are extensively applied across a wide array of cutting-edge fields, including drug design, material science, environmental science, catalysis, and theoretical and computational chemistry. These computations particularly excel in the domain of thermochemical property calculations, enabling molecular energy computations with accuracy down to sub-kJ/mol levels, thereby facilitating precise predictions of thermodynamic parameters such as enthalpy of formation and phase transition enthalpy [42-44]. Consequently, compared to traditional programs like CHETAH, quantum chemical computation methods significantly reduce errors in calculating a compound’s enthalpy of formation and enthalpy of phase transition, while effectively overcoming the inherent shortcomings and limitations associated with CHETAH’s reliance on the Benson group attribution method. These advantages render quantum chemical computations as indispensable and potent tools in predicting a compound’s heat of decomposition.

In a study aimed at predicting the heat of decomposition of nitroaromatic compounds (NACs), Mathieu et al. [17] employed the semi-empirical RM1 Hamiltonian method to compute the theoretical heat of decomposition. This process commenced by identifying potential decomposition products of NACs, based on the “maximum exothermicity rule”, following a sequence of priority: HF, CF₄, H₂O, CO₂, CCl₄, CO, and HCl, converting residual elements into their corresponding elemental forms where necessary. Subsequently, the RM1 Hamiltonian method was utilized to calculate the theoretical enthalpies of formation of NACs and their decomposition products. Ultimately, these enthalpies of formation data were input into the reaction equation to compute the theoretical heat of decomposition. While the RM1 Hamiltonian method demonstrated superior accuracy in enthalpy of formation calculations compared to the CHETAH program, its precision within the domain of existing quantum chemical calculation methods remains relatively modest, leading to a discernible discrepancy between the theoretical heat of decomposition and the values obtained through DSC. To address this issue, researchers introduced a heat of decomposition correction model, incorporating the electronegativity and chemical hardness parameters of NAC molecules. This correction model is expressed as Eq. (1):

where Δ _dH (DSC) represents the experimental heat of decomposition acquired through DSC experiments, Δ _dH⁰ is the theoretical heat of decomposition calculated via the aforementioned methods, χ denotes molecular electronegativity, and η signifies the chemical hardness of the molecule. Utilizing this correction model, researchers successfully enhanced the predictive precision of heat of decomposition for sealed samples tested via DSC, achieving a more desirable corrective effect.

In the domain of high-energy materials, such as propellants, the thermodynamic properties of these substances are critically important for the development and deployment of advanced high-performance tanks, artillery, electrothermal chemical systems, and naval bombardment systems. Against this backdrop, Rice et al. [45] successfully predicted the enthalpy of formation for high-energy molecules in both gaseous and condensed phases via quantum chemical computations. The structure of some high-energy molecules is shown in Figure 4(a). Initially, adopting the DFT computational method, the enthalpy of formation of high-energy molecular gas phases was calculated using an atom equivalent scheme. Specifically, the equation for calculating the gaseous phase enthalpy of formation is as Eq. (2):

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Figure 4.

(a) The structure of some high-energy molecules. (b) Calculated gas-phase heats of formation and (c) heats of vaporization versus experimental values for 35 energetic molecules.

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where E_i is the energy of molecule i, and ϵ _j refers to “atom equivalent” defined as ϵ _j = E_j - x_j, where E_j is the energy of atom j within molecule i, x_j is the correction for atom j at the employed theoretical level, and n_j indicates the number of j atoms within molecule i. The adoption of the atom equivalent method offers significant benefits, particularly in obviating the need for high-level electron correlation processing or reliance on experimental input data, while effectively correcting inherent computational errors, like zero-point energy discrepancies. This distinctive feature has rendered the method a prevalent and extensively applied tool in gaseous phase enthalpy of formation prediction, not only simplifying the computation process but also enhancing prediction accuracy and reliability to some extent. In this study, researchers compared computational results across different basis sets and functionals, revealing that the B3LYP functional is not only economical and reasonable in calculating enthalpy of formation but also demonstrates high concordance with experimental values for the predicted gaseous phase enthalpy of formation (Figure 4b). Specifically, the RMSE of gaseous phase enthalpy of formation stands at 3.1 kcal/mol, with a maximum deviation of 7.3 kcal/mol from experimental values. Given that the standard state of materials typically corresponds to the condensed phase, predicting condensed phase enthalpy of formation is of paramount importance. To achieve this goal, researchers employed gaseous phase enthalpy of formation and phase transition enthalpies, such as sublimation enthalpy and vaporization enthalpy, utilizing Hess’s Law [46] to extrapolate the condensed phase enthalpy of formation. Hess’s Law is expressed as Eq. (3) and Eq. (4):

Furthermore, researchers formulated a functional relationship between evaporation enthalpy, sublimation enthalpy, and the electrostatic potential of isolated molecules obtained through quantum chemical computations, expressed as Eq. (5) and Eq. (6) [47]:

Here, SA denotes the surface area corresponding to an isosurface at an electron density of 0.001 electrons/bohr³; the electrostatic potential for this isosurface is used to generate two statistically-based quantities, σ²_Tot and υ, where σ²_Tot serves as an indicator of molecular surface electrostatic potential variability, and υ reflects the degree of balance between the positive and negative electrostatic potentials on the molecular surface. Using least squares fitting on these parameters, researchers derived correction coefficients a, b, and c consistent with the enthalpy of phase transition. This method was successfully applied to predict the condensed phase enthalpy of formation, with phase transition enthalpy predictions exhibiting good agreement with experimental data (Figure 4c). To further enhance the predictive accuracy of enthalpy of formation and phase transition enthalpy, Byrd and Rice [16] conducted calculations with a larger basis set (6-311++G(2df,2p)), based on the same computational process, which significantly reduced the prediction error.

In summary, quantum chemical computation methods demonstrate substantial advantages and efficacy in overcoming the CHETAH program’s deficiencies in gaseous phase enthalpy prediction accuracy and addressing the challenges inherent in condensed phase enthalpy calculations.

4.2. Challenges in predicting decomposition reaction equations

Quantum chemistry calculation methods, owing to their high accuracy in energy calculations, can enable precise predictions of enthalpy of formation and phase transition enthalpy, thereby demonstrating potential advantages over traditional methods, such as the CHETAH program, in predicting heat of decomposition. However, despite the significant value of quantum chemistry in this area, its application in predicting the heat of decomposition still faces several inherent limitations and challenges.

Firstly, the prediction of decomposition reaction equations for reactive compounds remains a significant challenge. Like the CHETAH program, quantum chemistry methods typically rely on the “maximum exothermicity rule” as a general approach for predicting decomposition reaction equations. This strategy often leads to overestimations of the heat of decomposition. As previously mentioned, Rice and Hare [15] accurately calculated the gas-phase enthalpy of formation and phase transition enthalpy for explosives using quantum chemistry methods, subsequently employing the “maximum exothermicity rule” to infer the formation of explosive products, ultimately calculating the heat of decomposition of the explosives. However, this strategy, based on the “maximum exothermicity rule”, tends to result in generally overestimated predictions of heat of decomposition.

For the above problems, a significant advantage of quantum chemistry methods lies in their ability to accurately infer the reaction transition states and combine experimental methods to determine the reaction pathways [48-51]. This advantage allows for a deeper theoretical understanding of the microscopic mechanisms of chemical reactions, particularly in predicting the mechanisms of complex decomposition reactions. By leveraging this method, researchers are able to systematically identify specific pathways of decomposition reactions, providing a reliable basis for accurate heat of decomposition calculations. For instance, Gong et al. [52] combined experimental and theoretical methods to investigate the initial decomposition mechanisms of di-tert-butyl peroxide (DTBP), tert-butyl peroxyisopropyl carbonate (TBCP), tert-butyl peroxybenzoate (TBPB), and tert-butyl peroxy-2-ethylhexanoate (TBPEH) (Figure 5). Initially, gas chromatography-mass spectrometry (GC-MS) experiments were conducted to identify thermal decomposition products (Figure 5a), and based on the analysis, decomposition pathways were proposed (Figure 5b). Furthermore, the researchers utilized DFT calculations to compute the energy changes at each step of the decomposition pathway (Figure 5c). The experimental and DFT theoretical results were combined to validate the proposed decomposition pathways from a microscopic perspective. This demonstrates the validity and feasibility of utilizing quantum chemistry methods to infer reaction pathways.

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Figure 5.

(a) The first-level mass spectrogram of DTBP and TBCP. (b) Initial decomposition pathways of DTBP and TBCP. (c) Optimized configuration of reactants, intermediates, transition states and products.

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However, despite the high theoretical accuracy demonstrated by this method, several challenges remain in its practical application. Specifically, the process of inferring reaction pathways is often cumbersome and time-consuming, especially when dealing with multi-step reaction systems, where the computational demands are enormous, leading to prolonged calculation times for heat of decomposition. Additionally, the method’s general applicability is relatively limited, making it difficult to apply to all types of decomposition reactions. Thus, its practical use faces constraints that need to be overcome.

Apart from these primary drawbacks, the use of quantum chemistry software typically requires operators to possess advanced expertise, as the process is relatively complex and the hardware requirements for computational devices are high. To address the challenges related to the complexity of quantum chemistry software operation and the high level of user expertise required, the development of integrated computational software is undoubtedly an effective solution. For instance, the quantum chemistry software T1 is designed for the direct calculation of thermodynamic parameters such as the enthalpy of formation [53]. Its user-friendly design allows users to perform relevant calculations more efficiently.

In conclusion, quantum chemistry methods, while offering significant potential for predicting the heat of decomposition of reactive compounds, face several challenges, particularly in the prediction of decomposition reaction equations. The prediction of these equations often relies on the “maximum exothermicity rule,” which, although simplifying the prediction process to some extent, generally leads to overestimations of decomposition heat, thus impacting the accuracy of the predictions. Furthermore, although quantum chemistry methods can predict reaction pathways, this process is not only time-consuming but also computationally intensive, especially when complex reaction mechanisms are involved, further limiting the method’s applicability and generalizability. Therefore, to overcome these inherent limitations, there is an urgent need to develop more efficient, precise, and widely applicable predictive methods for the determination of decomposition reaction equations.

4.3. Deep learning (DL)-assisted prediction of decomposition reaction equations

4.3.2. Decomposition reaction equation prediction based on LLMs

In response to the challenge of accurately predicting the decomposition reaction equations of reactive compounds, it is possible to develop LLMs specifically tailored for reaction prediction, leveraging advanced DL techniques [79]. These models could serve as a valuable tool to assist in the determination of decomposition reaction equations, thereby enhancing the precision and reliability of the prediction process. For instance, the first billion-scale specialized model for the chemical science domain, ChemDFM, collaboratively released by Zhao et al. [80], showcases the ability to predict reaction product structures given specific reactants and conditions. The construction of ChemDFM primarily consists of two processes: domain pre-training and instruction tuning (Figure 6a). Firstly, to address the lack of domain-specific knowledge in general LLMs, the research team employed a multi-source data fusion strategy to construct a high-quality chemical corpus comprising 34 billion tokens for domain-adaptive pre-training of the general large model LLaMa. This corpus not only integrates nearly 4 million rigorously screened cutting-edge research articles in chemistry but also incorporates foundational chemical textbooks and reference materials, effectively balancing the dynamics of disciplinary frontiers with fundamental knowledge systems. Secondly, to overcome the bottleneck in chemical semantic understanding of large models, the team developed a structured instruction dataset of 1.7 million entries covering diverse tasks such as molecular identification, property prediction, and reaction prediction, based on PubChem (the world’s largest molecular database) and USPTO (the authoritative chemical reaction database) (Figure 6b). Multi-task fine-tuning significantly enhanced the model’s specialized representational capacity. Experimental validation demonstrates that ChemDFM possesses robust chemical knowledge comprehension and reasoning capabilities, outperforming commercial large models like GPT-4 in numerous chemical tasks. Notably, ChemDFM has achieved exceptional performance in reaction prediction (Figure 6c), proving the practical feasibility of using LLMs for predicting chemical reaction equations.

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Figure 6.

(a) Two-step training procedure to obtain chemical LLM ChemDFM. (b) Itemized list of the instruction tuning dataset. MD: Molecule Description, TBMD: Text-Based Molecule Design, MPP: Molecular Property Prediction, RC: Reaction Completion, MNA: Molecular Notation Alignment. (c) Accuracy scores of different models in reaction prediction and retrosynthesis tasks. YP: Yield Prediction, RP: Reactant Prediction, RS: Reagent Selection, Retro: Retrosynthesis.

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Additionally, the ChemLLM model developed by Zhang et al [81] also possesses reaction product prediction capabilities. This model employs a two-stage instruction fine-tuning strategy (general corpus pre-training + chemical data hybrid optimization), which precisely adapts to chemical task requirements while maintaining the model’s general language capabilities (Figure 7a). Notably, the researchers collected chemical data from numerous online repositories, including PubChem, ChEMBL, ChEBI, and ZINC, and subsequently created a large-scale dataset named ChemData for fine-tuning ChemLLM (Figure 7b). The ChemData dataset utilizes a template-based instruction construction method to transform structured chemical data into natural conversational formats suitable for LLMs training. This dataset comprises 7 million question-answer pairs for instruction fine-tuning, covering extensive chemical domain knowledge, with the categories of these QA pairs aligned with molecular, reaction, and other chemistry-related task categories. Experimental results demonstrate that ChemLLM achieves performance comparable to the commercial large-scale model GPT-4 in multiple chemical tasks, including reaction product prediction.

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Figure 7.

(a) Two-stage instruction tuning pipeline for ChemLLM. (b) The data of ChemData and Chembench. ChemData contains 7 million Instruction Tuning Q&A, aligned with three principal task categories: molecules, reactions, and other domain-specific tasks. ChemBench contains 4k multiple choice, aligned with two principal task categories: molecules and reactions.

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Thus, the development of efficient prediction models integrating DL technologies to assist in precisely determining compound decomposition reaction equations is anticipated to become a promising and forefront research direction with significant application prospects. This research domain not only addresses the shortcomings of current methods in predicting decomposition reaction equations but also promotes further development of thermodynamic parameter prediction through the robust pattern recognition and data-driven prowess of DL.

5.1. Data-driven approaches for predictive modeling

5.1.1. Introduction to QSPR methodology

Quantitative Structure-Property Relationships (QSPR) represent a sophisticated scientific methodology designed to predict the physical and chemical properties of compounds by establishing a mathematical relationship between the properties and molecular structure descriptors. The foundational principle of QSPR is based on the assumption that a quantifiable correlation exists between a compound’s properties and its molecular structure, with such structural features represented by molecular descriptors that encapsulate critical information such as molecular shape, size, and charge distribution [82-84]. The construction of QSPR models involves initially assembling a dataset comprising multiple compounds, each annotated with molecular descriptors and corresponding physical and chemical property values. Subsequently, statistical techniques are employed to ascertain the optimal mathematical relationship between these descriptors and the target properties, thereby enabling accurate prediction of relevant properties for novel compounds (Figure 8). Critical to the predictive performance of these models are both the selection of molecular descriptors and the modeling methodologies employed. Depending on the dimensionality of the molecular descriptors employed, QSPR models may be categorized into multiple dimensions: 1D, 2D, 3D, and even higher dimensions [85,86]. Specifically, 1D descriptors typically include attributes such as molecular weight, atom type counts, number of hydrogen bond donors or acceptors, number of rings, or specific functional groups. In contrast, 2D descriptors are derived from analyzing molecular graphs to compute various molecular indices; 3D descriptors are contingent upon geometric molecular knowledge, such as polar surface area; while 4D descriptors arise from conformation searches or molecular dynamics simulations. As the variety of molecular descriptors continues to expand, increasingly sophisticated ML algorithms, such as k-nearest neighbors, support vector machines, random forests, and artificial neural networks, have been extensively incorporated into QSPR modeling, significantly enhancing the models’ predictive accuracy and generalization capabilities [87-90].

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Figure 8.

Mechanism of QSPR method employing input data representing molecules in 1D to 4D.

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5.1.2. Methods for molecular descriptors screening

The methods for molecular descriptor screening can be categorized into unsupervised and supervised approaches. Unsupervised methods perform dimensionality reduction or redundancy elimination based on the intrinsic properties of descriptors, with principal component analysis (PCA) and its nonlinear extension kernel principal component analysis (Kernel PCA) being representative examples [91]. PCA transforms high-dimensional descriptors into low-dimensional principal components through linear combinations, significantly reducing data dimensionality while retaining most information, though it cannot handle nonlinear relationships. Kernel PCA addresses this limitation by introducing nonlinear mapping via kernel functions. For instance, Wen et al. [92] employed both PCA and Kernel PCA to process 200 topological descriptors in a flash point study, obtaining 8 principal components via PCA and 5 via Kernel PCA (Figure 9). This approach enhanced model stability and simplicity while further minimizing the loss of critical information. However, unsupervised methods do not incorporate target property information, limiting their applicability.

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Figure 9.

Schematic diagram of molecular descriptor screening process using PCA and KPCA.

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Supervised methods are further divided into traditional regression techniques and intelligent search algorithms. Traditional methods include stepwise selection (SS), partial least squares (PLS), and an improved variant of all subsets regression (VSMP). Although intuitive and efficient, these methods exhibit limited performance when addressing complex nonlinear problems or large-scale descriptor pools. Intelligent search algorithms employ optimization strategies to identify globally optimal descriptor combinations. Among these, genetic algorithms (GA) simulate biological evolution, utilizing crossover and mutation operations to screen optimal subsets, combining efficiency with global search capability. Its derivative method, genetic function approximation (GFA), further integrates adaptive regression splines, enabling simultaneous variable selection and model construction [93]. Particle swarm optimization (PSO) mimics bird flock foraging behavior, employing a velocity-position update mechanism to search for optimal solutions, characterized by few parameters and ease of implementation [94]. Ant colony optimization (ACO) guides path selection through a pheromone feedback mechanism, with its probabilistic search nature making it particularly effective for multi-solution problems [95]. Compared to traditional methods, intelligent algorithms can effectively handle high-dimensional, nonlinear data, though a trade-off between computational cost and model complexity must be considered. Currently, these algorithms have become mainstream descriptor screening tools in QSPR research.

5.2. Application of QSPR techniques in heat of decomposition prediction

QSPR technology has found extensive applications across multiple disciplines, particularly in chemical safety assessment and risk evaluation. Research dedicated to the prediction of heat of decomposition for reactive compounds has gradually proceeded, achieving significant advancements. Organic peroxides, given their high energy potential, are widely utilized in industrial and military spheres; however, their thermal instability can present safety hazards during storage and transportation. Thus, assessing the thermal stability of these compounds becomes imperative, particularly focusing on key parameters such as initial decomposition temperature and heat of decomposition, which are crucial for evaluating the thermal stability of organic peroxides. Prana et al. [25] developed a database consisting of experimental heat of decomposition data for 38 organic peroxides and constructed a multiple linear regression model utilizing quantum chemical descriptors derived from DFT computations to successfully predict the thermal stability of organic peroxides (Figures 10a and b). Within this model, all molecular descriptors exhibited similar importance, with concentration emerging as a significant descriptor. Additionally, the descriptors of local softness and NBO charge on oxygen were directly associated with the peroxide bond, corroborating the critical role of peroxide bond dissociation in the decomposition process.

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Figure 10.

(a) Families of organic peroxides. (b) Prediction model and values of the heat of decomposition versus experimental data (Zohari, 2016). (c) Experimental vs. calculated heats of decomposition (Fayet, 2022). (d) Williams’ plot illustrating the applicability domain. (e) Distribution of absolute deviations observed between predicted and measured heats of decomposition in the training and in the validation set.

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Moreover, Zohari et al. [27] employed simpler descriptors, such as the number of carbon atoms, oxygen atoms, and the presence of specific functional groups, to formulate innovative QSPR models for predicting the thermal stability parameters of organic peroxides. This approach obviated reliance on complex quantum chemical computational parameters, thereby rendering the model easier to build and more practically applicable.

Except for organic peroxides, self-reactive substances represent another class of highly unstable chemicals, prone to decomposition during transport, storage, or processing, and potentially resulting in severe outcomes like explosions under extreme conditions. Consequently, evaluating their thermal stability is vital for addressing potential process safety concerns and classification purposes. Fayet et al. [29] have developed a QSPR model targeting self-reactive substances, with the objective of predicting their heat of decomposition. The model leverages three-dimensional molecular structures and SMILES codes, demonstrating effective validation, particularly the SMILES-based model, deemed the most practical tool owing to its robust predictive performance on smaller datasets and its circumvention of intricate quantum chemical computations (Figures 10c-e). Recent trends indicate a preference among researchers to eschew quantum chemical descriptors with high computational costs and time demands, instead opting for simpler molecular descriptors like composition and topology descriptors to construct heat of decomposition prediction models, thus reducing computational burdens and enhancing prediction efficacy.

5.3. Enhancement of QSPR models through DL techniques

QSPR methods exhibit promising potential in the domain of heat of decomposition prediction, primarily due to their capacity to deliver relatively precise predictive outcomes. The fundamental rationale of this method lies in the existence of a quantitative relationship between the compound’s heat of decomposition and its molecular structure; employing statistical methodologies to elucidate this relationship enables the prediction of properties for novel compounds. Thus, compared to the CHETAH program, QSPR methods eliminate the need for calculating the compound’s enthalpy of formation and enthalpy phase transformation, unrestricted by the limitations of the Benson group attribution method regarding comprehensive coverage of all groups and consideration of molecular spatial structures, serving as an effective alternative for heat of decomposition prediction. However, QSPR methods continue to suffer from several challenges: (1) The substantial sample size required to achieve high-precision predictive results poses a formidable hurdle [100,101]. Central to the QSPR approach is the dependence on statistical methodologies to establish mathematical relationships between molecular descriptors and target properties, thereby necessitating extensive, high-quality sample data for accurate predictions. (2) The applicability range of predictive models is relatively constrained [102,103]. For different classes of compounds, separate predictive models typically need to be constructed, thereby limiting the models’ widespread applicability. Particularly in the domain of heat of decomposition prediction, the challenge of constructing multiple high-precision models becomes particularly pronounced, primarily due to the insufficient sample size of heat of decomposition for any single class of compounds. Despite these challenges, QSPR methods remain a significant focus in chemical safety assessment research owing to their simplicity and efficiency.

Over recent years, DL techniques have been extensively adopted in QSPR modeling due to their robust feature learning capabilities and adeptness at capturing complex patterns. Utilizing deep neural networks, generative adversarial networks, RNN, and other DL techniques has effectively enhanced the predictive accuracy of physical and chemical properties, with promising potential to diminish the need for large sample sizes. The methodology has already secured notable successes in pioneering fields such as drug discovery [104-107]. Notably, Uesawa et al. introduced the “Deepsnap” method, employing compound images as input features for DL, thereby obviating the use of traditional molecular descriptors and achieving superior performance in prediction results (Figure 11) [108-110].

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Figure 11.

Approaches of contrasting traditional and deep QSPR models.

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As a pivotal extension of DL, transfer learning offers an innovative solution to the data scarcity challenge in QSPR modeling. As illustrated in Figure 12, transfer learning mitigates the dependence on target domain data volume by transferring molecular representation knowledge acquired from pre-trained models in source domains (e.g., large-scale compound databases) to target domains (e.g., specific property prediction tasks) [111]. For instance, Li et al. [112] proposed a Convolutional Recurrent Neural Network and Transfer Learning (CRNNTL) framework, which integrates the local feature extraction capability of CNNs, the global sequence modeling strength of RNNs, and transfer learning. By leveraging transfer learning technology to effectively transfer knowledge from larger datasets to smaller ones, this approach demonstrated superior predictive performance across 27 drug and material property datasets compared to conventional methods, substantially alleviating the challenges of small dataset training.

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Figure 12.

Schematic diagram of model construction process using transfer learning.

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Furthermore, Li et al. [113] introduced the MolPMoFiT method, an efficient transfer learning strategy based on self-supervised pre-training followed by task-specific fine-tuning for QSPR/QSAR modeling. The large-scale molecular structure prediction model was pretrained in a self-supervised manner using one million unlabeled molecules from ChEMBL, followed by fine-tuning on smaller chemical datasets with specific endpoints across various QSPR/QSAR tasks. Ultimately, this method outperformed existing DL approaches in tasks such as lipophilicity prediction, HIV inhibition, and blood-brain barrier penetration, demonstrating robust predictive performance even in few-shot learning scenarios.

These groundbreaking advancements indicate that integrating transfer learning with established DL techniques (e.g., Deepsnap) will significantly reduce the sample size requirements for QSPR model construction while enhancing predictive accuracy. Consequently, applying DL techniques to the construction of heat of decomposition prediction models is anticipated to further elevate the accuracy of predictions and provide new breakthroughs for the advancement of QSPR technologies.