Graph-theoretical optimization of the aspirin synthesis pathway: Enhancing green chemistry in pharmaceutical manufacturing

Shanmugavel Kannan Rooban Sanjai; Rangarajan Nagarathinam

doi:10.1515/cmb-2025-0027

Artikel Open Access

Graph-theoretical optimization of the aspirin synthesis pathway: Enhancing green chemistry in pharmaceutical manufacturing

Shanmugavel Kannan Rooban Sanjai und Rangarajan Nagarathinam

Veröffentlicht/Copyright: 9. Oktober 2025

Veröffentlicht von

Veröffentlichen auch Sie bei De Gruyter Brill

Manuskript einreichen Informationen für Autor*innen

Aus der Zeitschrift Computational and Mathematical Biophysics Band 13 Heft 1

Abstract

Aspirin, one of the most widely produced and consumed pharmaceuticals globally, presents an ideal case for exploring sustainable synthesis methods in pharmaceutical manufacturing. The conventional synthesis of aspirin, though widely practiced, often suffers from inefficiencies, excessive waste generation, and environmental concerns. This study presents a graph-theoretical framework for optimizing the aspirin synthesis pathway with a quantifiable alignment to green chemistry principles. A directed weighted graph was constructed, representing chemical species as nodes and reactions as edges, with weights derived from empirical reaction energy barriers and environmental impact metrics. Dynamic optimization algorithms, including an adaptation of the Bellman-Ford algorithm and cycle basis analysis, were employed to minimize total energy consumption and waste output. The proposed model achieved a 92% product yield, reduced waste generation by 63% (from 2.2 to 0.8 kg of waste per kg of aspirin), and lowered the energy requirement by 40% compared to the traditional synthesis process. The reaction efficiency index improved by 18.28%, while the average environmental impact factor decreased by 60.32%, validating the environmental and operational benefits of the approach. Although demonstrated using the aspirin pathway, the framework’s modular structure and reliance on quantifiable reaction parameters suggest its potential adaptability to other pharmaceutical syntheses, provided sufficient reaction data are available. This research not only offers a rigorous pathway optimization method but also bridges computational graph theory with industrial green chemistry applications.

Keywords: graph theory; aspirin synthesis; green chemistry; dynamic optimization; pharmaceutical manufacturing

MSC 2020: 05C90

1 Introduction

Aspirin, chemically known as acetylsalicylic acid, stands as one of the most widely produced and consumed pharmaceutical compounds worldwide. Since its commercial introduction by Bayer in 1899, it has played a pivotal role in public health due to its analgesic, antipyretic, anti-inflammatory, and antithrombotic properties [7]. With annual global consumption estimated at over 40,000 tons, aspirin is prescribed for a wide array of ailments including arthritis, fever, cardiovascular disease, and as a prophylactic for stroke and heart attack prevention. Its inclusion in the World Health Organization’s Model List of Essential Medicines underscores its critical value across healthcare systems worldwide [15]. Despite its pharmacological utility and widespread adoption, the conventional industrial synthesis of aspirin continues to pose environmental and efficiency challenges that demand modern reevaluation, especially in light of growing emphasis on sustainable chemical manufacturing.

The traditional method of aspirin synthesis involves the acetylation of salicylic acid using acetic anhydride in the presence of acid catalysts such as sulfuric acid or phosphoric acid. While this route offers high yields and relatively simple processing, it relies on hazardous reagents and generates undesirable by-products such as acetic acid [1]. Moreover, the process often demands elevated temperatures and pressures, which contribute to excessive energy consumption. These characteristics make the process increasingly misaligned with modern environmental standards and sustainability goals. In an era marked by climate change mitigation, circular economy initiatives, and stricter environmental regulations, there is a compelling need to redesign legacy pharmaceutical processes, like that of aspirin, to conform to the principles of green chemistry.

Green chemistry, as formulated by Paul Anastas and John Warner in the 1990s, provides a transformative framework for the design of chemical products and processes that reduce or eliminate the generation of hazardous substances [2]. The 12 principles of green chemistry advocate for preventive approaches to waste, improved atom economy, the use of safer solvents and auxiliaries, and energy-efficient reaction conditions, among others [9]. These principles are particularly applicable to pharmaceutical manufacturing, where high-value products are often produced via energy-intensive and waste-generating multi-step processes. In the context of aspirin synthesis, green chemistry calls for alternative reaction pathways that minimize by-product formation, reduce energy input, and favor the use of benign catalysts and solvents.

The pharmaceutical industry has put significant efforts to adopt greener approaches to drug synthesis. Recent studies have explored various alternatives to the classical aspirin synthesis route. For example, Heravi and Gharib [6] proposed the use of solid acid catalysts such as zeolites and sulfonated carbon-based materials in place of corrosive mineral acids. Their experiments demonstrated reduced corrosion risk and catalyst reusability, which translates to lower operational and environmental costs. Biocatalysis was explored in the literature using acetyltransferase enzymes [8], achieving comparable yields under milder reaction conditions with significantly reduced environmental footprints. Another approach by Montes et al. [11] utilized microwave-assisted synthesis to cut down the reaction time and energy usage by more than 50%, highlighting the potential of alternative energy sources to improve process efficiency. More recently, Solares-Briones et al. [16] implemented solvent-free reaction conditions and mechanochemistry techniques to totally avoid the use of volatile organic solvents. Despite these advancements, challenges remain in achieving a holistic synthesis model that concurrently addresses efficiency, sustainability, and scalability.

One of the key limitations of many existing approaches is their narrow scope – optimizing either yield or waste independently, rather than integrating both dimensions into a comprehensive framework. Furthermore, most methodologies are highly empirical, often lacking a systems-level perspective that accounts for reaction interdependencies, kinetic feasibility, and thermodynamic constraints. This research identifies a crucial gap in the application of computational and mathematical modeling tools, such as graph theory, in the optimization of synthesis pathways under green chemistry criteria.

Graph theory, a well-established discipline in mathematical modeling, has recently emerged as a powerful tool in chemical reaction engineering. In the context of chemical synthesis, graph-theoretical models represent chemical species as nodes and reactions as edges, with edge weights encoding important parameters such as the reaction energy, environmental impact, and reaction time. Notable applications include those of Wang et al. [18], who demonstrated the use of shortest-path algorithms to identify optimal synthetic routes in large reaction networks. Nagy et al. [13] further expanded this approach by integrating real-time process parameters into dynamic graph models, showcasing how computational tools can drive adaptive optimization in industrial systems.

Building upon these computational advancements, this study proposes a novel graph-theoretical optimization framework for redesigning the aspirin synthesis pathway to align with the core principles of green chemistry. A directed, weighted graph is constructed in which intermediates, reactants, and products are represented as nodes, while reactions are mapped as directed edges weighted by energy barriers and waste generation metrics. The graph model is further enriched by incorporating thermodynamic and kinetic data derived from the literature and simulations. To identify the optimal synthesis path, the Bellman-Ford algorithm is applied to minimize cumulative energy consumption, while cycle basis analysis is used to eliminate reaction loops contributing to excessive waste. Additionally, custom metrics such as the reaction efficiency index (REI) and environmental impact factor (EIF) are introduced to quantify the performance of each pathway in alignment with the 12 principles of green chemistry.

The key contributions of this research are threefold. First, it introduces a quantitative and modular framework for green synthesis optimization using graph theory, which enables researchers to simulate and evaluate numerous synthesis routes based on multiple performance criteria. Second, it demonstrates the practical application of this model through a case study on aspirin synthesis, where the optimized pathway achieved a 92% yield, reduced waste by 63%, and lowered energy consumption by 40% compared to the traditional process. Finally, the research presents a scalable methodology with potential applicability to other pharmaceutical compounds, provided that reaction data can be appropriately curated and modeled.

This study positions itself at the intersection of green chemistry and computational process optimization. It not only contributes to the development of sustainable pharmaceutical manufacturing practices but also exemplifies the power of mathematical modeling in transforming traditional chemical processes. The proposed methodology represents a forward-looking approach to synthesis design, one that is not only cleaner and more efficient but also grounded in rigorous scientific computation. As environmental sustainability becomes an increasingly urgent priority across industries, integrating such multidisciplinary tools into chemical manufacturing will be essential for achieving long-term ecological and economic viability.

2 Literature review

The existing body of literature on aspirin synthesis and graph-theoretical modeling provides a solid foundation for advancing sustainable pharmaceutical manufacturing. Significant efforts have been made to improve the environmental and operational efficiency of aspirin production through catalytic innovation, alternative energy sources, and biological synthesis techniques. Concurrently, graph theory has gained traction in chemical engineering as a robust analytical tool for optimizing complex reaction networks. By enabling the visualization and computational evaluation of multiple synthetic pathways, graph-based approaches have shown promise in identifying routes that minimize cost, time, and waste. This dual evolution, toward green chemistry in synthesis and mathematical rigor in optimization, sets the stage for integrative research aimed at overcoming the limitations of traditional methods and advancing process sustainability.

2.1 Synthesis of aspirin

The synthesis of aspirin (acetylsalicylic acid) has been extensively researched since its industrial development by Felix Hoffmann in 1897 while working at Bayer. The classical method, involving the acetylation of salicylic acid using acetic anhydride and an acid catalyst, remains the standard for industrial production. However, challenges such as waste generation and environmental impact have prompted researchers to explore more sustainable alternatives.

Li et al. [10] achieved aspirin synthesis through a rapid and eco-friendly flow esterification process within 2D sub-nanoconfined graphene oxide (GO) membranes. The reaction occurs at room temperature (23°C) with nearly 100% conversion in under 6.36 s, mimicking the efficiency of enzymatic synthesis. Thermally annealed GO membranes act as catalysts, where spatial confinement and surface electronic properties enhance reactivity. This innovative setup offers a safe, energy-efficient alternative to traditional batch synthesis methods.

Zhang et al. [19] synthesized aspirin using a novel cadmium phosphomolybdate crystal as a green solid acid catalyst, featuring a unique 4,8-connected open-framework topology. The catalyst, synthesized via hydrothermal methods, efficiently promotes the esterification of salicylic acid and acetic anhydride at 80°C in 25 min, matching the performance of concentrated sulfuric acid but with reduced environmental impact. Unlike corrosive liquid acids, this solid catalyst offers high conversion, reusability, and operational safety, aligning with sustainable pharmaceutical practices.

Srour et al. [17] synthesized aspirin derivatives by conjugating acetylsalicylate acid chlorides with 4-piperidone-based scaffolds to create novel aspirin–curcumin mimics with potential antitumor and anti-SARS-CoV-2 activities. The synthesized compounds demonstrated enhanced antiproliferative effects across multiple cancer cell lines (A431, HCT116, and MCF7), surpassing standard drugs like 5-fluorouracil and Sunitinib in potency. Additionally, several conjugates exhibited selective COX-2 inhibition and tyrosine kinase inhibitory activity (EGFR, VEGFR-2), alongside promising antiviral properties, suggesting their utility as multi-target therapeutic agents with minimal toxicity to normal cells.

Moreira et al. [12] synthesized biobased carbonaceous composites from a blend of Kraft black liquor and tannin using hydrothermal and pyrolysis methods to develop eco-friendly adsorbents. The resulting materials, RFA and RFC, exhibited oxygen-rich functional groups and mesoporous structures, respectively, enabling effective adsorption of aspirin and paracetamol from wastewater. With maximum aspirin adsorption capacities reaching 91.66 mg/g, these low-cost, renewable composites demonstrate strong potential for pharmaceutical pollutant removal, offering a sustainable solution for water treatment applications.

Building on these studies, this research adopts a graph-theoretical framework to optimize the aspirin synthesis pathway. By representing the synthesis as a network of intermediates and reactions, this approach integrates kinetic and thermodynamic data into optimization algorithms. This methodology aims to bridge the gap between sustainability and industrial feasibility, offering a holistic solution for green pharmaceutical manufacturing.

2.2 Graph theory in chemistry

Graph theory has become an essential tool in the optimization of chemical synthesis due to its ability to model complex reaction networks and identify optimal pathways. In chemical engineering and pharmaceutical manufacturing, graph-theoretical approaches provide a powerful method for visualizing and analyzing reaction mechanisms, optimizing process flows, and minimizing energy consumption and waste generation. Various studies have explored its application in optimizing chemical processes, particularly in areas such as reaction network analysis, synthesis route design, and green chemistry.

Fujita and Smarandache [4] applied graph theory by extending classical graph structures using concepts from non-standard and uncertain set theories – such as neutrosophic sets, fuzzy sets, and soft sets – to model uncertainty in complex systems. Graphing these uncertain sets introduces generalized structures like hypergraphs and superhypergraphs, enabling more expressive and nuanced representations of indeterminacy in real-world data. These innovations bridge combinatorics, set theory, and graph theory, offering a rich framework for mathematical modeling under uncertainty.

Reiser et al. [14] used graph neural networks (GNNs), which model molecules and materials as graphs, where atoms are nodes and bonds are edges, enabling the capture of intricate structural and chemical information. GNNs learn from these graph representations to predict material properties, design novel compounds, and propose efficient synthesis pathways. This graph-based approach leverages the inherent connectivity in molecular structures, making it highly suitable for tasks in chemistry and materials science.

Chen et al. [3] applied graph theory through algebraic graph representations that encode 3D stereochemical information of molecules using element-specific multiscale weighted colored graphs. These algebraic graphs are fused with bidirectional transformer models in a hybrid framework (AGBT) to enhance molecular property prediction across diverse datasets. By integrating graph invariants with deep learning, the method significantly improves accuracy in predicting molecular toxicity, physical chemistry, and physiological properties.

Fung et al. [5] used graph theory via GNNs to model atomic and structural relationships in materials, enabling accurate predictions of properties like crystal stability and surface reactivity. It introduces MatDeepLearn, a benchmarking platform for systematically evaluating GNN performance across diverse datasets in materials chemistry. The research highlights GNNs’ adaptability to complex compositional data via learned representations, while also noting limitations such as high data demands, guiding future improvements in material-focused machine learning.

The use of graph theory in chemical synthesis optimization has proven invaluable in enhancing efficiency, minimizing waste, and promoting sustainability. However, there is still a gap in integrating graph-theoretical models with practical, large-scale industrial applications. This research aims to bridge this gap by applying a dynamic graph-theoretical approach, wherein “dynamic” refers to the framework’s ability to re-optimize synthesis pathways as reaction conditions or data input change. In real-world settings where parameters like temperature, pressure, or catalyst efficiency fluctuate, edge weights (e.g., Gibbs free energy and environmental impact) can be updated. The model’s modularity enables the Bellman-Ford algorithm to be re-applied, generating revised optimal routes that maintain both sustainability and industrial feasibility.

2.3 Research gap

Despite meaningful advancements, the current strategies for optimizing aspirin synthesis often address isolated aspects of sustainability, such as energy efficiency or catalyst safety, without a unified framework that evaluates both environmental and operational metrics holistically. Moreover, while graph-theoretical models have been successfully used to map reaction pathways and identify shortest routes, their application has rarely been extended to simultaneously optimize green chemistry parameters, such as atom economy, energy input, and waste generation, in pharmaceutical contexts. Most existing models remain static, lacking the ability to dynamically adapt to changing reaction conditions or integrate real-time data. This research aims to bridge this critical gap by introducing a dynamic, data-driven graph-theoretical optimization framework specifically tailored for green pharmaceutical synthesis. By applying this model to the case of aspirin, the study contributes a novel methodology that integrates energy and waste minimization objectives, introduces quantifiable sustainability metrics (REI and EIF), and demonstrates a scalable approach for broader application across pharmaceutical manufacturing.

3 Proposed research methodology

3.1 Graph construction

3.1.1 Representation of the reaction network

In order to mathematically model and optimize the aspirin synthesis pathway, a directed weighted graph G = (V, E) was constructed. In this representation, the set of nodes V = { v 1 , v 2 , v 3 , v 4 } corresponds to individual chemical species involved in the reaction sequence, encompassing both intermediates and final products. Specifically, the primary chemical entities included the following:

Salicylic acid ( v 1 ): A core reactant and starting material in aspirin synthesis.
Acetic anhydride ( v 2 ): The acetylating agent.
Acetylsalicylic acid ( v 3 ): The target product (aspirin).
Acetic acid ( v 4 ): A by-product generated during the acetylation process.

The edges E ⊆ V × V in the graph represent chemical reactions that transform one species into another (Tables 1 and 2). Each edge e ij ∈ E is directed from the node v i to v j , indicating the direction of reaction progress. Furthermore, weights are assigned to each edge to capture critical reaction attributes, thereby allowing quantitative analysis and optimization. These weights include the following:

Activation energy (kJ/mol): Reflects the energy barrier associated with the reaction.
Gibbs free energy change (ΔG): Indicates thermodynamic favorability.
EIF: A normalized metric reflecting the degree of environmental burden, combining waste generation and resource inefficiency.

Table 1

Node definitions in the reaction network

Node symbol	Chemical species	Role
v 1	Salicylic acid (SA)	Primary reactant
v 2	Acetic anhydride (AA)	Acetylating agent
v 3	Acetylsalicylic acid (ASP)	Target product (aspirin)
v 4	Acetic acid (AcA)	By-product

Table 2

Edge definitions and descriptions

Edge eije_{ij}	Reaction description
v 1 → v 2	Salicylic acid engages with acetic anhydride
v 2 → v 3	Acetic anhydride yields acetylsalicylic acid
v 2 → v 4	Acetic anhydride concurrently generates acetic acid

This structure enables a multidimensional evaluation of each transformation in the synthesis pathway, thus facilitating optimization based on energy efficiency and environmental sustainability.

3.1.2 Construction of adjacency and weight matrices

To systematically encode the aspirin synthesis pathway, two key matrices were developed:

Adjacency matrix A: A binary matrix representing the presence or absence of direct reactions between species. If a directed reaction exists from species v i to v j , then A[i][j] = 1; otherwise, A[i][j] = 0 (Table 3).

Table 3

Sample adjacency matrix AA

	v 2	v 3	v 4
v 1	1	0	0
v 2	0	1	1
v 3	0	0	0
v 4	0	0	0

Weight matrix W: A numerical matrix encoding the quantitative cost of each reaction (i.e., edge), with entries W[i][j] denoting the associated energy cost or environmental impact for the reaction v i → v j .

The graph structure defined here reflects both the transformation logic and chemical dependencies of the synthesis process. The dual role of acetic anhydride, as a reactant producing both the desired product and an undesirable by-product, is explicitly captured through multiple directed edges, each associated with distinct energy and environmental costs.

This matrix indicates, for example, that a reaction exists from salicylic acid ( v 1 ) to acetic anhydride ( v 2 ), and from acetic anhydride ( v 2 ) to both aspirin ( v 3 ) and acetic acid ( v 4 ) (Table 4).

Table 4

Sample weight matrix WW (energy cost in kJ/mol)

	v 2	v 3	v 4
v 1	50	0	0
v 2	0	30	20
v 3	0	0	0
v 4	0	0	0

These entries quantify the energy costs of individual reactions. For example, the edge from v 1 → v 2 has a weight of 50 kJ/mol, representing a high activation energy, while v 2 → v 3 and v 2 → v 4 exhibit moderate and lower energy requirements, respectively.

The graph-theoretical construction of the aspirin synthesis pathway offers a scalable and quantitative framework for modeling chemical transformations. By assigning multiple attributes to the edges, representing not just chemical feasibility but also sustainability indicators, this graph enables dynamic pathway optimization. The resulting structure serves as the foundation for the advanced optimization algorithms detailed in subsequent sections, including energy minimization via shortest path analysis and waste minimization through cycle elimination strategies.

3.2 Advanced optimization techniques

Following the construction of the directed weighted graph representing the aspirin synthesis network, this section details the advanced optimization techniques used to enhance both energy efficiency and environmental sustainability. The optimization approach integrates two primary objectives: (1) minimizing total reaction energy (TRE) to align with green chemistry principles, and (2) reducing waste generation by eliminating inefficient or redundant reaction cycles. These objectives are achieved through a combination of path-based analysis and graph-theoretical cycle detection methods.

3.2.1 Energy-based pathway optimization

One of the central goals in optimizing a chemical synthesis pathway is the minimization of cumulative energy consumption, which directly correlates with reaction efficiency and environmental impact. To this end, the graph model is analyzed to identify the lowest-energy path from the starting reactant (salicylic acid) to the final product (aspirin).

The optimization begins with a systematic enumeration of all reaction paths between the source node v 1 (salicylic acid) and the destination node v 3 (acetylsalicylic acid). This is achieved using a depth-first search (DFS) traversal algorithm, which exhaustively explores all acyclic paths in the directed graph G = (V, E).

For each candidate path P = {v _i, …, v _j}, the total path cost is computed as the sum of edge weights:

Total energy cost ( P ) = ∑ e ij ∈ P w ( e ij ) .

Here, w ( e ij ) represents the activation or Gibbs free energy associated with the chemical transformation from v i to v j .

After evaluating all possible paths, the algorithm selects the minimum-energy path P * , which satisfies

P * = arg min P ∑ w ( e ij ) .

This path represents the energetically optimal route for synthesizing aspirin and becomes the foundation for subsequent waste minimization and green chemistry assessments.

3.2.2 Waste minimization using cycle elimination

While identifying the minimum-energy synthesis path is essential, the presence of reaction cycles in the network may contribute to excessive waste and resource inefficiency. Cycles often represent side reactions, recycling of by-products, or redundant transformations that do not contribute meaningfully to product formation. Therefore, it becomes critical to identify and eliminate high-waste cycles in the graph to align the pathway with green chemistry principles.

The process begins by applying a cycle detection algorithm to identify all simple cycles C = {v _i → v _j → … → v _i} within the graph. For each cycle, a waste generation score (WGS) is computed using the environmental impact weights associated with each edge:

WGS ( C ) = ∑ e ∈ C EIF ( e ) ,

where EIF ( e ) quantifies the waste or environmental cost of the reaction e . Cycles exhibiting high cumulative EIF values are considered environmentally inefficient and are prioritized for elimination.

The cycle elimination procedure consists of the following steps:

Cycle identification: All cycles are detected using the modified DFS traversal or a dedicated algorithm like Johnson’s or Horton’s cycle basis algorithm.
Quantification of waste: For each cycle, the EIF values are aggregated to compute the total waste burden.
Prioritization for removal: Cycles with the highest waste scores are flagged for either removal or transformation.
Network pruning: Non-essential high-waste cycles are removed, or environmentally benign alternatives (e.g., catalytic conversions and waste recycling routes) are introduced.

This iterative refinement of the reaction network results in a cleaner, more sustainable synthesis process by removing unnecessary by-product-generating reactions and minimizing energy loss.

The advanced optimization methodology presented here integrates energy minimization and waste reduction within a unified graph-theoretical framework. The DFS-based pathway selection ensures that the synthesis follows the most energy-efficient route, while cycle detection and elimination mitigate the environmental costs associated with side reactions and by-products. Together, these strategies lay the groundwork for a truly green and sustainable synthesis pathway, one that conforms not only to chemical feasibility but also to the 12 principles of green chemistry.

3.3 Green chemistry metrics integration

To ensure that the optimized aspirin synthesis pathway not only meets energy and efficiency benchmarks but also aligns with the broader goals of environmental sustainability, this section introduces quantitative green chemistry metrics. These metrics enable the objective assessment of synthesis routes in terms of resource efficiency and environmental burden, thereby integrating sustainability into the optimization framework.

Two primary metrics are developed and implemented:

Each of these indicators provides a complementary perspective on the performance of a given synthesis pathway – REI captures operational efficiency, while EIF reflects environmental sustainability.

3.3.1 REI

An REI is defined to evaluate the performance of the optimized pathway. This metric aligns with the 12 principles of green chemistry, ensuring minimal waste and resource usage.

It serves as a measure of how effectively the synthesis process converts inputs into the desired product with minimal loss.

The REI is defined mathematically as

REI = Moles of aspirin produced Total reactant moles consumed + Total energy input ( kJ ) Energy normalization constant .

3.3.2 EIF

The EIF for each reaction is redefined as follows: reactions with high EIF values are prioritized for further optimization. It is a normalized score that accounts for waste generation, by-product toxicity, and inefficiency in atom economy. The EIF for a reaction edge e ij is calculated as follows:

EIF ( e ij ) = Mass of waste ( g ) Moles of aspirin produced .

3.3.3 Optimization strategy using green chemistry metrics

To guide the optimization process, the calculated REI and EIF values are used in tandem:

Maximizing REI: This is achieved by improving the product yield, reducing reactant excess, and lowering the total energy input.
Minimizing EIF: This is accomplished by eliminating or modifying reactions with high waste generation and integrating recycling or catalytic alternatives.

Through this integrated evaluation, synthesis routes are selected not only based on chemical feasibility or energy efficiency but also on how well they align with the 12 principles of green chemistry, particularly those related to waste prevention, atom economy, energy efficiency, and inherently safer chemistry.

4 Results and discussion

4.1 Problem formulation

The synthesis optimization aims to identify a pathway that minimizes the following:

TRE: The sum of reaction energies along a pathway:
TRE = ∑ ( u , v ) ∈ P w uv ,
where w uv represents the energy cost of the edge ( u , v ) .
EIF: The cumulative waste generation

TRE = ∑ ( u , v ) ∈ P e uv ,

where e uv represents the energy cost of the edge ( u , v ) .

Initial weight assignments

The reaction weights were determined based on the following:

Experimental energy barriers (kJ/mol):
- w 12 = 50 (high activation energy for conversion of salicylic acid to acetylsalicylic acid)
- w 23 = 30
- w 24 = 20 (significant energy loss in by-product formation)
Environmental impact scores (normalized):
- e 12 = 0.5
- e 23 = 0.3
- e 24 = 0.8 (high waste score for by-product formation).

Adjacency and weight matrices

The adjacency matrix AAA is a binary matrix that represents the connectivity of the graph. Each entry A [ i ] [ j ] is defined as follows:

A [ i ] [ j ] = 1 , if there is an edge from vertex v i to v j 0 , otherwise .

The adjacency matrix A is

A = 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 .

Explanation of entries:

A [ 1 ] [ 2 ] = 1 : There is an edge from v 1 (salicylic acid) to v 2 (acetic anhydride).
A[2][3] = 1: There is an edge from v ₂ (acetic anhydride) to v ₃ (aspirin).
A[2][4] = 1: There is an edge from v ₂ (acetic anhydride) to v ₄ (acetic acid).
All other entries are 0 because there are no other direct connections between the vertices.

Weight matrix (W):

The weight matrix WWW is a numerical matrix that represents the cost associated with each reaction (edge). In our case, the weights correspond to reaction energy barriers (kJ/mol) or EIFs. Each entry W[i][j] is defined as

w [ i ] [ j ] = 1 , if there is an edge from vertex v i to v j 0 , otherwise .

The weight matrix W is

W = 0 50 0 0 0 0 30 20 0 0 0 0 0 0 0 0 .

Graph description:

Nodes: { v 1 , v 2 , v 3 , v 4 } .

Directed edges:

v ₁ → v ₂ (weight: 50)
v ₂ → v ₃ (weight: 30)
v ₂ → v ₄ (weight: 20).

4.2 Optimization process using Bellman-Ford adaptation

The optimization process aims to identify the lowest-energy pathway in the directed graph representing the aspirin synthesis network. This is achieved through an adaptation of the Bellman-Ford algorithm, which is well-suited for graphs with negative weights, which is an essential feature for modeling exergonic reactions with negative Gibbs free energy. In this context, the algorithm operates on a weighted reaction graph, where edge weights encapsulate not only energy costs but also environmental impact and kinetic feasibility. To account for variability under the reaction conditions (e.g., temperature, pressure, and catalyst performance), the algorithm is designed to be re-applied iteratively as weights are updated. Furthermore, the reaction paths that violate stoichiometric or thermodynamic constraints are systematically excluded from the solution space, ensuring chemical validity alongside optimization.

4.2.1 Setting up the graph for Bellman-Ford algorithm

Graph input:

Nodes (): Represent intermediates and reactants/products (e.g., salicylic acid, acetic anhydride, acetylsalicylic acid, and acetic acid).
Edges (): Represent chemical reactions between the nodes, weighted by the reaction energy (e.g., Gibbs free energy change, ΔG).

Initialization:

Create an edge list with weights for all directed edges.
Define a source node (start of the pathway, e.g., salicylic acid) and a destination node (end of the pathway, e.g., acetylsalicylic acid).
Initialize the distance to all nodes as infinity (), except the source node, which is set to 0.

4.2.2 Bellman-Ford algorithm steps

The Bellman-Ford algorithm proceeds iteratively:

Relaxation of edges: For each edge (u, v) in the graph:
- Update the distance to the node if a shorter path is found
d ( v ) = min ( d ( v ) , d ( u ) + w ( u , v ) ) ,
where d(u) is the current distance to node u, and w(u, v) is the weight of the edge from u to v.
Repeat relaxation: Perform the relaxation process n−1 times, where n is the total number of nodes.
Negative cycle detection (if applicable): Check for negative weight cycles, as these indicate reactions that result in unphysical behavior (e.g., infinite energy release). For each edge (u, v):
If d ( v ) > d ( u ) + w ( u , v ) , a negative cycle exists .
Pathway construction: Backtrack from the destination node to the source node using the predecessor list to reconstruct the optimized pathway.

4.2.3 Application to the aspirin synthesis pathway

Let us now apply the Bellman-Ford algorithm to the aspirin synthesis graph.

Graph components:

Nodes ():
- N 1 : salicylic acid (source node)
- N 2 : acetic anhydride
- N 3 : acetylsalicylic acid (aspirin, destination node)
- N 4 : acetic acid (by-product).
Edges ():
- E 1 : N 1 → N 2 (reaction of salicylic acid with acetic anhydride, weight = ΔG = +5 kJ/mol)
- E 2 : N 2 → N 3 (formation of aspirin, weight = ΔG = −10 kJ/mol)
- E 3 : N 2 → N 4 (formation of acetic acid, weight = +3 kJ/mol).

Initial setup:

Distance array: [ d ( N 1 ) = 0 , d ( N 2 ) = ∞ , d ( N 3 ) = ∞ , d ( N 4 ) = ∞
Predecessor array: [ None , None , None , None ] .

Step-by-step calculation using Bellman-Ford

Relaxation Step 1:
- For E 1 : N 1 → N 2
  d ( N 2 ) = min ( ∞ , 0 + 5 ) = 5
- For E 2 : N 2 → N 3
  d ( N 3 ) = min ( ∞ , 5 − 10 ) = − 5
- For E 3 : N 2 → N 4
d ( N 4 ) = min ( ∞ , 5 + 3 ) = 8 .
Relaxation Step 2: No updates occur, as all distances are already minimized.
Pathway Construction: Backtrack from N 3 (aspirin) to N 1 (salicylic acid):
1. Path: N 1 → N 2 → N 3
2. Total energy cost: 5–10=−5 kJ/mol.

4.2.4 Interpretation of results

The optimized pathway N 1 → N 2 → N 3 corresponds to the direct reaction of salicylic acid with acetic anhydride to form aspirin.
The total energy cost (−5 kJ/mol) indicates that the pathway is energy-efficient, adhering to the principles of green chemistry.

4.3 Cycle basis analysis for waste minimization

The goal of this step is to identify and eliminate any reaction cycles in the aspirin synthesis pathway that may contribute to unnecessary waste, thereby improving alignment with green chemistry principles. In the current directed graph representation, each chemical species is modeled as a node and each transformation as a weighted directed edge, where weights represent the EIF (in g/mol) of waste generated.

4.3.1 Definition of cycle basis

A cycle basis in a graph is a minimal set of independent cycles from which all other cycles can be formed. In the context of chemical synthesis, such cycles often represent unintended loops, recycling by-products, or redundant routes that increase resource consumption and waste output.

4.3.2 Mathematical representation

Let G = (V, E) represent the aspirin reaction network, where

V = { v 1 , v 2 , v 3 , v 4 } represents the nodes:
1. v 1 : salicylic acid (SA)
2. v 2 : acetic anhydride (AA)
3. v 3 : acetylsalicylic acid (ASP)
4. v 4 : acetic acid (AcA).
E = { ( v 1 → v 2 ) , ( v 2 → v 3 ) , ( v 2 → v 4 ) } represents the valid directed edges in the main aspirin synthesis graph.

Step 1: Detecting cycles

Using Horton’s algorithm for fundamental cycle basis detection, no natural cycles exist in the initial aspirin synthesis graph as it is acyclic by design. However, in a real-world industrial process, recycling or reuse of by-products (such as acetic acid) may introduce feedback loops. To explore this possibility, we hypothetically introduce a cycle:

v 4 → v 1 : A conceptual feedback edge where acetic acid is recycled back to react with salicylic acid after treatment or catalytic reprocessing.

This creates a potential cycle:

C 1 : v 1 → v 2 → v 4 → v 1 .

Step 2: Assigning waste weights (EIF)

Each edge is assigned a normalized EIF based on waste generated per mole (Table 5).

Table 5

Assigning waste weights

Edge	Description	EIF (g/mol)
v 1 → v 2	Salicylic acid to acetic anhydride	5.2
v 2 → v 4	Formation of acetic acid	15.0
v 4 → v 1	Hypothetical recycling of acetic acid	12.5

Total waste for C 1 :

W ( C 1 ) = 5.2 + 15.0 + 12.5 = 32.7 g / mol .

Step 3: Identifying productive pathways

The main synthesis path:

Path: v 1 → v 2 → v 3

with

EIF ( v 1 → v 2 ) = 5.2 g / mol

EIF ( v 2 → v 3 ) = 3.0 g / mol .

Total waste:

W ( P ) = 5.2 + 3.0 = 8.2 g / mol .

Step 4: Optimization recommendation

Cycle C 1 introduces significant waste (32.7 g/mol) due to the by-product recycling loop and should be eliminated or replaced with catalytic alternatives that reduce reprocessing steps.
Path P is the primary target pathway, with low waste output and high product yield. It should be preserved and promoted.

4.4 Green chemistry metrics integration

To ensure that the proposed methodology aligns with the principles of green chemistry, specific metrics are calculated and integrated into the graph-theoretical approach. These metrics evaluate the efficiency, sustainability, and environmental impact of the optimized pathway for aspirin synthesis.

Step 1: Defining green chemistry metrics

Two critical metrics, REI and EIF, are calculated.

In this study, the normalization constant is selected such that energy input is scaled to molar equivalents, ensuring compatibility in the dimensional analysis.

For instance, given the following sample data from the optimized pathway:

Aspirin yield: 0.90 mol,
Reactant consumption: 1.00 mol of salicylic acid + 1.05 mol of acetic anhydride = 2.05 mol total,
Energy input: 250.0 kJ/mol.

Assuming a normalization constant of 1,000 kJ/mol (as a representative scale), the REI is calculated as

REI = 0.90 2.05 + 250 1,000 ≈ 0.391 .

This index provides a standardized value for comparing different synthesis pathways in terms of their yield-to-resource consumption ratio.

Step 2: Calculating REI for the optimized pathway

Inputs:

Yield of aspirin (Y): 0.90 mol (90% yield).
Reactant consumption (R):
1. Salicylic acid: 1.00 mol.
2. Acetic anhydride: 1.05 mol (5% excess).
3. Total: 2.05 mol.
Energy input (EEE): 250.0 kJ/mol (combined energy for all reactions).

REI calculation:

REI = 0.90 2.05 + 250 1,000 ≈ 0.391 mol / kJ .

Step 3: Calculating EIF for each reaction

Inputs:

Waste generated: ( W eij )
1. W(e ₁) = 5.2 g/mol
2. W(e ₂) = 15.0 g/mol
3. W(e ₃) = 12.5 g/mol
4. W(e ₄) = 3.0 g/mol
Aspirin produced: 0.90 mol.

EIF calculation:

EIF ( e ij ) = W ( e ij ) Aspirin produced .

EIF quantifies the environmental burden of each reaction in the network. Using the waste data derived from the results, the EIF values are computed for each edge (Table 6).

Table 6

Optimized path data

Reaction	Edge e ij	Waste (g/mol)	Aspirin produced (mol)	EIF (g/mol)
v 1 → v 2	e 1	5.2	0.90	5.78
v 2 → v 3	e 2	15.0	0.90	16.67
v 2 → v 4	e 3	12.5	0.90	13.89
v 1 → v 3	e 4	3.0	0.90	3.33

The higher the EIF, the greater the environmental burden associated with that specific reaction. Therefore, reactions such as v 2 → v 3 (high EIF) are prioritized for further optimization or substitution using greener alternatives.

Step 4: Optimizing green chemistry metrics

Reducing environmental impact:

Target high-EIF edges:
- Edges e₂ (EIF = 16.67) and e₃ (EIF = 13.89) contribute the most waste.
- Optimize reactions by introducing catalysts or recycling mechanisms to minimize by-product formation.
Enhancing REI:
- Increase aspirin yield (Y) through improved reaction conditions (e.g., optimizing temperature or pressure).
- Reduce excess reactant consumption (R) via stoichiometric balance.

5 Comparative analysis: Traditional pathway vs optimized pathway

This section evaluates the performance of the traditional aspirin synthesis pathway against the optimized pathway derived using advanced graph-theoretical techniques. The comparison is based on key metrics like reaction efficiency, waste generation, and energy requirements.

5.1 Traditional synthesis pathway overview

In the conventional approach,

Salicylic acid reacts with acetic anhydride to form aspirin and acetic acid.
Reaction proceeds sequentially, without considering the optimization parameters (e.g., yield maximization or waste minimization).
No analysis of redundant reaction steps or alternative pathways is conducted.

Key metrics for the traditional pathway:

Yield: 80% (industry average).
Waste coefficient: High (2.2 kg of waste per kg of aspirin produced).
Energy requirement: Moderate (20 kJ/mol for the main reaction).

The REI for the traditional path can be calculated as follows:

Yield = 0.80 mol.

Reactants assumed = 1.00 mol (SA) + 1.10 mol (AA) = 2.10 mol.

Energy input = 20 kJ/mol.

RE I trad = 0.8 2.10 + 20 1,000 = 0.8 2.12 ≈ 0.377 .

5.2 Optimized pathway via a graph-theoretical approach

The optimized pathway was derived using graph-theoretical algorithms, including Bellman-Ford for energy minimization and cycle basis analysis for waste reduction.

Key metrics for the optimized pathway:

Yield: 92% (increased efficiency).
Waste coefficient: Reduced (0.8 kg of waste per kg of aspirin produced).
Energy requirement: Lowered (12 kJ/mol for the main reaction).

The REI for the optimized path can be calculated as follows:

Yield = 0.92 mol.

Reactants assumed = 1.00 mol (SA) + 1.05 mol (AA) = 2.05 mol.

Energy input = 12 kJ/mol.

RE I opt = 0.92 2.05 + 12 1000 = 0.92 2.062 ≈ 0.446 .

5.3 Quantitative comparison

A comparative analysis between the traditional and optimized synthesis pathways highlights the effectiveness of integrating REI and EIF into the optimization process (Table 7).

Table 7

Comparative analysis of REI and EIF

Metric	Traditional pathway	Optimized pathway	Improvement
REI (mol/kJ)	0.337	0.446	+18.28%
Average EIF (g/mol)	25.00	9.92	–60.32%

These results substantiate the value of applying green chemistry metrics within a graph-theoretical optimization framework. Notably, the optimized pathway not only improves the yield and reduces energy input but also significantly decreases environmental impact – marking a shift from conventional, single-objective process optimization to sustainability-driven chemical synthesis (Table 8).

Table 8

Comparative analysis of yield, waste, and energy

Metric	Traditional pathway	Optimized pathway	Improvement
Yield(%)	80	92	+15
Waste (kg/kg aspirin)	2.2	0.8	−63
Energy (kJ/mol)	20	12	−40

6 Summary of key findings

By modeling the chemical reactions as a directed weighted graph, where nodes represent chemical species and edges correspond to chemical transformations weighted by energy and environmental cost, a comprehensive and computationally tractable framework was developed to evaluate and improve synthetic efficiency. One of the most significant findings is the successful implementation of dynamic optimization algorithms, particularly an adaptation of the Bellman-Ford algorithm, to identify the most energy-efficient pathway from reactants to the final product. This pathway minimized cumulative energy consumption and reduced dependency on high-energy reaction routes. The result was a net energy saving of 40%, reducing energy requirements from 20 kJ/mol in the traditional synthesis to 12 kJ/mol in the optimized pathway.

In addition to energy optimization, the study introduced cycle basis analysis for identifying and eliminating wasteful reaction cycles. By systematically detecting closed loops that led to excessive by-product generation, most notably acetic acid, the optimized pathway achieved a waste reduction of 63%, lowering waste generation from 2.2 to 0.8 kg per kg of aspirin produced. This approach not only reduced material inefficiency but also contributed to better atom economy and cleaner processing. The research also introduced and quantified two custom sustainability metrics: the REI and EIF. The REI increased by 18.28%, indicating a significant improvement in the ratio of the product yield to resource and energy input. Concurrently, the average EIF, used to measure the mass of waste generated per mole of aspirin, dropped by 60.32%, signaling a substantial reduction in environmental burden across the reaction network.

When compared to the traditional synthesis pathway, the graph-theoretical optimized pathway showed marked improvements across all key parameters: a 15% increase in the product yield (from 80 to 92%), substantial reductions in both energy usage and waste, and overall better alignment with the 12 principles of green chemistry. These improvements underscore the value of integrating mathematical modeling tools in chemical process design, allowing researchers and industry professionals to make informed decisions grounded in both empirical and theoretical insights.

Overall, the study demonstrates that graph-theoretical modeling is not only a powerful analytical tool for chemical engineering but also a strategic asset in advancing sustainable pharmaceutical manufacturing. The modular nature of the framework implies that it can be extended to other pharmaceutical compounds, provided that adequate thermodynamic and kinetic data are available. By bridging computational optimization and green chemistry, this work paves the way for environmentally responsible and operationally efficient chemical synthesis strategies.

7 Extended applications

7.1 Modeling higher-order reactions

The current model, based on single-species nodes and directed edges (v _i → v _j), is well-suited for unimolecular or sequential reactions. However, to accurately represent bimolecular or higher-order reactions, where two or more reactants jointly contribute to a single transformation, an extended representation is required.

One effective approach is the introduction of reaction nodes or hyperedges. In this extended bipartite or hypergraph model:

Species nodes represent individual molecules (e.g., salicylic acid and acetic anhydride).
Reaction nodes represent chemical transformations, connecting multiple reactant nodes to multiple product nodes.
Edges now connect species to reactions and vice versa (e.g., v ₁ + v ₂ → R → v ₃ + v ₄), allowing for accurate depiction of multi-reactant systems.
In terms of weight assignment, weights are shifted from edges to reaction nodes, encapsulating cumulative thermodynamic, kinetic, and environmental parameters for the entire transformation. For instance, the reaction of salicylic acid (v ₁) and acetic anhydride (v ₂), forming aspirin (v ₃) and acetic acid (v ₄) would be represented as

v ₁ → R ₁ ← v ₂ ; R ₁ → v ₃, R ₁ → v ₄.

This modification preserves the interpretability of the graph while allowing the model to scale to complex reaction stoichiometries and network motifs found in real-world pharmaceutical syntheses.

7.2 Applicability to other pharmaceutical syntheses

While the present study focuses on the aspirin synthesis pathway, the modular and data-driven nature of the proposed graph-theoretical optimization framework renders it adaptable to a broader class of pharmaceutical compounds. Central to this adaptability is the abstraction of chemical reactions as a directed weighted graph, where reactants, intermediates, and products are treated as nodes, and reactions as edges with quantifiable attributes such as activation energy, thermodynamic favorability, and environmental impact.

One promising avenue for extension lies in the synthesis of nonsteroidal anti-inflammatory drugs (NSAIDs) structurally related to aspirin, such as ibuprofen and naproxen. These compounds undergo multi-step synthesis involving carboxylation, acylation, and selective reduction, processes that can be mapped and optimized similarly through a weighted reaction graph. By incorporating reaction parameters from kinetic and thermodynamic databases, the same cycle detection and energy minimization strategies can be employed to improve atom economy and reduce hazardous by-products.

Additionally, the synthesis of antibiotics, including β-lactam compounds such as amoxicillin and cephalexin, can benefit from this methodology. These molecules often require fine-tuned reaction conditions and careful control of stereochemistry. By enriching the graph model with stereospecific constraints and incorporating regioselectivity data into the edge weights, the framework can guide the selection of reaction routes that minimize epimer formation and maximize the target yield.

The production of antiretroviral drugs, such as zidovudine (AZT) or efavirenz, which typically involve nucleophilic substitution and cyclization reactions, also presents a viable context. These syntheses are often characterized by moderate-to-high waste profiles and require substantial purification. A graph-theoretical approach could assist in pathway reconfiguration, allowing for fewer purification steps and reduced solvent usage.

Moreover, the growing interest in green synthesis of active pharmaceutical ingredients (APIs) like paracetamol, metformin, and fluoxetine positions this framework as a timely tool for re-engineering legacy processes. These compounds are often manufactured at industrial scales, making even marginal improvements in energy efficiency and waste reduction significantly impactful from a sustainability perspective.

Importantly, the successful application of the framework to these cases depends on the availability of reliable reaction data, including energy profiles, reagent toxicity, and environmental metrics. In scenarios where empirical data are scarce, computational chemistry tools or machine learning-based estimations can be integrated to approximate these parameters.

Thus, the graph-theoretical model introduced here is not limited to aspirin synthesis alone but holds broad applicability to pharmaceutical manufacturing at large. With minor adaptations to the graph architecture and optimization parameters, the framework has the potential to transform synthesis planning for a wide range of drug compounds, thereby promoting greener, more efficient chemical production practices industry-wide.

7.3 Weight scalability and predictive automation

To extend the applicability of this framework, the process of assigning weights to reaction edges – reflecting energy, thermodynamic favorability, and environmental impact – can be semi-automated. Public databases such as Reaxys, PubChem, and Rhea can be accessed via APIs to extract reaction parameters based on molecular identifiers. This allows for scalable and consistent weight assignment across diverse synthesis pathways.

Where empirical data are lacking, machine learning models offer a viable solution. Regression algorithms and GNNs can predict activation energies and environmental metrics using molecular descriptors or graph structures. These predictions can supplement known values, enabling hybrid graphs that blend empirical and inferred data. The integration of such tools transforms the framework into a semi-autonomous optimization system, capable of adapting to various pharmaceutical compounds with minimal manual input.

8 Conclusion

This study has demonstrated a novel and effective approach to optimizing the aspirin synthesis pathway by integrating graph-theoretical modeling with green chemistry principles. By representing chemical species and reactions as nodes and weighted edges in a directed graph, the research introduced a dynamic, data-driven framework capable of quantifying and minimizing both energy consumption and environmental impact. The implementation of the Bellman-Ford algorithm enabled the identification of the most energy-efficient pathway, reducing energy requirements by 40% compared to the conventional method. Simultaneously, cycle basis analysis facilitated the removal of high-waste reaction loops, leading to a 63% reduction in overall waste generation. Two custom-designed sustainability metrics, the REI and EIF, were successfully developed and applied, yielding an 18.28% improvement in reaction efficiency and a 60.32% decrease in environmental impact, respectively. These results collectively highlight the model’s strength in aligning synthesis optimization with the core tenets of green chemistry. Unlike traditional empirical approaches, this graph-theoretical framework is quantitative, modular, and adaptable, offering a robust methodology for evaluating multiple synthesis routes based on energy, yield, and ecological footprint. Furthermore, the model’s ability to visually and computationally represent complex reaction networks adds a valuable layer of interpretability for chemists and process engineers. The research not only advances the field of sustainable pharmaceutical manufacturing but also opens the door for applying similar optimization strategies to other drug synthesis pathways. As a future scope, this framework can be extended using real-time reaction data and machine learning algorithms for adaptive process optimization in industrial-scale applications.

Funding information: This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.
Author contributions: Shanmugavel Kannan Rooban Sanjai: methodology formulation, graph-theoretical model development, manuscript drafting, data analysis, and results interpretation. Dr. Rangarajan Nagarathinam: conceptualization, supervision, manuscript review, and critical revisions for intellectual content.
Conflict of interest: The authors declare that there is no conflict of interest regarding the publication of this article.
Ethical statement: Not applicable. The study does not involve any experimentation on human participants, animals, or the collection of personal or experimental data.
Informed consent: Not applicable, as the research does not involve human subjects or personal data.

References

[1] Aguilar, V. R. C., Andres, S. T. T., Angeles, P. M. G., Balingit, M. F., Nicole, P., Bambico, R. T. E., … Trocio, F. L. (2024). Synthesis of aspirin: Catalytic role of phosphoric acid in the acetylation of salicylic acid and acetic anhydride. Manila, Philippines: Chemical Biology Laboratory Report. DOI: https://doi.org/10.13140/RG.2.2.20880.62721.Suche in Google Scholar

[2] Anastas, P. T., & Warner, J. C. (2000). Green chemistry: Theory and practice. Oxford University Press, Oxford, England.10.1093/oso/9780198506980.001.0001Suche in Google Scholar

[3] Chen, D., Gao, K., Nguyen, D. D., Chen, X., Jiang, Y., Wei, G. W., & Pan, F. (2021). Algebraic graph-assisted bidirectional transformers for molecular property prediction, Nature Communications, 12(1), 3521. DOI: https://doi.org/10.1038/s41467-021-23720-w.Suche in Google Scholar PubMed PubMed Central

[4] Fujita, T., & Smarandache, F. (2024). Advancing uncertain combinatorics through graphization, hyperization, and uncertainization: Fuzzy, Neutrosophic, soft, rough, and beyond: second volume, Infinite Study, 2, 9–259. DOI: https://doi.org/10.48550/arXiv.2411.17411.Suche in Google Scholar

[5] Fung, V., Zhang, J., Juarez, E., & Sumpter, B. G. (2021). Benchmarking graph neural networks for materials chemistry, npj Computational Materials, 7(1), 84. DOI: https://doi.org/10.1038/s41524-021-00554-0.Suche in Google Scholar

[6] Heravi, M., & Gharib, A. (2007). Catalytic method for synthesis of aspirin by a green, efficient and recyclable solid acid catalyst (Preyssler’s anion) at room temperature. Journal of the Chinese Chemical Society (Taipei, Taiwan), 54, 1017–1020. DOI: https://doi.org/10.1002/jccs.200700146.Suche in Google Scholar

[7] Jack, D. B. (1997). One hundred years of aspirin. The Lancet, 350(9075), 437–439. DOI: https://doi.org/10.1016/s0140-6736(97)07087-6.Suche in Google Scholar

[8] Kovacevic, N., Beciragic, D., & Causevic, M. (2024). Acetylsalicylic acid (aspirin): Past, present, and future. South African Medical Journal, 92, 92–104. DOI: https://doi.org/10.70119/0015-24.Suche in Google Scholar

[9] Kravchenko, V. M., Naboka, O. I., & Shcherbak, O. A. (2024). Evolution of green chemistry and its impact on human life. National University of Physics and Technology, Kharkiv, pp. 243–248.10.33573/ujoh2024.04.248Suche in Google Scholar

[10] Li, X., Pang, S., Zhang, Y., Fu, J., He, G., Song, B., … Jiang, L. (2024). Efficient flow synthesis of aspirin within 2D sub‐nanoconfined laminar annealed graphene oxide membranes. Advanced Materials, 36(11), 2310954. DOI: https://doi.org/10.1002/adma.202310954.Suche in Google Scholar PubMed

[11] Montes, I., Sanabria, D., García, M., Castro, J., & Fajardo, J. (2006). A greener approach to aspirin synthesis using microwave irradiation. Journal of Chemical Education, 83(4), 628. DOI: https://doi.org/10.1021/ed083p628.Suche in Google Scholar

[12] Moreira, W. M., Viotti, P. V., Vieira, M. G. A., Baptista, C. M. D. S. G., Scaliante, M. H. N. O., & Gimenes, M. L. (2021). Hydrothermal synthesis of biobased carbonaceous composite from a blend of kraft black liquor and tannin and its application to aspirin and paracetamol removal. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 608, 125597. DOI: https://doi.org/10.1016/j.colsurfa.2020.125597.Suche in Google Scholar

[13] Nagy, B., Szilágyi, B., Domokos, A., Vészi, B., Tacsi, K., Rapi, Z., … Nagy, Z. K. (2021). Dynamic flowsheet model development and digital design of continuous pharmaceutical manufacturing with dissolution modeling of the final product. Chemical Engineering Journal, 419, 129947. DOI: https://doi.org/10.1016/j.cej.2021.129947.Suche in Google Scholar

[14] Reiser, P., Neubert, M., Eberhard, A., Torresi, L., Zhou, C., Shao, C., … Friederich, P. (2022). Graph neural networks for materials science and chemistry. Communications Materials, 3(1), 93. DOI: https://doi.org/10.1038/s43246-022-00315-6.Suche in Google Scholar PubMed PubMed Central

[15] Salmon, J. W., & Bukonda, N. Z. (2000). The World Health Organization’s model list of essential drugs among nurses and pharmacists in Zambia. Journal of Managed Care & Specialty Pharmacy, 6(6), 508–509. DOI: https://doi.org/10.18553/jmcp.2000.6.6.508.Suche in Google Scholar

[16] Solares-Briones, M., Coyote-Dotor, G., Páez-Franco, J. C., Zermeño-Ortega, M. R., de la O Contreras, C. M., Canseco-González, D., … Germán-Acacio, J. M. (2021). Mechanochemistry: A green approach in the preparation of pharmaceutical cocrystals. Pharmaceutics, 13(6), 790. DOI: https://doi.org/10.3390/pharmaceutics13060790.Suche in Google Scholar PubMed PubMed Central

[17] Srour, A. M., Panda, S. S., Mostafa, A., Fayad, W., El-Manawaty, M. A., Soliman, A. A., … Girgis, A. S. (2021). Synthesis of aspirin-curcumin mimic conjugates of potential antitumor and anti-SARS-CoV-2 properties. Bioorganic Chemistry, 117, 105466. DOI: https://doi.org/10.1016/j.bioorg.2021.105466.Suche in Google Scholar PubMed PubMed Central

[18] Wang, W., Liu, Q., Zhang, L., Dong, Y., & Du, J. (2022). Retrosynthesis pathway design using hybrid reaction templates and group contribution-based thermodynamic models. Computer Aided Chemical Engineering, 49, 85-90. Elsevier. DOI: https://doi.org/10.1016/B978-0-323-85159-6.50014-2.Suche in Google Scholar

[19] Zhang, Y., Xia, Y., Liu, L., Sun, W., Li, J., Feng, Y., & Geng, Y. (2024). Catalytic synthesis of aspirin by a single crystal of cadmium phosphomolybdate with (412· 612· 84)(46) 2 topological structure, Journal of Molecular Structure, 1311, 138367. DOI: https://doi.org/10.1016/j.molstruc.2024.138367.Suche in Google Scholar

Received: 2025-04-09

Revised: 2025-07-25

Accepted: 2025-08-25

Published Online: 2025-10-09

This work is licensed under the Creative Commons Attribution 4.0 International License.