The [4 + 2] cycloaddition, also known as the Diels–Alder reaction, is a fundamental transformation in synthetic organic chemistry [[1], [2], [3]]. It provides an efficient pathway for the construction of a wide array of functionalized six-membered heterocyclic and carbocyclic frameworks, many of which correspond to natural products or their synthetic analogues [4,5]. This reaction involves the concerted interaction between a conjugated diene and a π-bonded dienophile, leading to the formation of complex cyclic systems with remarkable regio- and stereoselectivity [6,7]. Among the notable adducts obtained through asymmetric Diels–Alder transformations is the 3,4-dimethylcyclohex-3-ene-1-carboxylic acid (DM-CHCA) scaffold, which has drawn considerable attention due to its unique structural features and broad spectrum of biological and pharmacological activities [[8], [9], [10]].

Over the years, numerous synthetic strategies have been developed for the preparation of DM-CHCA derivatives. One of the most practical and attractive methods involves the [4 + 2] cycloaddition between isoprene, serving as the diene, and acrylic acid, acting as the dienophile [11,12]. Within this framework, Lewis acids play a pivotal role as catalysts in both homogeneous and heterogeneous systems [13,14]. Their catalytic activity arises from their ability to accept electron pairs and selectively activate substrates. Mechanistically, Lewis acids enhance reactivity by polarizing π-bonds or stabilizing electron-rich heteroatoms, thereby lowering activation barriers and facilitating the formation of highly reactive intermediates [15,16].

Such activation not only accelerates reaction kinetics but also improves chemo-, regio-, and stereoselectivity, enabling efficient control over key transformations such as cycloadditions, Friedel–Crafts reactions, rearrangements, and nucleophilic additions [17]. In addition, the versatility of Lewis acids lies in their capacity to promote reactions under mild conditions, often with higher yields and fewer synthetic steps, thereby enhancing both sustainability and cost-effectiveness in organic synthesis [18]. Recent advances in catalyst design including transition-metal-based Lewis acids, rare-earth elements, and hybrid systems such as metal–organic frameworks (MOFs), zeolites, and organometallic complexes have further expanded their scope [19,20]. These developments are particularly relevant to the fields of green chemistry and fine chemical synthesis, where atom economy and high selectivity remain critical to advancing sustainable methodologies [21,22].

The early discovery of metal halide-based catalysts, such as aluminum chloride (AlCl3) and titanium bromide (TiBr4), represented a decisive milestone in the advancement of Lewis acid catalysis within organic chemistry [23,24]. The use of AlCl3 was reported as early as the late nineteenth century, most notably in the Friedel–Crafts reaction, where it exhibited an extraordinary ability to activate alkyl and acyl halides, thereby facilitating electrophilic aromatic substitutions with remarkable efficiency. This breakthrough not only revolutionized synthetic methodology but also highlighted the broader potential of Lewis acids as promoters of highly selective organic transformations [25].

Subsequently, TiBr4 emerged as another powerful catalyst during the mid-twentieth century, particularly valued for its efficiency in addition and polymerization reactions. Its strong affinity for π-bonds and capacity to stabilize carbocationic intermediates established it as a versatile tool for modulating reactivity in complex systems. The catalytic activity of these pioneering compounds laid the foundation for understanding the fundamental principles of electrophilic activation by Lewis acids and provided a conceptual framework that continues to inform modern catalysis, from industrial-scale processes to sustainable synthetic approaches [26,27].

In this context, the influence of catalysts in Diels–Alder (DA) reactions has received substantial attention, both experimentally and theoretically. Lewis acids, in particular, exert a profound impact on the reaction mechanism by coordinating with the dienophile, thereby lowering the activation barrier and enhancing the electronic complementarity of the reacting partners [28]. This activation not only accelerates the reaction rate but also significantly improves regio- and stereoselectivity, rendering Lewis acid-catalyzed Diels–Alder reactions a cornerstone in the synthesis of structurally complex and biologically relevant molecules [29].

Beyond the experimental evidence supporting the efficiency of Lewis acid-catalyzed systems, a substantial body of computational chemistry research based on ab initio methods and density functional theory (DFT) has provided detailed insights into the nature of transition states and the effect of catalysts on the degree of asynchronicity in bond formation [30]. These theoretical investigations underscore the pivotal role of catalysts in modulating electronic polarization and stabilizing reactive intermediates, thereby deepening our understanding of the intricate relationship between electronic structure, selectivity, and catalytic efficiency in Diels–Alder cycloadditions [31].

In this context, the present theoretical study aims to follow the quantum variations that occur throughout the [4 + 2] cycloaddition reaction between isoprene (a) and acrylic acid (b), acrylic acid + AlCl3 (c) + acrylic acid + TiBr4 (d) (Fig. 1). This objective necessitates highly accurate computational calculations, employing appropriate methods to comprehensively describe the electronic and structural property changes that accompany the chemical transformation.

The study is organized into four main components, each addressing a critical aspect of reactivity and catalytic influence. First, the intrinsic reactivity of the reactants, both in the gas phase (absence of catalysts) and in the presence of catalysts, is evaluated through the FMO theory and global with local reactivity descriptors derived from conceptual density functional theory (CDFT). This analysis enables a systematic ranking of the reactants and provides valuable predictive insight into their cycloaddition behavior. Second, transition state theory (TST) and thermochemical parameter calculations are employed to investigate the influence of titanium (IV) bromide (TiBr4) and aluminum trichloride (AlCl3) on the energy landscape, kinetics, and electronic environment of the Diels–Alder reaction, previously studied experimentally by Kelly et al. [32]. Third, a topological analysis of the electron localization function (ELF) is conducted to explore the electronic structure of the products in their ground states, both uncatalyzed and catalyzed, thereby establishing a direct link between electronic configurations and the expected reactivity profiles. Finally, a noncovalent interaction (NCI) analysis is performed to identify the most significant attractive interaction regions within the molecular system, providing mechanistic insights into product stabilization and potential implications for biological activity.