Presenting GAELLE: An Online Genetic Algorithm for Electronic Landscapes Exploration of Reactive Conformers

Abstract

Identifying the most reactive conformation of a molecule is a central challenge in computational chemistry, particularly when reactivity depends on subtle conformational effects. While most conformation search tools aim to find the lowest-energy structure, they often overlook the electronic descriptors that govern chemical reactivity. In this work, we present GAELLE, a cheminformatics tool that combines conformer generation with quantum reactivity descriptors to identify the most reactive structure of a molecule in solution. GAELLE integrates an evolutionary algorithm with fast semiempirical quantum chemical calculations (xTB), enabling the automated ranking of conformers based on HOMO–LUMO gap minimization (Pearson’s principle of maximum hardness) and electrophilicity index (Parr’s electrophilicity scale). Solvent effects are accounted for via implicit solvation models (GBSA/ALPB) to ensure realistic evaluation of reactivity in solution. The method is fully SMILES-driven, open-source, and scalable to medium-sized drug-like molecules. Applications to reactive intermediates, bioactive conformations, and pre-reactive complexes demonstrate the method’s relevance for mechanism elucidation, molecular design, and in silico screening. GAELLE is publicly available and offers a reactivity-focused alternative to traditional energy-minimization tools in conformational analysis.

1. Introduction

The accurate identification of a molecule’s most reactive conformation is a crucial yet often overlooked step in computational chemistry workflows. While conformational sampling is widely employed to explore the potential energy surface (PES) and identify low-energy structures [1,2,3,4] most algorithms focus exclusively on thermodynamic stability, disregarding electronic properties that drive chemical reactivity. In many systems, particularly those involving flexible molecules, reactivity can be highly conformation-dependent, and relying solely on the lowest-energy conformer may lead to misleading conclusions regarding molecular behavior. For data-driven approaches such as machine learning [5,6] as well as for evolutionary search algorithms like genetic algorithms [7,8] the effectiveness of conformational or molecular optimization critically depends on the quality and physical interpretability of the objective function. In such frameworks, selecting an appropriate set of descriptors is essential to ensure meaningful navigation of chemical space. While classical energy-based metrics are often used, they do not capture the electronic predisposition of a molecule to engage in chemical interactions.

Moreover, several theoretical studies have emphasized that chemical reactivity is not solely governed by static structures but also by the molecular predisposition to reach a reactive geometry [9]. In particular, Toro-Labbé and collaborators introduced the concept of a “reactant zone,” [10,11,12] wherein molecules adapt their geometry in preparation for a chemical event. In this region of the potential energy surface, the system undergoes structural changes that enhance its reactivity before any actual bond-forming or bond-breaking process occurs. This reinforces the notion that the conformation adopted prior to reaction can be electronically activated, even if it is not the most stable in energy [13,14]. Identifying such pre-reactive conformers is thus critical for understanding reaction mechanisms, predicting bioactive poses, and designing responsive molecular architectures [15].

In this context, quantum chemically derived descriptors offer a compelling alternative. In parallel, Conceptual Density Functional Theory (CDFT) [16,17,18] has emerged as a powerful framework for quantifying and rationalizing chemical reactivity through well-defined quantum reactivity descriptors. Central among these are the Fukui function [19,20], the global hardness ($\eta$) [21], the chemical potential ($\mu$) [22], the electrophilicity index ($\omega$) [23,24], or higher-order descriptors such as the dual descriptor [25,26] or the linear response function [27,28]. These descriptors have been extensively used to understand and predict molecular behavior in donor–acceptor interactions, polar reactions, and catalytic processes [29,30]. The HSAB (Hard and Soft Acids and Bases) principle, originally formulated by Pearson [31,32], emerges theoretically within CDFT by asserting that hard acids preferentially react with hard bases, and soft acids with soft bases. Over the years, other reactivity principles have been put forward, such as the Maximum Hardness Principle (MHP) [33], which postulates that molecular systems evolve towards a state of maximum hardness. Conversely, the Minimum Electrophilicity Principle (MEP) [34] suggests that in many cases the most stable or favored species is the one with the lowest electrophilicity index $\omega$, especially in electron-rich environments.

Further elaborations such as the Maximum Probability Principle (MPP) [35] and the so-called “$\Delta \mu$ big is good” [36,37] rule extend the predictive power of CDFT by emphasizing the importance of changes in chemical potential during molecular interactions. Collectively, these principles form a physically interpretable rule set that offers strong potential for integration into data-driven approaches. When combined with machine learning techniques, CDFT descriptors offer transparent and chemically informed guidance, helping to steer model predictions in line with established reactivity theories [38,39]. Despite their promise, these reactivity-based descriptors are rarely incorporated into conformational search protocols, which traditionally prioritize minimization of total energy. However, the conformational state of a molecule can significantly influence its electronic descriptors [40] and thus its chemical behavior. Integrating CDFT-guided criteria such as $\eta$, $\mu$, and $\omega$ into conformational analysis enables reactivity-focused exploration of molecular structures, complementing and potentially surpassing thermodynamically driven approaches.

In this work, we present GAELLE (Genetic Algorithm for Electronic Landscapes Exploration), an AI chemistry pipeline that leverages evolutionary search, semiempirical quantum chemistry, and solvent modeling to identify the most electronically reactive conformer of a molecule in solution. This program is available at https://gaelle.univ-lyon1.fr (accessed on 1 July 2025). Rather than optimizing for energy alone, GAELLE ranks conformer quantum reactivity descriptors evaluated at each time and generated, accounting also for solvation effects via implicit models. The approach is fast, fully automated from SMILES input, and scalable to medium-sized drug-like compounds. We demonstrate the applicability of GAELLE across various chemical scenarios, including ligand conformational preorganization and reactive small systems. This work proposes a reactivity-driven alternative to traditional energy-based conformer ranking, integrating quantum information directly into molecular structure prediction from a genetic algorithm pipeline.

2. Computational Protocol

In this section, we present didactically the quantum reactivity descriptors used as quantum information and input for the genetic algorithm and the corresponding reactivity principles from CDFT, alongside the computational details for their evaluation.

2.1. Global Reactivity Descriptors

Within the canonical ensemble of CDFT, corresponding to a closed electronic system, the total electronic energy E is expressed as a function of the number of electrons N and as a functional of the external potential $v\left(\mathbf{r}\right)$ generated by the nuclei. According to the Hohenberg–Kohn formalism [41], this energy can be written as follows:

$$E\left[\rho \right]=E[N,v(\mathbf{r}\left)\right]=F\left[\rho \right]+\int \rho \left(\mathbf{r}\right)v\left(\mathbf{r}\right)d\mathbf{r}$$

(1)

where $F\left[\rho \right]$ is the universal Hohenberg–Kohn functional, accounting for the kinetic and electron–electron interaction energies, and $\rho \left(\mathbf{r}\right)$ is the ground-state electron density. Taking the total differential of the energy functional with respect to its variables yields the following:

$$dE=\mu dN+\int \rho \left(\mathbf{r}\right)\delta v\left(\mathbf{r}\right)d\mathbf{r}$$

(2)

This differential expression allows one to identify the first-order response properties of the system. Here, $\mu$ is the chemical potential [22], written as follows:

$$\mu ={\left({\displaystyle \frac{\partial E}{\partial N}}\right)}_{v\left(\mathbf{r}\right)}$$

(3)

which quantifies the tendency of the system to accept or donate electrons. More generally, by expanding the energy functional $E[N,v(\mathbf{r}\left)\right]$ in a Taylor series with respect to N and $v\left(\mathbf{r}\right)$, one obtains higher-order derivatives that define the global and local reactivity descriptors of CDFT, such as the global hardness [21], written as follows:

$$\eta ={\left({\displaystyle \frac{{\partial }^{2}E}{\partial N^2}}\right)}_{v\left(\mathbf{r}\right)}={\left({\displaystyle \frac{\partial \mu }{\partial N}}\right)}_{v\left(\mathbf{r}\right)}$$

(4)

These descriptors, and the reactivity principles derived from them, have been extensively studied and successfully applied to a wide variety of molecular systems. Derivated descriptors can also be defined, such as the electrophilicity index, written as follows:

$$\omega ={\displaystyle \frac{{\mu }^2}{2\eta }}$$

(5)

which is then defined as the energetic stabilization during charge transfer.

2.2. The Maximum Hardness Principle (MHP)

Building upon frontier molecular orbital theory and the HSAB concept, Pearson proposed in 1993 the Maximum Hardness Principle (MHP), which states the following [33]:

“There seems to be a rule of nature that molecules arrange themselves so to be as hard as possible.”

This principle implies that, during a chemical reaction, molecules evolve toward a state of maximum chemical hardness, defined as the energy gap between the HOMO and LUMO orbitals. The validity of this principle can be illustrated through a simple model of a charge-transfer reaction between two molecules A and B, written as follows:

$$A+B\to AB$$

(6)

The energy change $\Delta E$ associated with the reaction is given by the following:

$$\Delta E=-{\displaystyle \frac{1}{2}}{\displaystyle \frac{{({\mu }_A-{\mu }_B)}^2}{{\eta }_A+{\eta }_B}}$$

(7)

where $\mu$ is the chemical potential and $\eta$ the global hardness. The resulting hardness of the product species $AB$ is calculated as follows:

$${\eta }_{AB}={\displaystyle \frac{{\eta }_A{\eta }_B}{{\eta }_A+{\eta }_B}}$$

(8)

The change in hardness $\Delta \eta$ during the reaction is as follows:

$$\Delta \eta ={\eta }_{AB}-({\eta }_A+{\eta }_B)$$

(9)

which simplifies to the following:

$$\Delta \eta =-{\displaystyle \frac{{\eta }_A^2+{\eta }_B^2+{\eta }_A{\eta }_B}{{\eta }_A+{\eta }_B}}$$

(10)

This expression is always negative, indicating that the overall hardness tends to increase. Moreover, the partial derivatives with respect to ${\eta }_A$, while keeping B constant, yield the following:

$${\left({\displaystyle \frac{\partial \Delta \eta }{\partial {\eta }_A}}\right)}_B=-{\eta }_A\left({\displaystyle \frac{{\eta }_A+2{\eta }_B}{{\eta }_A+{\eta }_B}}\right)<0$$

(11)

$${\left({\displaystyle \frac{\partial \Delta E}{\partial {\eta }_A}}\right)}_{{\mu }_A,{\mu }_B}={\displaystyle \frac{1}{2}}{\left({\displaystyle \frac{{\mu }_A-{\mu }_B}{{\eta }_A+{\eta }_B}}\right)}^2>0$$

(12)

Hence, increasing the overall hardness ($\Delta \eta$) leads to a more exothermic reaction ($\Delta E$ becomes more negative), written as follows:

$${\left({\displaystyle \frac{\partial \Delta E}{\partial \Delta \eta }}\right)}_{{\mu }_A,{\mu }_B}<0$$

(13)

This analytic result supports the idea that chemical systems tend to rearrange to maximize their hardness during charge transfer processes [42,43]. The MHP provides a physically grounded criterion to evaluate the favorability of reactions and conformations based on reactivity descriptors.

2.3. The Minimum Electrophilicity Principle (MEP)

The Minimum Electrophilicity Principle (MEP) is a conceptual extension of the Maximum Hardness Principle. In 2003, Chamorro, Chattaraj, and Fuentealba [34] demonstrated that if the hardness $\eta$ of a molecular system increases during the course of a chemical reaction, then its electrophilicity index $\omega$ will correspondingly decrease. This relationship suggests that molecules tend to evolve toward states of minimal electrophilicity, especially in processes where the chemical potential remains constant.

The electrophilicity index is formally defined within the canonical ensemble of conceptual DFT as a functional of the number of electrons N and the external potential $v\left(\mathbf{r}\right)$, written as follows:

$$\omega \equiv \omega [N,v(\mathbf{r}\left)\right]$$

(14)

Its total differential is expressed as follows:

$$d\omega ={\left({\displaystyle \frac{\partial \omega }{\partial N}}\right)}_{v\left(\mathbf{r}\right)}dN+\int {\left({\displaystyle \frac{\delta \omega }{\delta v\left(\mathbf{r}\right)}}\right)}_{N}dv\left(\mathbf{r}\right)d\mathbf{r}$$

(15)

These functional derivatives can be rewritten as follows using known CDFT descriptors such as the chemical potential $\mu$, the global hardness $\eta$, the hyperhardness $\gamma$ [44] the Fukui function $f\left(\mathbf{r}\right)$, and the dual descriptor $f^{\left(2\right)}\left(\mathbf{r}\right)$:

$$\begin{array}{cc}\hfill {\left({\displaystyle \frac{\partial \omega }{\partial N}}\right)}_{v\left(\mathbf{r}\right)}& ={\displaystyle \frac{\mu }{\eta }}-{\displaystyle \frac{{\mu }^2}{2{\eta }^2}}\gamma \hfill \end{array}$$

(16)

$$\begin{array}{cc}\hfill {\left({\displaystyle \frac{\delta \omega }{\delta v\left(\mathbf{r}\right)}}\right)}_N& ={\displaystyle \frac{\mu }{\eta }}f\left(\mathbf{r}\right)-{\displaystyle \frac{{\mu }^2}{2{\eta }^2}}{f}^{\left(2\right)}\left(\mathbf{r}\right)\hfill \end{array}$$

(17)

Substituting these into the full differential yields the following:

$$\begin{array}{cc}\hfill d\omega & ={\displaystyle \frac{\mu }{\eta }}\left[\eta dN+\int f\left(\mathbf{r}\right)\delta v\left(\mathbf{r}\right)d^3\mathbf{r}\right]\hfill \\ \hfill & -{\displaystyle \frac{1}{2}}{\left({\displaystyle \frac{\mu }{\eta }}\right)}^2\left[\gamma dN+\int f^{\left(2\right)}\left(\mathbf{r}\right)\delta v\left(\mathbf{r}\right)d^3\mathbf{r}\right]\hfill \end{array}$$

(18)

Under the assumption of constant chemical potential (i.e., $d\mu =0$), a simplified relation can be derived as follows:

$$d\omega =-{\displaystyle \frac{1}{2}}{\left({\displaystyle \frac{\mu }{\eta }}\right)}^{2}d\eta$$

(19)

This expression directly connects the variation in electrophilicity to the variation in hardness. It implies that, for a given chemical potential, an increase in hardness necessarily leads to a decrease in electrophilicity. The MEP can thus be formally stated as follows:

“The natural direction of chemical evolution is toward a state of minimum electrophilicity.”

This principle provides a useful conceptual guideline for interpreting reactivity trends, especially in combination with the MHP, and reinforces the idea that reactivity descriptors can be used to rationalize the preferred conformations or reactive forms of molecules beyond simple energetic arguments [45,46].

2.4. Computational Details

All calculations were performed using an automated pipeline implemented in GAELLE, our in-house Python 3-based tool. The protocol begins from a simplified molecular input line entry system (SMILES) string input, from which a three-dimensional structure is generated using the ETKDG algorithm [47] implemented in RDKit [48]. This allows us to adjust bonding and add missing hydrogens. Multiple conformers are then sampled, and each candidate geometry is subjected to a geometry optimization using the extended tight-binding method GFN2-xTB [49], which provides a fast and robust semiempirical approach. Implicit solvent effects are incorporated using the generalized Born solvation model (GBSA) [50,51,52] or the analytical linearized Poisson–Boltzmann (ALPB) solvation model [53] as implemented in extended tight-binding (xTB) [54], depending on the solvent selected by the user (e.g., water, DMSO, etc.). All optimizations and property evaluations are thus carried out in the presence of solvent if specified, which is essential for realistic modeling of reactivity in solution.

Following geometry optimization, conceptual DFT descriptors are computed based on a Koopmans-like approximation of the frontier molecular orbitals (FMO) [55,56]. Specifically, the HOMO and LUMO orbital energies ${\epsilon }_{\mathrm{HOMO}}$ and ${\epsilon }_{\mathrm{LUMO}}$ are used to estimate the global hardness ($\eta$) and the chemical potential ($\mu$) as follows:

$$\mu ={\displaystyle \frac{1}{2}}\left({\epsilon }_{\mathrm{LUMO}}+{\epsilon }_{\mathrm{HOMO}}\right)\eta ={\epsilon }_{\mathrm{LUMO}}-{\epsilon }_{\mathrm{HOMO}}$$

(20)

These descriptors are then used to rank the conformers according to the reactivity principles. This workflow allows rapid and chemically informed screening of conformational space with a direct focus on reactivity, rather than solely on thermodynamic stability. A genetic algorithm [57] is then employed to evolve the conformer population based on the calculated reactivity descriptors, steering the search toward structures with optimal characters. The workflow, including evolutionary strategy and ranking criteria, is detailed in the next section.

All density functional theory (DFT) calculations were performed using the Gaussian 16 software package [58]. Geometry optimizations and vibrational frequency calculations were carried out at the B3LYP level of theory [59,60] with the aug-cc-pVTZ basis set [61] for selected systems. Frequency analyses were used to ensure that the optimized structures correspond to true minima on the potential energy surface (i.e., no imaginary frequencies). For all other conformers, single-point energy calculations and descriptor evaluations were performed at the same level of theory using the geometries provided by GAELLE. For visualizing the dual descriptor ($f^{\left(2\right)}\left(\mathbf{r}\right)$), we generated cube files from the Gaussian single-point calculations and rendered the molecular isosurfaces using GaussView 6. All isovalue plots shown in this article were generated with GaussView’s default visualization settings and grid parameters.

For clarity, we specify here the protocol applied to the case study molecule N-Acetyl-L-cysteine methyl ester. All conformers of this molecule were first generated and geometry-optimized using the GAELLE pipeline with GFN2-xTB (including implicit solvent as selected). The GAELLE-selected conformer and the DFT reference conformer were then fully re-optimized at the B3LYP/aug-cc-pVTZ level in Gaussian16, and harmonic frequency analyses were carried out to confirm that these structures are true minima (no imaginary frequencies). For the remaining conformers used in the comparative analyses, single-point DFT calculations at the same B3LYP/aug-cc-pVTZ level were performed on the GAELLE/GFN2-xTB geometries.

3. Results and Discussions

3.1. Workflow and Algorithmic Strategy

The genetic algorithm used in GAELLE operates on a population on a fixed set by the users of conformers per generation. The algorithm runs over 10 generations by default, but these parameters can be customized. At each generation, conformers are scored based on a selected reactivity criterion, such as minimal electrophilicity index $\omega$, maximal hardness $\eta$, or a composite function. The top-performing 50% of the population are selected for crossover and mutation.

Crossover is implemented as a dihedral angle recombination scheme: each child conformer inherits a subset of torsion angles from two parent structures, promoting the exploration of new spatial arrangements while preserving chemically plausible geometries. The mutation operator introduces random torsional perturbations (typically $\pm 10$–${30}^{\circ }$) on rotatable bonds, maintaining conformational diversity and avoiding premature convergence. Convergence is assessed either by stabilization of the best fitness score across successive generations or by reaching a fixed generation count. Additional stopping criteria can include structural similarity thresholds or stagnation of population diversity. This evolutionary strategy enables a reactivity-oriented conformational refinement beyond conventional energy minimization approaches.

For the demonstration of GAELLE’s conformational exploration and reactivity optimization, we selected N-Acetyl-L-cysteine methyl ester, a flexible molecule containing several rotatable bonds and a reactive group often used as a textbook example for its known therapeutic derivative [62]. The corresponding SMILES notation being COC(=O)[C@H](CS)NC(=O)C. This choice allows us to illustrate how conformational changes influence electronic descriptors such as the electrophilicity index and the HOMO–LUMO gap. Figure 1 presents the evolution of the electrophilicity index $\omega$ over successive generations of the genetic algorithm with a selected 30 conformer criteria.

We emphasize that the absolute values of the electrophilicity index $\omega$ can be influenced by the chosen reference state, the computational level of theory, and molecular size/electronic structure. For flexible molecules, conformational changes such as cis ↔ trans isomerization can lead to significant variations in electronic delocalization and polarizability, resulting in large $\Delta \omega$ values. This sensitivity of global descriptors to conformational flexibility has been reported previously.

The results show that the conformer with the lowest electrophilicity index ($\omega =11.676$ eV) was already identified within the first 10 iterations of the genetic algorithm, demonstrating the method’s ability to efficiently converge toward electronically activated conformations. The majority of conformers exhibit intermediate $\omega$ values clustered between 12.5 and 13.5 eV, indicating the presence of a broad but non-uniform reactivity landscape. This highlights the importance of an informed exploration strategy, as random sampling alone would be unlikely to identify the optimal conformer. Conversely, the bottom panel illustrates the hardness ranking where the most reactive conformers, corresponding to the highest $\eta$ values (up to 3.37 eV), are also obtained and explored over 10 iterations. This analysis confirms that GAELLE rapidly navigates the conformational space to isolate geometries with tailored electronic properties, which are not necessarily the lowest in force-field energy but may be the most chemically relevant in a reactivity-driven context. We then compared the properties of the conformer identified by GAELLE (with a 100 criteria) towards several force fields and their energy-minimized most stable conformer using the balloon software (MMFF94) [63], the Universal Force Field (UFF) directly from RDKIT [64], the General AMBER Force Field (GAFF) from OpenBabel [65] and OpenFF from the OpenFF toolkit [66]. All calculations for the quantum reactivity descriptors are performed with a single point from xTB. The results are presented in

Table 1. Computed quantum reactivity descriptors (in eV) for N-Acetyl-L-cysteine methyl ester within different force fields and GAELLE. Orbital energies are extracted from xTB.

Method	$\mathit{\mu }$	$\mathit{\eta }$	$\mathit{\omega }$
GAELLE	−8.88	3.37	11.68
MMFF94	−8.80	3.09	12.54
UFF	−9.03	3.14	12.97
GAFF	−8.71	3.12	12.16
OpenFF	−9.12	2.87	14.49

:

As expected, the chemical potentials are consistently negative across all methods, reflecting the electron-accepting nature of the molecule and validating the consistency of the orbital reference levels. GAELLE identifies a conformer with the lowest electrophilicity index ($\omega =11.68$ eV), indicating a significantly reduced propensity to accept electrons compared to the conformers generated by MMFF94 ($\omega =12.54$ eV), UFF, GAFF, or OpenFF. From an energetic standpoint, the chemical potential $\mu$ represents the first derivative of the total energy with respect to electron number. As such, the most negative $\mu$ value, observed for the OpenFF-derived conformer ($\mu =-9.12$ eV), is consistent with a lower electronic energy for that structure. However, this conformation also exhibits the highest electrophilicity ($\omega =14.49$ eV) and the lowest hardness, suggesting that energy-based stability and electronic reactivity are not necessarily aligned, further justifying the use of reactivity descriptors as optimization criteria.

These results support the premise that force-field-based conformer selection does not necessarily capture the most electronically relevant structure. In contrast, GAELLE employs a genetic algorithm to evolve a population of conformers through crossover and mutation operations, guided by quantum-derived reactivity criteria. This strategy enables the discovery of geometries with lower electrophilicity and higher hardness—conformational states that may more accurately reflect pre-reactive configurations in chemical or biological systems.

3.2. Web Interface

To maximize accessibility and usability of the GAELLE platform, we developed a dedicated web interface available at https://gaelle.univ-lyon1.fr (accessed on 1 July 2025). This online tool allows users to perform reactivity-driven conformer selection without the need for local installation or programming skills, making the method broadly available to chemists, computational scientists, and educators.

The web interface is centered around a simple and intuitive input form. Users are prompted to enter an SMILES string representing the molecule of interest. Optional parameters include the choice of implicit solvent (e.g., water, methanol, DMSO), which is applied in the xTB calculation via the GBSA model, and the number of conformers to be generated and screened. For computational efficiency and server stability, the number of conformers is limited to a maximum of 150 per submission. Once the job is submitted, the server performs conformer generation, geometry optimization using GFN2-xTB in the selected solvent, descriptor evaluation (HOMO–LUMO gap, chemical potential, hardness $\eta$, and electrophilicity index $\omega$), and selection of the optimal conformer according to the default or user-defined criterion. The entire process is typically completed within a few seconds, depending on molecular size and number of conformers. Upon completion, the interface displays the values of the computed reactivity descriptors corresponding to the final selected conformer. The optimized molecular geometry is visualized using an embedded 3D viewer, allowing the user to inspect the spatial structure interactively. In addition, the Cartesian coordinates of the final conformer are provided in standard XYZ format and can be easily copied or downloaded for further use (e.g., docking, quantum calculations, or visualization in external software).

This web-based deployment of GAELLE facilitates the exploration of reactivity-guided conformations directly from a browser, bridging the gap between conceptual quantum chemistry and practical applications in drug design, mechanism prediction, and chemical education. Due to ongoing development, the implementation details of GAELLE are currently available on request.

3.3. Examples of Applications

To investigate the applicability of GAELLE in a pharmacologically relevant context, we designed two complementary case studies. First, we applied the method to bioactive ligands and discussed the different structural differences observed. In the second part of the study, we selected a diverse set of five bioactive molecules known to undergo covalent or strongly polarized interactions with nucleophilic residues such as cysteine or serine. For each molecule, GAELLE was used to generate and rank conformers according to quantum-derived reactivity descriptors.

3.3.1. Case Study: Ligands

As a demonstration of GAELLE’s applicability to biologically relevant systems, we applied the workflow to three covalent inhibitors co-crystallized with their respective protein targets: Nirmatrelvir (PDB: 7SI9) [67], Ibrutinib (PDB: 5P9J) [68], and Afatinib (PDB: 4G5J) [69]. These compounds were selected for their diverse chemical scaffolds, their flexibility, and, most importantly, their electrophilic warheads designed to form covalent bonds with nucleophilic residues (typically cysteines) in the active site of enzymes such as viral proteases, kinases, or EGFR. Nirmaltrevir is, for example, the active component of Paxlovid and a covalent inhibitor of SARS-CoV-2 main protease; this molecule features a flexible scaffold with multiple rotatable bonds and a reactive nitrile warhead targeting the catalytic Cys145 residue. Each molecule was processed through the GAELLE pipeline starting from its SMILES representation. Conformers were generated and evaluated based on RMSD (Root Mean Square Deviation) towards the structure file from the PDB and later on electrophilicity ($\omega$) and hardness ($\eta$) using xTB single point calculations.

The data presented in

Table 2. Comparison of GAELLE-selected conformers and force-field-optimized conformers (MMFF94 and UFF) for three covalent inhibitors. The RMSD (in Å) quantifies the deviation from the crystallographic ligand pose (PDB structure). The absolute differences in chemical hardness ($|\Delta \eta |$) and electrophilicity index ($|\Delta \omega |$), in eV, are computed relative to the crystallographic conformation using xTB single-point calculations.

Structure	Method	RMSD	$\left|\mathbf{\Delta }\mathit{\eta }\right|$	$\left|\mathbf{\Delta }\mathit{\omega }\right|$
Nirmaltrevir	GAELLE	1.774	−1.36	25.60
	MMFF94	1.815	0.23	0.10
	UFF	1.859	−1.35	25.96
Ibrutinib	GAELLE	5.774	1.76	−39.79
	MMFF94	1.497	0.91	−12.48
	UFF	6.143	1.80	−39.06
Afatinib	GAELLE	2.047	−0.27	12.52
	MMFF94	2.124	0.91	−12.48
	UFF	2.145	−0.73	57.09

illustrate the structural and electronic differences between conformers selected by GAELLE and those obtained from classical force-field optimization (MMFF94 and UFF) for three covalent inhibitors. The results obtained demonstrate first that for Nirmatrelvir, GAELLE identifies a conformer with a lower RMSD (1.774 Å) to the crystallographic pose than MMFF94 and UFF and exhibits a significant reduction in electrophilicity ($|\Delta \omega |=25.60$ eV) compared to the experimental geometry. This supports the notion that GAELLE favors conformers with distinct electronic activation while maintaining a structurally plausible geometry. In the case of Ibrutinib, the GAELLE-selected conformer differs markedly from the crystallographic reference in geometry (RMSD = 4.774 Å), but shows a much stronger decrease in electrophilicity ($|\Delta \omega |=-39.79$ eV), indicating a geometry that is electronically pre-activated for interaction, although more distant from the bound pose. Interestingly, the MMFF94-optimized conformer yields a much lower RMSD (1.497 Å), but also a milder change in $\omega$, suggesting that it captures steric complementarity more effectively but lacks the electronic enhancement that GAELLE targets.

The comparison of Ibrutinib conformers in Figure 2 highlights the structural divergence introduced by different conformer selection strategies. The GAELLE-selected conformer (center) displays a geometry optimized for electronic reactivity, characterized by a reduced electrophilicity index and an increased global hardness relative to the crystallographic pose. In contrast, the MMFF94-derived conformer (right) is geometrically closer to the experimental structure (RMSD = 1.497 Å) but exhibits less pronounced reactivity features. Interestingly, although the GAELLE conformer deviates more significantly in geometry (RMSD = 5.774 Å), it shows a substantial decrease in $\omega$ (−39.79 eV), suggesting a conformation that is electronically predisposed for nucleophilic attack—consistent with the mechanism of covalent inhibition targeting Cys481. These results underscore the complementarity of reactivity-guided and energy-based conformer selection, particularly for covalent ligands where electronic activation is a prerequisite for biological function.

For Afatinib, the RMSD values relative to the crystallographic pose remain similar across all methods, with GAELLE yielding, slightly, the lowest value at 2.047 Å, MMFF94 at 2.124 Å, and UFF at 2.145 Å. These results suggest that all three conformers approximate the bound geometry reasonably well from a structural standpoint. However, significant differences emerge at the electronic level. The GAELLE-selected conformer displays an increase in electrophilicity ($|\Delta \omega |=12.52$ eV) compared to the experimental structure, coupled with a slight decrease in hardness ($|\Delta \eta |=-0.27$ eV), indicating a geometry that is more electronically predisposed for reaction. In contrast, the MMFF94 conformer exhibits a reduction in electrophilicity ($|\Delta \omega |=-12.48$ eV), suggesting a conformation less activated for covalent interaction despite its structural proximity to the bound pose. Notably, the UFF-optimized structure shows a large positive shift in $\omega$ ($57.09$ eV), pointing to an unrealistically high electrophilicity, likely due to geometric distortions that significantly affect orbital energies.

We note that no docking simulations or experimental structural validation (e.g., X-ray or NMR) were performed in this study; for ligand-like small molecules GAELLE selects low-energy, electronically reactive conformers expected to be relevant for binding, and explicit docking/experimental validation will be addressed in future work.

Overall, these results confirm that GAELLE explores conformational space in a way that prioritizes electronic reactivity over purely energetic or steric criteria. While this may occasionally result in geometries further from the crystallographic pose, it allows the identification of chemically meaningful pre-reactive states that may otherwise be overlooked by classical methods. The observed trade-off between structural fidelity and electronic activation is expected, and highlights the complementary nature of reactivity-guided conformer selection.

3.3.2. Case Studies: Small Reactive Molecules

To assess the broader applicability of GAELLE beyond large, drug-like compounds, we selected a set of five small reactive molecules: Donepezil, Captopril, Aspartame, Methylphenidate, and once again the N-Acetyl-L-cysteine methyl ester.

These small reactive molecules, characterized by electrophilic warheads or well-defined reactive centers, provide ideal test systems to investigate how conformational variations influence electronic activation and local reactivity. Unlike bioactive ligands, whose conformations are often constrained by protein environments, these flexible compounds allow for a more direct examination of the relationship between molecular geometry and electronic structure. To complement the global reactivity descriptors such as chemical hardness ($\eta$) and electrophilicity index ($\omega$), we performed additional quantum chemical analyses on selected conformers. In particular, we computed the dual descriptor $f^{\left(2\right)}\left(\mathbf{r}\right)$, derived from the difference between the condensed Fukui functions for nucleophilic and electrophilic attack ($f^{\left(2\right)}\left(\mathbf{r}\right)\approx {\rho }_{LUMO}\left(\mathbf{r}\right)-{\rho }_{HOMO}\left(\mathbf{r}\right)$). These spatially resolved descriptors provide complementary insights into local reactivity: while the dual descriptor identifies regions preferentially susceptible to electrophilic or nucleophilic interaction. All electronic properties were evaluated at the same level of theory (B3LYP/aug-cc-pVTZ) to ensure consistency. For the dual descriptor, a negative value at a given point $\mathbf{r}$ corresponds to $f^{+}\left(\mathbf{r}\right)<f^{-}\left(\mathbf{r}\right)$, indicating a region more prone to nucleophilic character, whereas a positive value implies $f^{+}\left(\mathbf{r}\right)>f^{-}\left(\mathbf{r}\right)$, highlighting an electrophilic site. Figure 3 presents the computed dual descriptors for each selected system:

The results obtained from the dual descriptor $f^{\left(2\right)}\left(\mathbf{r}\right)$, visualized as color-mapped isosurfaces, highlight differences in local nucleophilic and electrophilic character between conformers. For instance, GAELLE-selected conformers of N-Acetyl-L-cysteine methyl ester and captopril show enhanced reactivity at the ester moiety, with a more pronounced localization of the dual descriptor on the carbonyl group compared to their DFT-optimized counterparts. This suggests a higher electrophilic activation in these geometries. A complementary analysis based on Hirshfeld atomic charges supports this interpretation. For the oxygen atom of the carbonyl group in N-Acetyl-L-cysteine methyl ester, the GAELLE conformer exhibits a slightly more negative charge ($-0.288$ a.u.) than the DFT reference structure ($-0.259$ a.u.), indicating a greater charge polarization and, consequently, an enhanced reactivity.

In the case of aspartame, the DFT-optimized conformer displays a strongly localized reactive basin around the nitrogen atoms, while the GAELLE-derived structure reveals a more delocalized and distributed reactivity profile. This reflects differences in electronic distribution linked to conformational changes. Finally, for more rigid systems such as donepezil and methylphenidate, no substantial difference in local descriptors is observed between conformers. This is likely due to the presence of aromatic scaffolds, which limit conformational freedom and reduce the impact of geometry on electronic localization. Minor variations in local reactivity are observed but are not considered chemically significant.

These observations reinforce GAELLE’s ability to identify not only globally more reactive conformers based on descriptors such as $\omega$ and $\eta$ but also structures exhibiting refined and chemically meaningful local reactivity patterns. Such insights are particularly valuable for covalent docking, mechanistic modeling, and reactivity-driven virtual screening.

4. Conclusions

We have presented GAELLE, a reactivity-driven conformer selection tool based on conceptual DFT descriptors and a genetic optimization scheme. Unlike traditional conformer analysis methods that rely solely on thermodynamic criteria, GAELLE prioritizes molecular structures that are electronically predisposed to react, based on hardness, chemical potential, and electrophilicity.

Our results demonstrate that conformers exhibiting maximal reactivity, quantified by minimal electrophilicity index or HOMO–LUMO gap, are often distinct from those corresponding to energy minima. This observation aligns with the idea that the conformation adopted by a molecule upon interacting with a biological target, such as a protein, is not necessarily the most stable one, but rather the most electronically activated. Consequently, GAELLE opens the door to new applications in pharmacophore modeling, covalent inhibitor design, and reactivity-guided docking.

By providing an open-access, SMILES-based platform that integrates quantum-inspired reactivity principles, GAELLE contributes a chemically meaningful alternative to conventional force-field-based conformational analysis. Its combination of efficiency, interpretability, and conceptual rigor makes it a valuable tool in both mechanistic studies and early-stage molecular design. Future work will explore the integration of GAELLE-selected conformers directly into docking pipelines, where reactivity-oriented geometries may improve the identification of biologically relevant binding poses.