Abstract
Structural activity cliffs are a well-established concept in structure–activity relationship studies, describing cases in which small structural modifications produce large changes in biological activity. Whether an analogous phenomenon exists for molecular physicochemical properties has received less attention and remains conceptually underdeveloped. Here, we examine the notion of property cliffs through a comparative analysis of structure–activity and structure–property landscapes. Using examples spanning acid–base behavior, lipophilicity, chemical reactivity, spectroscopy, molecular materials, and supramolecular systems, we argue that abrupt property changes associated with relatively small structural perturbations can occur across diverse chemical domains. We further discuss how property cliffs differ from activity cliffs in terms of their underlying mechanisms, potential frequency, and degree of mechanistic interpretability. Rather than proposing a universal definition, we outline a conceptual framework in which the identification of a property cliff depends on the property under consideration, the magnitude of the structural perturbation, and the property variation. Finally, we discuss how recognizing and systematically characterizing property cliffs may provide new opportunities for QSPR modeling, molecular machine learning, materials discovery, and the analysis of discontinuities in chemical space.
Graphical Abstract
Introduction
The cheminformatics community has long been interested in understanding how molecular structure determines physicochemical properties and biological activity. In this context, quantitative structure–property and structure–activity relationship (QSPR/QSAR) approaches, together with machine learning methods, have contributed to the analysis of these relationships. Most of these approaches rely on the similarity principle, which states that compounds with similar structures tend to exhibit similar physicochemical properties or biological activities.
However, this principle is not universally valid. Numerous examples show that compounds with high structural similarity can exhibit markedly different biological activities or molecular properties. Such deviations have attracted considerable attention because they represent discontinuities in molecular landscapes and pose significant challenges for the development of robust predictive models (; ; ).
Within structure–activity relationships, these discontinuities are known as activity cliffs (ACs), defined as pairs or groups of compounds that display high structural similarity but large differences in biological activity. ACs are frequently found in bioactivity data and can strongly affect QSAR model performance, reflecting the nonlinear and complex nature of ligand-target interactions (; Stumpfe et al., 2014; ).
An analogous concept can be defined for physicochemical properties. Property cliffs (PCliffs) correspond to structurally related molecular or material syst ems in which a relatively small structural modification produces a disproportionately large change in a physicochemical property, such as lipophilicity (logP), solubility, acid dissociation constant (pKa), conductivity, electronic transport, or catalytic activity. In contrast to ACs, however, this concept has received less attention. More critically, the term PCliffs is used inconsistently throughout the literature and is often treated as an extension or generalization of ACs (; ; ; ), rather than as an independently characterized concept within structure–property relationships (; ; ).
This raises the question of why PCliffs have remained comparatively underexplored. One possible explanation is that many commonly studied molecular properties exhibit approximately additive behavior with respect to chemical structure. This is reflected in the success of fragment-based approaches developed for the prediction of physicochemical properties (Wildman and Crippen, 1999; ; Tetko and Tanchuk, 2002). For example, widely used lipophilicity models, such as the Ghose–Crippen model () or the Moriguchi method (), estimate logP as the sum of local contributions associated with specific structural fragments. Likewise, topological polar surface area (TPSA) can be approximated from additive contributions of structurally defined polar fragments (). These approaches reflect the largely additive nature of many physicochemical properties, which often leads to gradual changes in response to structural modifications. This apparent continuity might suggest that PCliffs are incompatible with the physicochemical nature of such properties. However, this conclusion is not necessarily justified. Changes in protonation state, electronic structure, conformational preferences, inter- and intramolecular interactions, and crystal packing can all produce important variations in molecular properties as a consequence of relatively small structural modifications.
The present work examines the concept, existence, and nature of PCliffs within structure–property relationships and places them in the broader context of ACs. Rather than proposing a universal definition, we explore PCliffs as discontinuities in structure–property landscapes in which relatively small structural perturbations are associated with unexpectedly large changes in a molecular property. Because both structural similarity and the magnitude of property variation are inherently context-dependent, and because the boundaries between continuous variation and a cliff are not universally defined, the identification of PCliffs may require different criteria depending on the property under consideration. For small organic molecules, established approaches such as matched molecular pair analysis, molecular fingerprints, and scaffold-based comparisons provide practical ways to assess structural similarity and identify relatively small structural perturbations. For more complex chemical systems, including supramolecular assemblies and extended materials, structural similarity should instead be evaluated using descriptors appropriate to the system under investigation, such as topological, crystallographic, or other materials-specific representations.
With the aim of developing a conceptual framework for future studies, we discuss the definition, existence, underlying causes, relative frequency, and interpretability of PCliffs and compare these characteristics with those of ACs. Accordingly, we view PCliffs as property-dependent discontinuities in structure–property landscapes rather than as phenomena defined by fixed numerical thresholds. A change of one pKa unit, a tenfold variation in a rate constant, a large shift in conductivity, or a transition from semiconducting to metallic behavior may all represent discontinuities of practical significance despite occurring on different scales.
PCliffs refer to abrupt discontinuities in structure–property relationships between structurally similar compounds. Rationalization in terms of an underlying physicochemical mechanism may or may not be pursued, depending on the goal of the study. Discontinuities may arise from measurement error, data quality issues, limitations of the molecular representation, or other factors unrelated to the property itself.
Existence of ACs and PCliffs
ACs are a well-established feature of structure–activity landscapes and have been extensively documented in medicinal chemistry and cheminformatics studies over the past two decades (Stumpfe et al., 2014; ; Stumpfe et al., 2020). Such discontinuities are generally interpreted as a consequence of the nonlinear nature of molecular recognition processes, where small structural modifications can alter ligand–receptor interactions, binding modes, or conformational equilibria. Analyses of bioactivity repositories, including ChEMBL (Zdrazil et al., 2024) and BindingDB (), have shown that ACs are not isolated observations (). As a result, they remain an important challenge for QSAR modeling and a useful framework for understanding the limits of the molecular similarity principle. ACs can emerge from a wide range of structural modifications. The compounds involved may differ in stereochemistry, contain variations in peripheral substituents while retaining the same molecular core or even possess distinct scaffolds that preserve key pharmacophoric features. Regardless of the specific structural change, an AC is identified when a relatively small modification produces a disproportionately large change in biological response, such as a substantial potency difference or a switch between distinct pharmacological profiles (Stumpfe et al., 2014).
Recent studies also suggest that the occurrence of an AC does not depend exclusively on structural changes. Ramírez-Palma and Martinez-Mayorga () showed that variations in experimental conditions, such as dose, can also generate disruptions in bioactivity. This highlights that activity landscapes may be shaped not only by molecular structure but also by the context in which biological responses are measured. ACs have been documented across a broad range of biological endpoints. Representative examples include μ-opioid receptor agonists, where the removal of a methoxyethene group leads to an approximately two-order-of-magnitude loss of activity (Tun-Rosado et al., 2025); acylcyclohexene derivatives, in which a positional substituent change alters odor perception (); and thalidomide, where stereochemistry is associated with markedly different biological effects ().
Unlike ACs, PCliffs have rarely been discussed as a distinct concept within the chemoinformatics literature, despite the widespread recognition of abrupt structure–property relationships across many areas of chemistry. This is partly because many molecular physicochemical properties, such as lipophilicity or polar surface area, are commonly described using approximately additive models based on fragment contributions (; ; ). However, not all molecular properties follow additive behavior. While extensive properties depend on the amount of matter and are inherently additive, many relevant molecular properties are intensive and do not directly depend on the mass or size of the molecule. These include electronic properties such as reactivity, acid–base parameters such as pKa, as well as spectroscopic properties. These quantities depend on the electronic distribution and on inter- and intramolecular interactions throughout the system and therefore cannot be described as a simple sum of independent contributions. Consequently, they may exhibit nonlinear behavior that gives rise to discontinuities in structure–property landscapes.
The examples presented below were intentionally selected to illustrate that PCliffs can emerge at different levels of chemical organization, including molecular, supramolecular, and materials systems. Although the nature of the structural perturbation differs among these examples, they all illustrate the same conceptual phenomenon: a relatively modest structural perturbation associated with a large change in a physicochemical property.
A classical case, commonly discussed in introductory chemistry courses, is provided by the chlorine oxyacid series at 25 °C: HClO (pKa ≈ 7.4), HClO2 (pKa ≈ 1.94), and HClO3 (pKa ≈ −2.7) (). The progressive incorporation of oxygen atoms enhances charge delocalization in the conjugate base, resulting in a marked decrease in pKa. Similar behavior has been reported in propylpiperidine-derived antimigraine agents (Figure 1a) (van et al., 1999). In these compounds, introduction of a single fluorine atom lowers the pKa by approximately one unit relative to the parent molecule, whereas incorporation of a second fluorine atom produces an additional substantial decrease. These stereoelectronic effects can significantly alter molecular basicity and, consequently, influence receptor affinity and oral bioavailability.
FIGURE 1
Lipophilicity provides another example of property changes that can become disproportionately large following relatively modest structural modifications. Although logP is frequently described using additive fragment-based models, deviations can occur. For example, phenol () has a logP of approximately 1.5, whereas p-methylphenol () and p-tert-butylphenol () exhibit values of about 2.0 and 3.3, respectively. Thus, replacing the hydrogen atom of phenol with a tert-butyl group increases lipophilicity by approximately 1.8 logP units, corresponding to nearly two orders of magnitude in the octanol/water partition coefficient. This behavior reflects the combined influence of hydrophobic effects, molecular volume, and solvent reorganization, showing that lipophilicity is not always strictly additive (Kellogg and Abraham, 2000).
A third example arises from chemical reactivity, which is highly sensitive to electronic effects introduced by seemingly minor structural modifications. Murillo et al. () investigated the formation of diarylamines through a Smiles rearrangement and identified a base-catalyzed concerted 3-exo-trig pathway as the most probable mechanism. Their study further revealed that relatively small changes in the substitution pattern of the S-aryl ring produce dramatic changes in reactivity (Figure 1b). For example, the progressive introduction of nitro groups (–NO2) decreases the activation barrier from 29.0 kcal mol−1 in the monosubstituted system to 21.0 and 18.6 kcal mol−1 in the di- and trisubstituted derivatives, respectively. As a consequence, the corresponding rate constants increase from 2.0 × 10−9 to 2.4 × 10−3 and 1.9 × 10−1 s−1 at 298.15 K. Even larger effects are found for trifluoromethanesulfonyl (–SO2CF3) substituents, for which activation barriers decrease to as little as 9.9 and 8.4 kcal mol−1, while the calculated rate constants increase by more than twelve orders of magnitude relative to the parent system. From a mechanistic perspective, these trends can be readily rationalized in terms of well-established electronic effects. However, when viewed within a structure–property framework, the same behavior appears as an extreme discontinuity in the reactivity landscape, where relatively modest structural modifications produce changes spanning many orders of magnitude. In this sense, these systems exhibit the defining characteristics of a PCliff.
Analogous behavior can also be identified in solid-state systems, where subtle structural perturbations may trigger abrupt changes in electronic properties (Figure 1c). A representative example is provided by blue phosphorene bilayers, in which small variations in stacking arrangement or interlayer distance can induce a transition between semiconducting and metallic behavior. Several stacking modes have been reported, most of which are semiconducting. However, the A1B−1 arrangement exhibits metallic character and is also the most energetically stable configuration. Remarkably, increasing the interlayer distance within this same arrangement from 3.01 to 4.93 Å restores semiconducting behavior ().
A related example is found in Tp-BTD covalent organic frameworks (COFs), where variations in interlayer stacking—AA (eclipsed), AB (offset), and ABC—produce substantial functional differences without altering the chemical composition of the material (Yang et al., 2021). The most striking effect is observed in the generation of type I reactive oxygen species during the photoinduced oxidation of amines to imines. Whereas the ABC polymorph achieves 72% conversion, the AA and AB structures exhibit conversions close to 20%. These differences arise from stacking-dependent structural features, including variations in pore size, relative stability, and tautomeric equilibrium.
Finally, Figure 1d illustrates a PCliff associated with antiaromaticity and electronic transport. HDHA and ODHA (Uriostegui et al., 2026) are closely related 12π-electron macrocycles that formally satisfy Hückel’s 4n rule and are therefore antiaromatic. Despite their structural similarity, they exhibit markedly different degrees of antiaromaticity, as reflected by the strength of their paratropic ring currents. Whereas HDHA sustains a paratropic current of −15.6 nA T−1, the corresponding value for ODHA reaches −95 nA T−1, representing an approximately sixfold increase. This enhancement of antiaromatic character is accompanied by a substantial change in electronic transport properties. Near the Fermi level, HDHA exhibits moderate transmission values (T ≈ 0.03–0.17), whereas ODHA reaches considerably higher values (T ≈ 0.66–0.76). From a chemical perspective, these differences can be rationalized in terms of changes in electron delocalization and antiaromatic stabilization. Within a structure–property framework, however, they correspond to a pronounced discontinuity in which a relatively modest structural modification produces a disproportionately large change in both magnetic and transport properties.
In summary, these examples show that abrupt discontinuities are not exclusive to structure–activity relationships but also emerge in structure–property landscapes spanning classical molecular parameters, chemical reactivity, electronic materials, and π-conjugated systems.
Relative frequency of ACs and PCliffs
Unlike ACs, whose frequency has been extensively investigated through systematic analyses of large bioactivity databases, the prevalence of PCliffs remains unknown. At present, the absence of standardized definitions and context-dependent criteria for identifying PCliffs precludes direct comparisons across different physicochemical properties. To the best of our knowledge, no comprehensive studies have quantified the occurrence of PCliffs or compared their frequency with that of ACs.
In contrast, ACs have been characterized using large repositories such as ChEMBL, enabling quantitative analyses of their frequency. Bajorath and Stumpfe (Stumpfe and Bajorath, 2012b) reported that, based on the analysis of 27,610 bioactive compounds tested against 414 targets, ACs account for approximately 5% of molecular pairs that satisfy commonly used structural similarity criteria. Because individual compounds can participate in multiple pairs, the fraction of compounds involved in at least one AC is substantially higher, ranging from approximately 22%–34%. Comparable analyses are currently unavailable for structure–property relationships.
Although no quantitative comparison is presently possible, we suggest that ACs may be more prevalent than PCliffs. This hypothesis is not based on statistical evidence, but rather on the distinct nature of the phenomena underlying each type of discontinuity.
ACs arise from molecular recognition processes that are intrinsically nonlinear, non-additive, and highly context dependent. Biological activity depends on multiple interconnected factors, including conformational effects, desolvation processes, specific ligand–receptor interactions, active-site reorganization, alternative binding modes, and the coexistence of orthosteric and allosteric binding sites. Consequently, relatively small structural modifications can produce abrupt and often difficult-to-predict changes in bioactivity. By contrast, many physicochemical properties, such as logP, pKa, or polar surface area, exhibit behavior that is closer to additivity and is frequently governed by relatively local structural contributions. Although PCliffs clearly occur, as illustrated in the previous section, they often originate from identifiable phenomena, including electronic effects, steric effects, conformational changes, state crossings, or alterations of the potential energy surface. As a result, even when the resulting property changes are large, the underlying mechanisms are often more systematic and mechanistically interpretable than those responsible for many ACs.
Table 1 summarizes representative phenomena that can give rise to ACs and PCliffs together with their mechanistic origins. This compilation is not intended to be exhaustive, nor does the presence of any individual phenomenon necessarily imply the formation of a cliff.
TABLE 1
| Cause | Explanation | Ref. |
|---|---|---|
| ACs | ||
| Change in binding mode | Small structural modifications alter the orientation of the ligand within the active site | , Stensbøl et al. (2002) |
| Specific ligand–receptor interactions | Loss or gain of hydrogen bonds, π–π, hydrophobic, or ionic interactions | , |
| Conformational effects | Changes in ligand flexibility or accessible conformation | |
| Desolvation and entropic effects | Changes in desolvation energy or entropic contributions | |
| Orthosteric vs. allosteric sites | Binding to different regions of the receptor with distinct effects | , |
| Induced fit | Structural adaptation of the receptor upon ligand binding | , |
| PCliffs | ||
| Nonlinear electronic effects | Small changes in substituents alter charge delocalization, orbital energies, or resonance stabilization, leading to variations in properties such as pKa, reactivity, or spectroscopic properties | , van Niel et al. (1999), |
| Steric and volume effects | Changes in size or steric hindrance affect accessibility, stability, or interactions with the surrounding environment | Kellogg and Abraham (2000) |
| Interaction coupling (non-additivity) | Multiple weak intra- and intermolecular interactions act cooperatively, producing property changes that cannot be explained by the sum of their individual contributions | , |
| Conformational changes | Small structural modifications favor different molecular geometries, altering the spatial distribution of functional groups and, consequently, the observed properties (e.g., dipole moment, logP, etc.) | |
| Change in dominant state | Variations in pH, tautomerism, or other equilibria alter the predominant species | Yang et al. (2021) |
| Solvation/environmental effects | Interactions with the solvent or surrounding medium significantly modify the observed property | |
| Switch in the dominant pathway | Small structural modifications alter the relative rates or activation barriers of competing pathways, causing a different mechanism or physicochemical process to become dominant and producing abrupt changes in the observed property | |
| Supramolecular organization effects | Differences in stacking, packing, or solid-state structure produce abrupt changes in properties | , Yang et al. (2021), |
Main causes underlying ACs and PCliffs.
So, PCliffs generally emerge from structural perturbations that induce nonlinear changes in electronic structure, conformational equilibria, state stability, or collective material properties. In contrast to ACs, they do not typically depend on specific ligand–receptor recognition events, but rather on intrinsic physicochemical processes that can often be identified and rationalized mechanistically. This distinction may influence the prevalence of PCliffs. As a starting point to evaluate this prevalence, the methodologies currently used for AC detection could be explored. Several approaches have been developed for the identification of ACs, including matched molecular pair analysis, structure–activity landscape indices, and similarity-based cliff metrics. None of these have been used to assess PCliffs. As much as the presence of AC affects QSAR modeling, it is expected that the identification of PCliffs will also influence the development of QSPR models. Furthermore, the development of criteria for identifying and quantifying discontinuities in molecular property landscapes, together with consideration of the applicability domain concept, represents an important direction for future research.
Interpretability of ACs and PCliffs
Beyond their relative frequency, ACs and PCliffs also differ in their degree of mechanistic interpretability. Although both phenomena represent discontinuities in molecular landscapes, the factors underlying them are not equally easy to rationalize. In general, PCliffs tend to be more interpretable because physicochemical properties are often governed by well-established principles of physical chemistry, including electronic effects, solvation, conformational equilibria, and kinetic or thermodynamic stability. By contrast, ACs emerge from molecular recognition processes involving multiple interconnected factors, making it difficult to establish direct causal relationships between structural modifications and biological activity.
In an effort to rationalize ACs, based on protein–ligand complexes, Bajorath and co-workers (Stumpfe et al., 2014; ; ) examined crystallographic complexes associated with multiple therapeutic targets and defined six mechanistic categories. Particularly informative are categories 5 and 6. Category 5, which accounts for approximately 13%–23% of the analyzed ACs, corresponds to cases in which activity changes arise from the combined action of several factors, including hydrogen bonding, hydrophobic interactions, and steric effects. Because no single contribution dominates, mechanistic interpretation becomes challenging. Category 6, representing roughly 10% of the analyzed ACs, is even more striking. In these cases, structurally similar ligands display nearly indistinguishable binding modes yet differ in activity by at least two orders of magnitude. The absence of an obvious structural explanation suggests the involvement of subtle and difficult-to-quantify factors beyond those directly observable in the complexes.
More than two decades after these observations, model interpretability remains a central objective in QSAR research. Recent studies continue to place considerable emphasis on identifying molecular descriptors associated with biological activity and on developing approaches that facilitate the chemical interpretation of predictive models. These efforts include descriptor-level analyses, substructure-based interpretations, atomic contribution mapping, and dimensionality reduction strategies designed to preserve chemical meaning while improving model interpretability. Although such approaches enhance our understanding of QSAR models, they also illustrate that interpreting the molecular determinants of biological activity remains an active and unresolved challenge (Zapadka et al., 2025; ).
By contrast, PCliffs generally originate from intrinsic physicochemical phenomena that can often be isolated, quantified, and rationalized using theoretical models and computational tools. Consequently, more direct links can frequently be established between a structural perturbation and the resulting property change. This does not imply that all PCliffs are straightforward to interpret. In systems involving competing mechanisms, non-obvious electronic reorganizations, spin-state effects, or complex collective behavior, identifying the dominant factor may require extensive analysis. Nevertheless, the interpretation of PCliffs usually remains grounded in established conceptual frameworks of physical chemistry.
Additional support for this view comes from molecular-property prediction. In many applications, QSPR models tend to exhibit greater robustness and transferability than QSAR models, suggesting that currently available molecular descriptors often capture variations in physicochemical properties more effectively than variations in biological activity. While this observation is not universal, it is consistent with the notion that structure–property relationships are generally easier to rationalize than structure–activity relationships.
The available evidence suggests that PCliffs are not only conceptually distinct from ACs but also tend to be more amenable to mechanistic interpretation. Although exceptions certainly exist, the underlying causes of PCliffs can often be identified within established physicochemical frameworks, whereas ACs frequently reflect the complexity and context dependence of biological recognition processes.
Discussion
In this Perspective, we examined ACs and PCliffs within the broader context of structure–activity and structure–property relationships, focusing on three central questions: their existence, relative frequency, and mechanistic interpretability. The available evidence indicates that, although ACs are a well-established and extensively studied phenomenon in medicinal chemistry, analogous discontinuities also occur across a wide range of physicochemical properties. The examples discussed here show that abrupt changes are not restricted to biological activity but can emerge in acidity, lipophilicity, chemical reactivity, spectroscopy, electronic transport, and materials properties.
The identification of a discontinuity in a structure–property landscape and the interpretation of its origin are conceptually distinct steps. From a cheminformatics perspective, discontinuities are first identified operationally using molecular representations and structural similarity criteria. Their subsequent interpretation then seeks to determine whether the observed discontinuity originates from an underlying physicochemical mechanism or instead arises from experimental uncertainty, data-quality issues, limitations of the molecular representation, or extrapolation beyond the applicability domain of predictive models.
Although the prevalence of PCliffs has not yet been quantified, we propose that ACs may be more common than PCliffs. This view is motivated by the intrinsically nonlinear and context-dependent nature of molecular recognition processes, which can amplify the consequences of relatively small structural modifications. In contrast, many physicochemical properties are more closely linked to local structural features and often exhibit behavior that is closer to additivity.
A second distinction concerns interpretability. While ACs frequently reflect the combined influence of multiple interacting factors that are difficult to disentangle, PCliffs can often be rationalized within established frameworks of physical chemistry. Even when complex mechanisms are involved, the underlying causes of PCliffs are typically more amenable to mechanistic analysis through theoretical and computational approaches.
More broadly, recognizing PCliffs as a distinct class of structure–property discontinuities could provide further improvements in QSPR modeling, computational chemistry, materials science, and data-driven molecular design. Modern predictive models are increasingly applied to electronic, optical, catalytic, spectroscopic, and transport properties, extending the scope of structure–property relationships far beyond their traditional role in medicinal chemistry. In this context, systematic investigation of abrupt property changes may provide valuable insights into molecular function, materials performance, and the limitations of predictive models.
Future development demands practical frameworks for identifying and characterizing PCliffs across different chemical domains. Because the significance of a property change is inherently property dependent, universal numerical thresholds are unlikely to be useful. Instead, property-specific criteria, molecular similarity metrics, matched molecular pair analysis, error quantification, and applicability domain assessment may provide a more robust foundation for identifying discontinuities in structure–property landscapes. Such advances would not only enable quantitative assessments of the frequency of PCliffs but could also improve the interpretability, reliability, and predictive performance of machine-learning models for molecular properties.
Statements
Data availability statement
The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding authors.
Author contributions
EEA-M: Writing – original draft, Investigation, Conceptualization. DR-P: Writing – review and editing, Investigation. GM: Investigation, Writing – review and editing, Supervision, Resources. KM-M: Conceptualization, Supervision, Writing – review and editing, Resources.
Funding
The author(s) declared that financial support was not received for this work and/or its publication.
Conflict of interest
The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
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Summary
Keywords
activity cliffs, physicochemical properties, property cliffs, QSAR, QSPR
Citation
Abreu-Martínez EE, Ramírez-Palma D, Merino G and Martinez-Mayorga K (2026) Do property cliffs exist? A conceptual analysis of structural changes and molecular properties. Front. Drug Discov. 6:1899616. doi: 10.3389/fddsv.2026.1899616
Received
03 June 2026
Revised
27 July 2026
Accepted
03 August 2026
Published
03 September 2026
Volume
6 - 2026
Edited by
Alan Talevi, National University of La Plata, Argentina
Reviewed by
Marcin Gackowski, Nicolaus Copernicus University in Toruń, Poland
Updates
Copyright
© 2026 Abreu-Martínez, Ramírez-Palma, Merino and Martinez-Mayorga.
This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Karina Martinez-Mayorga, kmtzm@unam.mx; Gabriel Merino, gmerino@cinvestav.mx
† Present Address: David Ramírez-Palma, Centro de Física Aplicada y Tecnología Avanzada, Universidad Nacional Autónoma de México, Querétaro, Mexico
Disclaimer
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