<p>Aromaticity represents a fundamental principle within the domain of chemistry, but it is not a physical observable and consequently cannot be directly measured. Over the past few decades, a wide array of aromaticity indicators have been suggested based on various properties of molecules such as structure, energy, magnetism, electronic configuration, and reactivity. Thus, aromaticity is usually characterized by means of a set of features grounded on various manifestations. This paper proposes the adoption of data dimensionality reduction and visualization methodologies to examine the aromaticity of a test bed of 150 <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="521_2025_11643_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\pi\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>π</mi> </math></EquationSource> </InlineEquation>-organic compounds, each characterized by 4 descriptors. In order to generate appropriate inputs for the dimensionality reduction and information visualization techniques, the compounds comparison is provided utilizing various distances. Self-organized maps (SOM) successfully identified meaningful clusters of five- and six-membered ring compounds, based on the dissimilarities between the energetic, magnetic, and structural descriptors, revealing patterns in aromaticity across structural types. Multidimensional scaling (MDS) and uniform manifold approximation and projection (UMAP) mappings preserved these patterns to varying degrees, with UMAP showing stronger alignment with the SOM-based clustering. Additional substructures emerged through K-means analysis of the MDS and UMAP outputs, supporting the robustness of the observed aromaticity trends. The findings suggest that, given the present day computational resources, modeling options such as dimensionality reduction and specialized complex data visualization tools are useful for displaying aromaticity.</p>

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Multidimensional analysis and visualization of aromaticity in five- and six-membered ring compounds

  • Mercedes Alonso,
  • Vitor M. R. Cunha,
  • Alexandra Galhano,
  • António M. Lopes,
  • J. A. Tenreiro Machado

摘要

Aromaticity represents a fundamental principle within the domain of chemistry, but it is not a physical observable and consequently cannot be directly measured. Over the past few decades, a wide array of aromaticity indicators have been suggested based on various properties of molecules such as structure, energy, magnetism, electronic configuration, and reactivity. Thus, aromaticity is usually characterized by means of a set of features grounded on various manifestations. This paper proposes the adoption of data dimensionality reduction and visualization methodologies to examine the aromaticity of a test bed of 150 \(\pi\) π -organic compounds, each characterized by 4 descriptors. In order to generate appropriate inputs for the dimensionality reduction and information visualization techniques, the compounds comparison is provided utilizing various distances. Self-organized maps (SOM) successfully identified meaningful clusters of five- and six-membered ring compounds, based on the dissimilarities between the energetic, magnetic, and structural descriptors, revealing patterns in aromaticity across structural types. Multidimensional scaling (MDS) and uniform manifold approximation and projection (UMAP) mappings preserved these patterns to varying degrees, with UMAP showing stronger alignment with the SOM-based clustering. Additional substructures emerged through K-means analysis of the MDS and UMAP outputs, supporting the robustness of the observed aromaticity trends. The findings suggest that, given the present day computational resources, modeling options such as dimensionality reduction and specialized complex data visualization tools are useful for displaying aromaticity.