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Conformal Coordinates for Molecular Geometry: From 3D to 5D.

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Title: Conformal Coordinates for Molecular Geometry: From 3D to 5D.
Authors: Camargo, Jesus1 (AUTHOR), Lavor, Carlile2 (AUTHOR) clavor@unicamp.br, Souza, Michael3 (AUTHOR)
Source: Journal of Computational Chemistry. 2/5/2026, Vol. 47 Issue 4, p1-7. 7p.
Subjects: Interatomic distances, Conformal geometry, Mathematical simplification, Analytic geometry, Molecular shapes
Abstract: This paper introduces the conformal model (an extension of the homogeneous coordinate system) for molecular geometry, where 3D space is represented within ℝ5$$ {\mathbb{R}}^5 $$ with an inner product different from the usual one. This model enables efficient computation of interatomic distances using what we call the Conformal Coordinate Matrix (C‐matrix). The C‐matrix not only simplifies the mathematical framework but also reduces the number of operations required for distance calculations compared to traditional methods. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Computational Chemistry is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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Header DbId: egs
DbLabel: Engineering Source
An: 191377057
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
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  Data: Conformal Coordinates for Molecular Geometry: From 3D to 5D.
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  Data: <searchLink fieldCode="AR" term="%22Camargo%2C+Jesus%22">Camargo, Jesus</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Lavor%2C+Carlile%22">Lavor, Carlile</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> clavor@unicamp.br</i><br /><searchLink fieldCode="AR" term="%22Souza%2C+Michael%22">Souza, Michael</searchLink><relatesTo>3</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Computational+Chemistry%22">Journal of Computational Chemistry</searchLink>. 2/5/2026, Vol. 47 Issue 4, p1-7. 7p.
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  Data: <searchLink fieldCode="DE" term="%22Interatomic+distances%22">Interatomic distances</searchLink><br /><searchLink fieldCode="DE" term="%22Conformal+geometry%22">Conformal geometry</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+simplification%22">Mathematical simplification</searchLink><br /><searchLink fieldCode="DE" term="%22Analytic+geometry%22">Analytic geometry</searchLink><br /><searchLink fieldCode="DE" term="%22Molecular+shapes%22">Molecular shapes</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This paper introduces the conformal model (an extension of the homogeneous coordinate system) for molecular geometry, where 3D space is represented within ℝ5$$ {\mathbb{R}}^5 $$ with an inner product different from the usual one. This model enables efficient computation of interatomic distances using what we call the Conformal Coordinate Matrix (C‐matrix). The C‐matrix not only simplifies the mathematical framework but also reduces the number of operations required for distance calculations compared to traditional methods. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Computational Chemistry is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1002/jcc.70256
    Languages:
      – Code: eng
        Text: English
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      Pagination:
        PageCount: 7
        StartPage: 1
    Subjects:
      – SubjectFull: Interatomic distances
        Type: general
      – SubjectFull: Conformal geometry
        Type: general
      – SubjectFull: Mathematical simplification
        Type: general
      – SubjectFull: Analytic geometry
        Type: general
      – SubjectFull: Molecular shapes
        Type: general
    Titles:
      – TitleFull: Conformal Coordinates for Molecular Geometry: From 3D to 5D.
        Type: main
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            NameFull: Camargo, Jesus
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            NameFull: Lavor, Carlile
      – PersonEntity:
          Name:
            NameFull: Souza, Michael
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          Dates:
            – D: 05
              M: 02
              Text: 2/5/2026
              Type: published
              Y: 2026
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              Value: 01928651
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              Value: 47
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              Value: 4
          Titles:
            – TitleFull: Journal of Computational Chemistry
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