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Molecular spaces and the dimension paradox

  • Ramon Carbó-Dorca EMAIL logo
Published/Copyright: June 22, 2021
Pure and Applied Chemistry
From the journal Pure and Applied Chemistry Volume 93 Issue 10

Abstract

In this study, the dimension or dimensionality paradox is defined and discussed in a dedicated context. This paradox appears when discrete vector representations of the elements of a molecular set are constructed employing several descriptor parameters, adopting specific values for each molecule. The dimension paradox consists in that when constructing discrete N-dimensional molecular vectors, the primal structure of the attached molecular set, chosen as a collection of different objects, cannot be well-defined if the number of descriptors N and the number of molecules M do not bear a convenient relation like: N ≥ M . This has implications for the linear independence of the vectors connected with each molecule.

Keywords: Chemistry and its applications; chemometrics; density functions; dimension or dimensionality paradox; discrete molecular representation; molecular space; molecular vectors; parameter or descriptor space; quantum mechanical molecular representation; QSPR; quantum similarity; VCCA-2020
Corresponding author: Ramon Carbó-Dorca, IQCC University of Girona, 17003 Girona, Catalonia, Spain, e-mail:
Article note: A collection of invited papers based on presentations at the Virtual Conference on Chemistry and its Applications (VCCA-2020) held on-line, 1–31 August 2020. This work has been presented as one of the contributions to the virtual meeting VCCA-2020 organized by the University of Mauritius.

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Published Online: 2021-06-22
Published in Print: 2021-10-26

© 2021 IUPAC & De Gruyter. This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. For more information, please visit: http://creativecommons.org/licenses/by-nc-nd/4.0/

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  2. In this issue
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  5. Invited papers
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  7. On cellulose spatial organization and interactions as unraveled by diffraction and spectroscopic methods throughout the 20th century
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https://doi.org/10.1515/pac-2021-0112
Keywords for this article
Chemistry and its applications; chemometrics; density functions; dimension or dimensionality paradox; discrete molecular representation; molecular space; molecular vectors; parameter or descriptor space; quantum mechanical molecular representation; QSPR; quantum similarity; VCCA-2020

Articles in the same Issue

  1. Frontmatter
  2. In this issue
  3. Preface
  4. Celebrating a centenary of macromolecules
  5. Invited papers
  6. Hermann Staudinger – Organic chemist and pioneer of macromolecules
  7. On cellulose spatial organization and interactions as unraveled by diffraction and spectroscopic methods throughout the 20th century
  8. Dielectric properties of processed cheese
  9. Drawing inspiration from nature to develop anti-fouling coatings: the development of biomimetic polymer surfaces and their effect on bacterial fouling
  10. Mitigating the charge trapping effects of D-sorbitol/poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate) (PEDOT:PSS) polymer blend contacts to crystalline silicon
  11. Influence of thermal treatment on the properties and intermolecular interactions of epoxidized natural rubber-salt systems
  12. Leveraging diversity and inclusion in the polymer sciences: the key to meeting the rapidly changing needs of our world
  13. Preface
  14. The virtual conference on chemistry and its applications, VCCA-2020, 1–31 August 2020
  15. Conference papers
  16. Effect of non-competitive inhibitors of aminopeptidase N on viability of human and murine tumor cells
  17. Evaluation of the catalytic activity of graphene oxide and zinc oxide nanoparticles on the electrochemical sensing of T1R2-Rebaudioside A complex supported by in silico methods
  18. Maximizing student learning through the use of demonstrations
  19. Molecular spaces and the dimension paradox
  20. Reaction of •OH with CHCl=CH-CHF2 and its atmospheric implication for future environmental-friendly refrigerant
  21. In silico study of the synergistic anti-tumor effect of hybrid topoisomerase-HDAC inhibitors
  22. Structural and electronic properties of Cu4O3 (paramelaconite): the role of native impurities
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