Particle on a Ring Model for Teaching the Origin of the Aromatic Stabilization Energy and the Hückel and Baird Rules
Open accessAbstract
Simple mathematical models can serve to reveal the essence of experimental phenomena and scientific concepts. The particle in a box (PIB), for example, is widely used in undergraduate programs to teach the quantum mechanical principles behind the UV-vis spectra of conjugated polyenes and polyynes. In this work, the particle on a ring (POR) and the PIB models are used to elucidate the concept of aromaticity in Introductory Chemistry courses. Thus, we explain the origin of the aromatic stabilization energy, Hückel's rule, and Baird's rule. Besides applications, the limitations of the POR and PIB models are also discussed.
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Solà and Bickelhaupt used simple particle-in-a-box (PIB) and particle-on-a-ring (POR) models to show that the POR model gives a lower first energy level and that higher energy levels come in pairs.
“Solà and Bickelhaupt used simple particle-in-a-box (PIB) and particle-on-a-ring (POR) models to show that the latter gives a lower first energy level and that higher energy levels come in pairs [56].”
From Aromaticity and Antiaromaticity: How to Define Them (2025) · cites this paper as [56]
The difference between the mathematical equations for linear (PIB) and cyclic (POR) systems with the same number of electrons can be considered an approximation of aromatic stabilization energy (ASE).
“The difference between the two mathematical equations for linear (PIB) and cyclic (POR) systems with the same number of particles (electrons) can be considered as an approximation of aromatic stabilization energy (ASE) [56].”
From Aromaticity and Antiaromaticity: How to Define Them (2025) · cites this paper as [56]
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Baird, N. C. (1972) · Journal of the American Chemical Society · doi:10.1021/ja00769a025 · Cited by 680 · see citing works
Experimental and Theoretical Evidence for Aromatic Stabilization Energy in Large Macrocycles
Jirásek, M., Rickhaus, M., Tejerina, L., & Anderson, H. L. (2021) · Journal of the American Chemical Society · doi:10.1021/jacs.0c12845 · Cited by 57 · see citing works
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Aromaticity and Antiaromaticity: How to Define Them
Baranac-Stojanović, M. (2025) · Chemistry · doi:10.3390/chemistry7040127 · Cited by 14 · see citing works
- Authors
- Solà, M., & Bickelhaupt, F. M.
- Affiliations
- Universitat de Girona (ES)
- Radboud University Nijmegen (NL)
- Corresponding author
- Solà, Miquel
- Bickelhaupt, F. Matthias
- Venue
- Journal of Chemical Education
- Publisher
- American Chemical Society (ACS)
- Published
- 2022-09-22
- Volume
- 99
- Issue
- 10
- Pages
- 3497-3501
- ISSN
- 0021-9584 (ISSN-L)
- 1938-1328
- PMC
- PMC9558373
- OpenAlex
- W4296669965
- Cited by
- 21
- References
- 2
- Citations by year
- 2026: 2 · 2025: 7 · 2024: 4 · 2023: 7 · 2022: 1
- FWCI
- 1.81
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Locations
- Journal of Chemical Education (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- VU Research Portal (publishedVersion, other-oa)
- Universitat de Girona Digital Repository (Universitat de Girona) (submittedVersion, cc-by)
- Radboud Repository (Radboud University) (submittedVersion)
- Radboud Repository (Radboud University) (submittedVersion, other-oa)
- Data Archiving and Networked Services (DANS) (submittedVersion, other-oa)
- Funders
- Ministerio de Ciencia e Innovaci?n (PID2020-13711GB-I00)
- Holland Research School of Molecular Chemistry
- Generalitat de Catalunya (2017SGR39)
- Nederlandse Organisatie voor Wetenschappelijk Onderzoek
- Topics
- Physical Sciences › Chemistry › Organic Chemistry › Synthesis and Properties of Aromatic Compounds
- Physical Sciences › Chemistry › Physical and Theoretical Chemistry › Various Chemistry Research Topics
- Social Sciences › Education › Science Education and Pedagogy
- Keywords
- particle-in-a-box model, aromatic stabilization energy, Baird's rule, aromaticity, conjugated polyenes, UV-Vis spectra, introductory chemistry teaching
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