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Cited by 52Advanced Chemical Physics StudiesSynthesis and Properties of Aromatic CompoundsPhysical Organic Chemistry and Reaction Kinetics

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The Resonance Energy of Benzene: A Revisit

Mo, Yirong·2009·The Journal of Physical Chemistry A
DOI 10.1021/jp808941h
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Abstract

Zielinski and van Lenthe recently extended the block-localized wave function (BLW) method by introducing the resonating BLW (RBLW) method and performed test calculations on hexagonal H(6) and benzene [J. Phys. Chem. A 2008, 112, 13197]. However, the Pauling's resonance energies from their RBLW and ab initio valence bond (VB) calculations were greatly underestimated largely due to the imperfect use of either one-electron orbitals (method = delocal) or resonance structures (method = local). Whereas it has been well recognized that electronic resonance within a molecular system plays a stabilizing role, there are many indirect experimental evidences available to evaluate the resonance energy and, thus, to justify computational results. Here we used the BLW method, which can be regarded as the simplest variant of modern ab initio VB theory, to re-evaluate the resonance energy of benzene at the B3LYP level, following the original definition by Pauling and Wheland, who obtained the resonance energy "by subtracting the actual energy of the molecule in question from that of the most stable contributing structure". The computed vertical resonance energy (or quantum mechanical resonance energy) in benzene is 88.8, 92.2, or 87.9 kcal/mol with the basis sets of 6-31G(d), 6-311+G(d,p), or cc-pVTZ, respectively, while the adiabatic resonance energy (or theoretical resonance energy) is 61.4, 63.2, or 62.4 kcal/mol, exhibiting insignificant basis set dependency for moderate basis sets. In line with predictions, the geometry optimization of the elusive cyclohexatriene (i.e., the Kekule structure) with the BLW method also resulted in carbon-carbon bond lengths (e.g., 1.322 and 1.523 A with the cc-pVTZ basis set) comparable to those in ethylene or ethane.

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  • The σ strain in benzene is overcome by the π-electron resonance energy.

    “This strain is overcome by the πelectron RE [69,70].”

    From Aromaticity and Antiaromaticity: How to Define Them (2025) · cites this paper as [69]

  • The block localized wavefunction (BLW) approach allows estimation of VRE by localizing certain bonds and disabling interactions between them.

    “The block localized wavefunction (BLW) approach allows the estimation of the VRE by localizing certain bonds and disabling interactions between them [69,70,78,79].”

    From Aromaticity and Antiaromaticity: How to Define Them (2025) · cites this paper as [69]

  • Benzene has strain in the σ-electron system due to compression of the σ bonds from the optimal value of 1.52 Å for Csp2-Csp2 single bond to 1.40 Å.

    “It has strain in the σ-electron system due to compression of the σ bonds from the optimal value of 1.52 Å for Csp 2 -Csp 2 single bond to 1.40 Å [69,70].”

    From Aromaticity and Antiaromaticity: How to Define Them (2025) · cites this paper as [69]

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Metadata

Authors
Mo, Y.
Affiliations
Western Michigan University (US)
Corresponding author
Mo, Yirong
ORCID
Mo, Yirong
Venue
The Journal of Physical Chemistry A
Publisher
American Chemical Society (ACS)
Published
2009-03-26
Volume
113
Issue
17
Pages
5163-5169
ISSN
  • 1089-5639 (ISSN-L)
  • 1520-5215
DOI
10.1021/jp808941h
OpenAlex
W2015903473
Cited by
52
References
1
Citations by year
2026: 3 · 2025: 4 · 2024: 2 · 2023: 1 · 2022: 5 · 2021: 3 · 2020: 5 · 2018: 3 · 2017: 2 · 2016: 3 · 2015: 2 · 2014: 3 · 2012: 6
FWCI
2.97
Type
journal article
Language
en
Open access
closed
Locations
  • The Journal of Physical Chemistry A (publishedVersion)
  • PubMed (publishedVersion)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Advanced Chemical Physics Studies
  • Physical Sciences › Chemistry › Organic Chemistry › Synthesis and Properties of Aromatic Compounds
  • Physical Sciences › Chemistry › Organic Chemistry › Physical Organic Chemistry and Reaction Kinetics
Keywords
benzene, resonance energy, Kekulé structures, basis set effects, carbon-carbon bond length

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