Theoretical Chemistry Accounts

, Volume 127, Issue 1–2, pp 27–38 | Cite as

How to properly compute the resonance energy within the ab initio valence bond theory: a response to the ZHJVL paper

  • Yirong Mo
  • Philippe C. Hiberty
  • Paul von Ragué Schleyer
Reply to Comment


Valence bond (VB) theory describes a conjugated system by a set of electron-localized Lewis resonance structures. VB assumes that the magnitude of the intramolecular electron delocalization can be measured in terms of a resonance energy (RE), taken to be the energy difference between the real conjugated system (delocalized) and the corresponding most stable virtual resonance structure (localized). Proper RE estimates within VB theory require both delocalized and localized states to be defined at the same theoretical level, and the definition of the localized state to closely correspond to the intuitive picture of the corresponding VB structure. In contrast, the VB-delocal and VB-local computational approaches adopted by Zielinski, et al. [preceding paper in this issue] used definitions for either the delocalized or the localized states which, in our view, depart from the intuitive chemical picture. Consequently, their RE estimates are much lower than seemingly appropriate experimental evaluations with which they strongly disagree. Very large basis sets approaching completeness blur the boundaries among resonance structures and result in “basis set artifact” problems within any variant of VB theory. However, block-localized wavefunction (BLW) computations with mid-size basis sets not only exhibit insignificant variations with theoretical levels, but the resulting RE estimates also are justified by comparisons with those employing experimental data and MO computations. We stress that RE differs from the aromatic stabilization energy (ASE). The RE measures the total stabilization of an aromatic system, whereas ASE measures only the part of the RE that exceeds that of appropriate conjugated (but non-aromatic) reference molecules.


Valence bond theory Resonance energy 



This paper is dedicated to Prof. Dr. Rolf Huisgen with warmth and esteem on the occasion of his 90th birthday. The work in Georgia was supported by NSF Grant CHE-0716718.


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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of ChemistryWestern Michigan UniversityKalamazooUSA
  2. 2.Laboratoire de Chimie Physique, Groupe de Chimie ThéoriqueUniversité de Paris-SudOrsay CédexFrance
  3. 3.Department of ChemistryUniversity of GeorgiaAthensUSA

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