Archive for March 11th, 2020

The singlet and open shell higher-spin states of [4], [6] and [8]-annulenes and their Kekulé vibrational modes

Wednesday, March 11th, 2020

In 2001, Shaik and co-workers published the first of several famous review articles on the topic A Different Story of π-Delocalization. The Distortivity of π-Electrons and Its Chemical Manifestations[1]. The main premise was that the delocalized π-electronic component of benzene is unstable toward a localizing distortion and is at the same time stabilized by resonance relative to a localized reference structure.  Put more simply, the specific case of benzene has six-fold symmetry because of the twelve C-C σ-electrons and not the six π-electrons. In 2009, I commented here on this concept, via a calculation of the quintet state of benzene in which two of the six π-electrons are excited from bonding into anti-bonding π-orbitals, thus reducing the total formal π-bond orders around the ring from three to one. I focused on a particular vibrational normal mode, which is usefully referred to as the Kekulé mode, since it lengthens three bonds in benzene whilst shortening the other three. In this case the stretching wavenumber increased by ~207 cm-1 when the total π-bond order of benzene was reduced from three to one by spin excitation. In other words, each C-C bond gets longer when the π-electrons are excited, but the C-C bond itself gets stronger (in terms at least of the Kekulé mode). This behaviour is called a violation of Badger’s rule[2] for the relationship between the length of a bond and its stretching force constant. 



  1. S. Shaik, A. Shurki, D. Danovich, and P.C. Hiberty, "A Different Story of π-DelocalizationThe Distortivity of π-Electrons and Its Chemical Manifestations†", Chemical Reviews, vol. 101, pp. 1501-1540, 2001.
  2. R.M. Badger, "A Relation Between Internuclear Distances and Bond Force Constants", The Journal of Chemical Physics, vol. 2, pp. 128-131, 1934.