Sason Shaik, David Danovich, Wei Wu, Peifeng Su, Henry S. Rzepa, Philippe C. Hiberty, Nature Chemistry 2012, 4, 195 (Paywall)
Contributed by Steven Bachrach.
Reposted from Computational Organic Chemistry with permission
Inspired by a blog post of Henry Rzepa (see here) Shaik and co-workers examined the C2 species with an eye towards the nature of the bond between the two carbon atoms. Using both a valence bond approach and a full CI approach, they end up at the same place: there is a quadruple bond here!
The argument rests largely on a definition of of an in situ
bond energy. For the VB approach, this requires choosing as a reference a
non-bonding interaction between the atoms with regards to a pair of
electrons. For the CI approach, the bond energy is half the energy of
the singlet-triplet gap. So, for C2, the VB/6-31G* estimate of the bond energy of the putative fourth bond is 14.3 kcal mol-1. For the full CI/6-31G* computations of the singlet-triplet gap, the bond energy estimate is 14.8 kcal mol-1, and using the experimental value of the gap, the estimate is 13.2 kcal mol-1. Not a strong bond, but certainly meaningful!
In the VB approach, the fourth bond is a weighted sum of the antibonding 2σu and bonding 3σg
orbitals – a combination that gives rise to small constructive overlap
between the two C atoms. In the CI model, the wavefunction is dominated
by the first two configurations; the first configuration, with a
coefficient of C0=0.828 has 2σu doubly occupied and the second coefficient, with CD=0.324, has the 3σg orbital doubly occupied. Considering that 3σg is a bonding orbital, the significant contribution of this configuration gives rise to the fourth bond.
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