Cyclobutadiene with Equal Bond Lengths

Our aim is to show that a superposition of the SDW and CDW wave functions leads to gronnd state currents. An effective intersite coupling p 0 is assumed for neighboring sites. Otherwise, there is no conpling. We assume one active orbital (or hole) per site, as in an aromatic system. In onr case, the active hole corresponds directly to the Cu with one missing electron in a bjg MO. The bjg MO energies form a half-filled band. 

The well-known Huckel eigenvalue problem for cyclobutadiene takes the form (see Chapter 3)  

In the ground state, ct)/ is always occupied. Since 2 and 4)3 are degenerate, there are a number of different possibilities for occupation and final many-electron states. In cyclobutadiene, we may occupy 2 by two electrons and obtain a short bond between atoms 2 and 3 and between atoms 1 and 4, since 2 is bonding between 2 and 3 and between 1 and 4. This is consistent with the experimental fact that two of the bonds are shorter in cyclobutadiene. 

FIGURE 17.7 Four sites—four electrons (L = 1). (a) Ordinary Hiickel orbitals and (b) transformed. 

If ( )2 is occupied by a spin-up electron and ([ 3 with a spin-down electron, we obtain (after symmetrization) the spin-coupled state. If ( 2 is occupied by two electrons or ( )3 is occupied by two electrons, we obtain the charged state. With these occupations the bond lengths remain the same, since in 2 and 4 3 two nonzero MOs are never on adjacent atoms. 

---

We can therefore now conclude that there are three contributions that determine the geometry of benzene and cyclobutadiene. The first contribution is that of the a-system which prefers equal bond lengths. The other two contributing factors are the 7l-bonds and the 7l-resonance. The 7i-bonds by themselves give rise to two states with a minimum at one of the geometries with alternating bond lengths. The resonance provides interaction between the two states and stabilises the symmetric structure. 

If we think of structural criteria for the aromaticity of benzene and the antiaromaticity of cyclobutadiene, we immediately end up with the observation that the bond lengths of benzene are all equal and the bond lengths of cyclobutadiene are pairwise quite different. 

In 1956 Longuet-Higgins and Orgel predicted that the unstable cyclobutadiene system would be stabilized by complex formation with a transition metal. Three years later Criegee isolated the first r-cyclobuta-diene complex, 7.12, as a red-violet powder, soluble in methylene chloride and in water. The C4Me4 group is nearly planar, and the annular C—C bonds are all equal in length. 

---