Antibonding orbitals, definition

Anti-aromaticity was predicted by the Hiickel approach for conjugated cyclic planar structures with 4n 7i electrons due to the presence of two electrons in antibonding orbitals, such as in the cydopropenyl anion, cydobutadiene, and the cydopentadienyl cation (n = 1), and in the cydoheptatrienyl anion and cydooctatetraene (n = 2). It has been argued that a simple definition of an anti-aromatic molecule is one for which the 1H NMR shifts reveal a paramagnetic ring current, but the subject is controversial. The power of the Hiickel theory indeed resides not only in the aromatic stabilization of cydic 4n + 2 electron systems, but also in the destabilization of those with An electrons [22, 27, 42]. 

Earlier in this chapter, you learned the definition of bond order in the valence bond theory. In molecular orbital theory, the bond order is defined as one-half the difference between the number of electrons in bonding orbitals and the number of electrons in antibonding orbitals. Mathematically, this can be expressed as... 

Conversely, using the definition of antibonding orbitals, the anti-bonding orbital for ethylene may be written as ... 

The anti-bonding MO s from the valence shell are of a and 61 t5rpe. Just as we can assign symmetry labels to bond orbitals, so we can have antibond orbitals of definite S3mimetry. For water we must take the sum and difference of the two anti-bonding orbitals to be consistent with C20 sjun-metry. 

A simple definition of the bond order is the number of electrons in bonding orbitals minus the number in antibonding orbitals, divided by two. Hence, H2 has a bond order of 1 while He2 would have a bond order of 0. 

The wave function of Eq. (20.3-15) corresponds to the electron configuration with two electrons occupying bonding orbitals and two occupying antibonding orbitals. In order to agree with the general chemistry definition, we define the bond order as ... 

---