Mixing of orbitals

Morrison & Boyd 6th ed., p. 1013

< img align=left src="dasymm.gif"> Of course, reality is more complicated than the models we use. That is what models are for.

The symmetrical bonding orbital shown on the left is clearly more than a simple HOMO(ethylene)/LUMO(butadiene) combination. On the previous page, and in textbooks, the mixing of orbitals is always illustrated using two orbitals. This suggests that a new MO can be seen as a linear combination of two MO's in the reactants.
In the initial stages of a reaction this approximation may be justified: the pi homo and lumo extend further in space than the sigma orbitals and will overlap first. They are also closest in energy.

When approaching the transition state however, this distinction between 'pure' pi and sigma orbitals has dissappeared. Completely new MO's will be calculated from the AO's, and these cannot simply be traced to two MO's of the separate reactants.

In a MOPAC MO calculation on cisoid butadiene, all orbitals are either symmetric or anti-symmetric with respect to the mirror plane in the molecule. Sigma C-H bonds will be listed as the symmetric and anti-symmetric combination of several C-H bonds, related by symmetry.
For instance, orbital no. 6 is shown on the right: an anti-symmetric combination in which we could detect at least four C-H sigma orbitals (the remaining two to a lesser extent).

Consequently, all asymmetric orbitals in the reactants contribute to the new asymmetric orbitals of the reaction complex, and it is neither possible nor useful to relate these new orbitals to one or two starting MO's.
The same holds for the symmetric ones.
At 1.8 Å distance between the reactants (which is beyond the transition state at ca. 2.1 Å), the high density part of the new C-C sigma orbitals looks rather pure.

If we look at a lower density level however, and from another direction, we see that AO's from other atoms in the molecule contribute too, albeit to a lesser extent.

In a MOPAC MO calculation on cisoid butadiene, all orbitals are either symmetric or anti-symmetric with respect to the mirror plane in the molecule. Sigma C-H bonds will be listed as the symmetric and anti-symmetric combination of several C-H bonds, related by symmetry. For instance, orbital no. 6 is shown on the right: an anti-symmetric combination in which we could detect at least four C-H sigma orbitals (the remaining two to a lesser extent).
Consequently, all asymmetric orbitals in the reactants contribute to the new asymmetric orbitals of the reaction complex, and it is neither possible nor useful to relate these new orbitals to one or two starting MO's. The same holds for the symmetric ones. At 1.8 Å distance between the reactants (which is beyond the transition state at ca. 2.1 Å), the high density part of the new C-C sigma orbitals looks rather pure.
If we look at a lower density level however, and from another direction, we see that AO's from other atoms in the molecule contribute too, albeit to a lesser extent.