Another example illustrates a situation somewhat similar to that we saw with
methane, and what was until some years ago a serious controversy: the best way to
represent the carbon/carbon double bond [ 28 ]. The currently popular way to
conceptualize the C¼C bond has it resulting from the union of twosp^2 -hybridized
carbon atoms (Fig.4.7); thesp^2 orbitals on each carbon overlap end-on forming as
bond and theporbitals on each carbon overlap sideways forming apbond. Note
that the usual depiction of a carbonporbital is unrealistically spindle-shaped,
necessitating depicting overlap with connecting lines as in Fig.4.7. Figure4.8
shows a picture in better accord with the calculated electron density in theporbital,
i.e. corresponding to the square of the wavefunction. The two leftoversp^2 orbitals
can be used to bond to, say, hydrogen atoms, as shown. From this viewpoint the
double bond is thus composed of asbond and apbond. However, this is not the
only way to represent the C¼C bond. One can, for example, mathematically
construct a carbon atom with twosp^2 orbitals and twosp^5 orbitals; the union of
two such carbons gives a double bond formed from twosp^5 /sp^5 bonds (Fig.4.9),
rather than from asbond and apbond. Which is right? They are only different
ways of viewing the same thing: the electron density in the C¼C bond decreases
smoothly from the central C/C axis in both models (Fig.4.10), and the experimental
(^13) C/H NMR coupling constant for the C-H bond would, in both models, be
predicted to correspond to about 33%scharacter in the orbital used by carbon to
bond to hydrogen [ 29 ]. The ability of the hybridization concept to correlate and
CC
H
H
C
H
H
C
Csp 2 / H1s overlap
Csp 2 / H1s overlap
H
H
C
H
H
C
and
H
H
H
H
Csp^2 /Csp^2 overlap
(the sigma bond)
Cp/Cp overlap, equal above
and below the C 2 H 4 plane
(the pi bond)
i.e.
Fig. 4.7The currently popular view of the C/C double bond: ansp^2 /sp^2 sbond and ap/ppbond.
Compare this with Figs.4.8and4.9
106 4 Introduction to Quantum Mechanics in Computational Chemistry