Interorbital angles

Exercise 1.8. What is the hybridization of the carbon orbitals which form the C—H and C—C bonds of cyclopropane (HCH = 114°) Verify that if the carbon hybrids which are used for the C—H bonds are exactly sp2, then the two equivalent hybrids for the C—C bonds must be sp5 and the interorbital angle is 101.5° ... 

TABLE 1. Hybridization and interorbital angles in cyclopropane using orthogonal hybrid orbitals... 

Hamilton and Palke50 determined the interorbital angle between the CC hybrid orbitals to be 123° at the position of the C nucleus given by the direction of the maximum orbital amplitude (see —line in Figure 8). With increasing distance from the nucleus the orbital... 

Assuming that the external H — B — H angle in B Hh accurately reflects the interorbital angle ... 

This equation can be solved by estimating De as one-half the bond distance either of a C=C bond if an sp2 carbon is bridging (De = 0.669 A), or of S2 if an sp2 sulfur atom is bridging (De = 0.994 A). The calculated values of a when added to the angle L—Cur—X provide an estimate for the interorbital angle y which reflects the coordination geometry of copper. 

The overlap can be improved somewhat by adjustment of hybridization. Increased p character in the C-C bonds reduces the interorbital angle and improves overlap, which means that the C-H bonds must have increased s character. Compared to ethane or propane, cyclopropane has slightly shorter C-C and C-H distances and an open CH2 bond angle," which is consistent with rehybridization. The C-H bonds in cyclopropane are significantly stronger than those in unstrained hydrocarbons, owing... 

Fig. 3.2 In cyclopropane the ring orbitals eannot overlap end-on, even if pure p atomic orbitals were used, as shown here the interorbital angle in that best-case scenario would be 90°, while the geometric angle is 60°, a deviation of 30°. In fact, by mixing in some s character stronger bonds are obtained although the deviation from the geometric angle is then even greater in the limit of sp hybridization, the usual ease for tetraeoordinate carbon, the interorbital/geometric deviation would be 109°-60° =49°...

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