Explanation of Cyclopropane Bond Angle provided by Chem3D

[Chem_Mod]

Hey guys,

so many of you asked me about the question dealing with the optimal bond angles of cyclopropane, cyclobutane, and cyclehexane. All three of these have carbons which attach to 4 atoms and no lone pairs. Ideally, these carbons would like to be under the tetrahedral shape with a bond angle of 109.5 degrees. All three of them ideally want this. There was an issue with the software, but whatever explanation I gave you guys in my office hours was correct :)

Best,

Idean

[Chem_Mod]

After all the questions today about cyclopropane's optimal bond angle being calculated as 60 degrees (rather than 109.5 for cyclobutane and the others):

Chem3D is calculating the optimal bond angle using the hybridization of the carbon atom. For all the cases where carbon is single-bonded to four different groups, we expect the hybridization to be sp³, and therefore angle of 109.5 deg.

Chem 3D is just comparing to ideal geometry angles.

Cyclobutane is sp³ hybridized so the optimal angle is 109.5, and it relieves its strain by adopting the butterfly conformation. Cyclopropane is planar and has no other conformations, so it cannot relieve its strain any other way but banana-bonding (bent single bonds that are highly reactive). It does not change the fact that cyclopropane still is the most strained (which is why it is more reactive compared to cyclobutane).

See your class notes in the course reader:
CYCLOPROPANE total strain energy is ~28 kcal/mol.
CYCLOBUTANE total strain energy is ~26 kcal/mol.

[Chem_Mod]

Chem3D is comparing the calculated angle to the expected angle given the geometry (60^o for cyclopropane and 90^o for cyclobutane). Since cyclobutane has a non-planar butterfly conformation the calculated bond angle is ~88^o and not 90^o.

However all cycloalkanes have sp³ carbon atoms and therefore should have bond angles of 109.5^o.
Clearly cyclopropane is a larger deviation than cyclobutane from 109.5^o and therefore cyclopropane has higher ring strain (as discussed in class, see my lecture notes).