Walsh Cyclopropane Molecular Orbitals

Conclusions

For reference, the molecular orbitals of methylene are shown; the order is from left (higher energy) to right (lower energy), with antibonding/nonbonding orbitals shown above bonding orbitals.

methylene orbital 3A1 methylene orbital 2B1 methylene orbital 1B2
3a1 2b1 1b2
methylene orbital 2A1 methylene orbital 1B1 methylene orbital 1A1
2a1 1b1 1a1

You may wish to refer to the calculated cyclopropane MOs (in a new window) during the following discussion.
Primary assumptions: the methylene orbitals 2a1 and 1b2 are fully separable (since they have different symmetries) and are the only fragment orbitals which contribute to net C-C bonding in cyclopropane.
1. Where the assumptions are correct
  1. An examination of the full set of EHT-derived molecular orbitals for cyclopropane (not shown on this web site) reveals that all combinations of 1a1 and 1b1 orbitals are filled; thus they have no net contribution to bonding between carbon atoms.
  2. All combinations of the antibonding methylene orbitals 2b1 and 3a1 are unfilled, so that they don't contribute to bonding in any way.
We can therefore see that, as we assumed, only the 2a1 and 1b2 methylene orbitals contribute to carbon-carbon bonding in cyclopropane.

2. Where the assumptions fail

We cannot fully separate the methylene a1 orbitals from each other, or from the b2 methylene orbitals, within the cyclopropane orbitals of E' symmetry.
  1. ψE',a and ψE',b, which are combinations of 2a1 orbitals, appear to have substantial contributions from the 3a1 orbitals of the methylene fragments.
  2. ψE',c appears to have minor contributions from the 1a1 methylene orbitals on carbons 2 and 3.
  3. ψE',d appears to have contributions from the 1a1 and 2a1 methylene orbitals on carbon 1.

The take-home lesson:

It is necessary to go back to symmetry-adapted combinations of the atomic orbitals to fully describe the molecular orbitals of any molecule. However, one can approximate molecular orbitals of interest (such as the carbon-carbon bonding orbitals in cyclopropane) by taking linear combinations of the frontier orbitals of component fragments, as long as the fragments fit the overall molecular symmetry.
Orbital energy diagram Walsh Cyclopropane home
Copyright © 1997 by Daniel J. Berger. This work may be copied without limit if its use is to be for non-profit educational purposes. Such copies may be by any method, present or future. The author requests only that this statement accompany all such copies. All rights to publication for profit are retained by the author.

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