• Partly this is an artificial construct

• Partly it is a basic fact of MO theory: only atomic orbitals of appropriate symmetry can be combined to form fully delocalized molecular orbitals.

  The fundamental rules are as follows:

  • y² must be the same at all points in the molecule that are related by the symmetry elements possessed by the molecule.

  • Therefore, y² must have the full symmetry of the molecule, and be unchanged by all symmetry operations.

  • In order for this to be the case, the atomic j that contribute to a y must all be either symmetric or antisymmetric with respect to each symmetry operation, so that y is likewise.

    • Antisymmetric is permissible because we are interested in y².

Consider the bonding in the methyl cation, CH₃⁺. The molecular plane is a plane of symmetry.

• Therefore, all atomic orbitals contributing to any particular molecular orbital of CH₃⁺ must be either symmetric or antisymmetric with respect to this plane.

On the left, the sp² carbon orbital and the H_1s both are symmetrical, and hence can interact to form an MO of the cation.

• This orbital is known as a SALC MO, for symmetry adapted linear combination.

However, the carbon 2p orbital on the right is antisymmetric, and cannot interact with the symmetric H_1s. Hence no MO can form from this pair of orbitals.

Another example: The two double bonds of bis(methylene)adamantane have been suggested to be s-conjugated; that is, to interact with each other by way of overlap with the intervening s-framework of the adamantane.

However, the p orbitals of one double bond must be orthogonal to the p orbitals forming the other.

• That is, they do not have the same symmetry with respect to all symmetry elements of the molecule

• Therefore, they cannot contribute to the same molecular orbital

The HOMO and LUMO of the molecule, from B3LYP/6-31G* density functional calculations show this very clearly:

HOMO	LUMO

This is the sense in which we commonly will make use of the symmetry of molecular orbitals: a qualitative determination of whether two orbitals can interact.

One can, for many simple molecules, describe the full set of molecular orbitals using these ideas. However, we have computer programs that can do this much more rapidly than we can.

If you would like to see a version of the construction of the MOs of ethylene different from that in your book, continue on through the rest of these pages.