Symmetry example: water

This orbital is made up from s-contributions from all three atoms. It is unchanged by any of the symmetry operations. We need to examine the parity of teh wavefunction. Applying one of the four operations in this example system will result in a molecular orbital which is identical to the starting case, or sign of the wave function will be multiplied by -1 (the positive lobes will become negative and visa versa). In the pictures of the molecular orbitals, the postive lobes are indicated in blue and the negative lobes in red. The parity under each operation corresponds in the current example to the character in the table below. There is no change of sign under any of the operations, so the characters must all be 1: the irreducible representation of the first orbital is a₁.