WEB TUTORIAL - Group Theory
H2O Worked Example
Applying the Reduction Formula
| C2v | E | C2 (z) |  v(xz) | v(yz) | Linear functions, rotations | Quadratic functions | Cubic functions |
| A1 | +1 | +1 | +1 | +1 | z | x2, y2, z2 | z3, x2z, y2z |
| A2 | +1 | +1 | -1 | -1 | Rz | xy | xyz |
| B1 | +1 | -1 | +1 | -1 | x, Ry | xz | xz2, x3, xy2 |
| B2 | +1 | -1 | -1 | +1 | y, Rx | yz | yz2, y3, x2y |
Now we have all of the required parts, we simply put them together into the Reduction Formula one row at a time.
It is worth doing this on a piece of paper rather than in your head before checking your answers!
