Molecular Symmetry and Group Theory |

Later we will consider how group theory enables us to analyse all the allowed vibrations of the H_{2}O molecule.

For this we have to consider motion of all three atoms along the x, y and z directions, as indicated opposite. These arrows provide our basis in this case and we need to find the character for each operation of the point group. | ||

By considering the extent to which the nine arrows are converted into themselves, determine the character of the matrix that represents the C
_{2} operation. [e.g. x_{1} → -x_{1} and therefore contributes -1; x_{2} moves and therefore contributes 0; etc.] | ||

In the same way determine the characters of the matrices that describe the other group operations. |
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