Molecular Symmetry and Group Theory

Workshop 4 — Matrices and degenerate representations

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  • Exercise 3

    Later we will consider how group theory enables us to analyse all the allowed vibrations of the H2O 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 C2 operation. [e.g. x1 → -x1 and therefore contributes -1; x2 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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    Operation Character

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