Educ. First nonvanishing multipole: quadrupole Literature. character tables and direct product table 24 Descent in symmetry and subgroups 26 Notes and Illustrations: General formulae 29 Worked examples 31 Examples of bases for some representations 35 Illustrative examples of point groups: I Shapes 37 II Molecules 39 . 72, 505 (1995) Multipoles and Symmetry

Character table for the symmetry point group D3h as used in quantum chemistry and spectroscopy, with an online form implementing the Reduction Formula for decomposition of reducible representations. Γ total = 2A1' + A2' + 4E' + 3A2" + 2E" The irreducible representation offers insight into the IR and/or Raman activity of the molecule in question. Add up each row, and divide each row by the total order. A. Gelessus, W. Thiel and W. Weber, J. Chem. Degrees of Freedom. From the character table predictions can be made for which symmetries can exist. Take Γtotal multiply by the number in front of the symbols (the order) and multiply by each number inside of the character table. For the D 3 h the order is 12. 3N where N represents the number of nuclei present in the molecule is the total number of coordinates needed to describe the location of a molecule in 3D-space.