Symmetry and Group Theory Summarized

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Symmetry and Group Theory 1. Using the 5 symmetry elements and their operations to determine the point group of a molecule (this was the basis of your sapling homework assignment) General operation Look for C2 axes perpendicular to the highest order Cn axis If a horizontal plane of symmetry exists If n vertical planes exist If no planes of symmetry exist D classifications n C2 axes ┴ Cn axis Dnh Dnd Dn C classifications No C2 axes ┴ Cn axis Cnh Cnv Cn Notes:  Vertical planes contain the highest order Cn axis. In the Dnd case, the planes are designated dihedral because they are between the C2 axes – thus the subscript d.  The presence of a Cn axis does not guarantee that a molecule will be in a D or C category; the high symmetry Td, Oh and Ih point groups and related groups have a large number of Cn axes.  When in doubt, you can always check the character tables for a complete list of symmetry elements for any point group. 2. How to use the point group of a molecule, including the x, y and z coordinates to come up with the irreducible and reducible representations of a point group  Use the representation flow chart for H2O and trans-N2F2 for review. 3. How to read a character table (Go over the “additional features of character tables” section of your text)  The far left column of the character table has letters with subscripts that represent the Mulliken symbols used to identify the irreducible representations. The letters tell you about the number of dimensions of the representation (dimensions are the characters under E on the character table).  A means 1D (E = 1) and symmetric (positive value) when rotating along the principal axis.  B means 1D (E = 1) and asymmetric (negative value) when rotating along the principal axis.  E means 2D (E = 2)  T means 3D (E = 3) 1 The subscripts and superscripts tell you about the symmetry of the reps with

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