Lecture 3

Lecture 3

1. Representations of the C2v point group e.g. H2O

   • look at how the p and d orbitals change with E, C2, σv(xz), σv(yz)
     • 1 if it stays the same
     • -1 if the signs swap over

2. Γ

   • Gamma is used for representing a group e.g. Γpy

3. Tables for group theory

   • Rows are irreducible representations of the point groups
     • irreps
   • A1
     • Totally symmetric
   • A
     • symmetric to C2
   • B
     • antisymmetric to C2
   • 1
     • symmetric to σv
   • 2
     • antiymmetric to σv
   • Tx, y, z
     • translation along x, y, z (also Px, y, z
   • Rx, y, z
     • rotation about x, y, z

4. Properties of irreducible representations

   • irreps are orthogonal
     • if two are multiplied then the sum is zero
   • the square of an irrep is the order of the group (number of operations