Molecular Symmetry and Group Theory |
In the lecture we used group theory to generate a qualitative MO energy diagram for the H2O molecule. To determine appropriate symmetries for the hydrogen orbitals we generated a reducible representation (Γ) using a 1s orbital on each of the two hydrogen atoms as a basis. Similarly in Exercise 3 we used a 1s orbital on each of the four H atoms in CH4 as a basis for generating Γ.
Suppose we attempt to generate a representation of the symmetry operations of the C2v point group using a hydrogen 1s orbital on only one of the hydrogen atoms.
C2v | E | C2 | σv(xz) | σv′(xz) | ||
A1 | 1 | 1 | 1 | 1 | z | x2,y2,z2 |
A2 | 1 | 1 | -1 | -1 | Rz | xy |
B1 | 1 | -1 | 1 | -1 | x,Ry | xz |
B2 | 1 | -1 | -1 | 1 | y,Rx | yz |