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.