Question

Consider the H₂O molecule, which belongs to the group C_2v. Take the molecule to lie in the yz-plane, with z directed along the C₂ axis; the mirror plane $\sigma$ ’_v is the yz-plane, and $\sigma$ _v is the xz-plane. Take as a basis the H1s orbitals and the four valence orbitals of the O atom and set up the 6 $\times$ 6 matrices that represent the group in this basis.

1. Confirm, by explicit matrix multiplication, that C₂$\sigma$_v = $\sigma$ ’_v and $\sigma$ _v$\sigma$’_v = C₂
2. Show that the representation is reducible and spans 3A₁+ B₁ + 2B₂

(Having trouble with part b)

Answer 1

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