3

3. Find the irreducible representations for the σ bonds in NH₃.

C_3v point group:

C_3v E 2C₃ 3σ_v

a₁ 1 1 1

a₂ 1 1 –1

e 2 –1 0

σ bonds 3 0 1

n(a₁) = [(1)(1)(3) + (2)(1)(0) + (3)(1)(1)]/6 = 1

n(a₂) = [(1)(1)(3) + (2)(1)(0) + (3)(–1)(1)]/6 = 0

n(e) = [(1)(2)(3) + (2)(–1)(0) + (3)(0)(1)]/6 = 1

a₁ + e