Question

List the symmetry operations for point groups of Ci,C2h,D2h,D4,C4v. (For example, Ci has an inversion operation that I = (x,y,z) → (−x,−y,−z)).

Answer 1

E, Identity operation is included in all point groups

i = (x,y,z) → (−x,−y,−z)

Cn = (x,y,z) → ((cosθ)X,(cosθ)Y, Z) where θ = 360/n

σ_h = σxy = (x,y,z) → (x,y,−z)

Ci has an inversion operation,(i)

C2h has an inversion, Rotation(C2) and mirror plane operation. (i,C₂,σ_h)

D2h has an inversion, Rotation(C2) and mirror plane operation.(i,C₂  perpendicular C₂,σ_h)

D4  has a Rotation(C2) (C_{4 ,}perpendicular C₂,)

C4v has rotation(C2) and mirror plane operations.(C_{4 ,}C₂,σ_h,σd)