Hydrogen sulfide,

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Group theory and symmetry · Group theory and symmetry

Invariance, Ch Point groups and crystallographic symmetry

Problem

Hydrogen sulfide,

\mathrm{H_2S}

, is a bent triatomic molecule with bond angle

\angle\mathrm{HSH} = 92.1^\circ

. Take

z

along the principal (

C_2

) axis and the molecular plane as

yz

. ((a)) Write the

3\times3

matrix of the

C_2

rotation about

z

that is a symmetry operation of

\mathrm{H_2S}

. State its trace and determinant, and use

\mathrm{tr} = 1+2\cos\theta

(for a proper rotation) to confirm which operation it is. ((b)) Using the point-group determination sequence, find the point group of

\mathrm{H_2S}

and its order. ((c)) Using the polarity rule, state whether

\mathrm{H_2S}

can carry a permanent dipole moment, and explain along which direction it would have to lie.