Solutions 7

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Q1:

Below are molecules of similar symmetry and the required symmetry elements.

a).

b).

c).

d).

Q2:

Symmetry elements

s orbital: inversion center, infinite planes of reflection, infinite axes of proper and improper rotations

p orbital: inversion center, 1 vertical plane of reflection, infinite horizontal planes of reflection, infinite \(C_2\) and \(S_2)\ axes, 1 \(C_\infty\) and \(S_\infty\) axis of rotation, inversion center

\(d_{z^2}\) : same as p orbital

\(d_{xy}\): 4 \(C_2\) and \(S_2)\ axes, 1 \(C_4\) and \(S_4)\, 4 vertical planes of reflection, 1 horizontal plane of reflection, inversion center

Q3:

a). center of inversion

b). center of inversion

c). neither

d). \(S_4\) axis

Q4:

a). \(C_1\)

b). \(T_d\)

c). \(C_\infty\)

d). \(C_1\)

e). \(C_{2v}\)

f). \(C_2\)

Q5:

a). An inversion center will prevent a molecule from being polar. Molecules (a), (c), (e), and (f) are all polar.

b). Planes of reflection exclude chirality. Molecule (d) is chiral.