Question

What's states of (i) benzene, (ii) naphthalene may be reached by electric dipole transitions from there (totally symmetrical) ground state

Answer 1

Refer to the character table for C3v

Deducing a selection rule

Is px→ py an allowed transition in a tetrahedral environment?
Method We must decide whether the product pyqpx , with q = x, y, or z, spans A1 by
using the Td character table.
Answer The procedure works out as follows:
E 8C3 3C2 6σd 6S4
f3(py) 3 0 −1 −1 1 T2
f2(q) 3 0 −1 −1 1 T2
f1(px) 3 0 −1 −1 1 T2
f1f2f3 27 0 −1 −1 1
We can use the decomposition procedure described in Section 12.5a to deduce that
A1 occurs (once) in this set of characters, so px → py is allowed.
A more detailed analysis (using the matrix representatives rather than the characters)
shows that only q = z gives an integral that may be nonzero, so the transition
is z-polarized. That is, the electromagnetic radiation involved in the transition has
its electric vector aligned in the z-direction.

Consider all three
components of the electric dipole moment operator μ.

Component of μ: x y z
f3 = A1 1 1 1 1 1 1 1 1 1
f2 = μ 2 -1 0 2 -1 0 1 1 1
f1 = A2 1 1 -1 1 1 -1 1 1 -1
f1*f2*f3 2 -1 0 2 -1 0 1 1 -1
E E A2
Since A1 is not present in any product, the transition dipole moment must be zero.

transition dipolemoment must be zero for benzene and naphthalene