1. Given trend in group 17

The halogen molecules show the following colors down the group:

• $F_2$ : pale yellow
• $Cl_2$ : greenish yellow
• $Br_2$ : reddish brown
• $I_2$ : violet

So, the absorbed light shifts gradually such that the observed color becomes deeper down the group.

2. Reason in terms of molecular orbital theory

For halogen molecules $X_2$, the important electronic transition responsible for visible color is from a filled orbital to an antibonding orbital.

The relevant transition is essentially: $\pi^* \to \sigma^*$

As we move down the group, atomic size increases and overlap changes, causing the energy difference between these molecular orbitals to decrease.

Thus, $\Delta E = E(\sigma^*) - E(\pi^*)$ decreases down the group.

Since $\Delta E = h\nu = \frac{hc}{\lambda}$ when $\Delta E$ decreases, the absorbed wavelength $\lambda$ increases.

Absorption shifts toward longer wavelength, and therefore the observed color changes from yellow to violet down the group.

Hence, decrease in $\pi^* - \sigma^*$ gap is correct.

So, Option C is correct.

3. HOMO-LUMO interpretation

The color of a molecule is generally governed by the energy needed for the lowest electronic excitation, i.e. the HOMO-LUMO gap.

For halogen molecules, the HOMO is essentially a $\pi^*$ orbital and the LUMO is essentially a $\sigma^*$ orbital. Therefore, decreasing $\pi^* - \sigma^*$ gap means decreasing HOMO-LUMO gap.

So, Option D is also correct.

4. Check the incorrect options

• Option A: Physical state changes from gas to liquid/solid down the group, but this is not the reason for the color trend. So A is incorrect.
• Option B: Ionization energy decreases down the group, but molecular color is not determined by atomic ionization energy here. So B is incorrect.

5. Final answer

Correct options are: $\boxed{C, D}$

6. Comparison with stored answer

Stored correct answer: $C, D$

My derived answer matches the stored answer.