If you mean a set of narrow sub-bands present in the PL spectrum (as e.g. is the case for antracene), this is due to vibrational structure, i.e. transitions to different vibrational states of the lowest electronic state. If you mean something different, please specify.

Thank you sir for the reply; I am confused a little bit; kindly help me in the following question;

1. PL spectrum in Anthracene has narrow sub bands in PL and at low temperature PL, these narrow bands show further splitting of the peaks, 1. Is that davydov splitting?

2. In the literature, the narrow peaks are called fine structure. I am confused what does it indicae, As per my assumption, it is linked to crystal, narrow peaks show high crystallinity and is thus called fine structures (by its name).

3. Can you kindly elaborate it a little bit further, What is meant by vibrational states? As far as I know only vibrational spectroscopy such as Raman can give the information of vibrational states such as bending, stretching and phonon modes. PL only gives bandgap information.  Does PL spectrum shows vibrational states of the molecule or only Raman do the same?

Further, Are the material's electric properties such as mobility rate depend on optical properties of the material?Moving further, Can we make an approximation of materials electrical properties such as electric mobility via Raman or PL spectra?

Because you have a lot of questions, I recommend you to my article:

https://www.researchgate.net/publication/239382916_Dispersion_interactions_electronic_absorption_spectra_of_anthracenes_in_polar_glassy_media_at_77-300_K_and_the_change_in_polarizability_upon_excitation

Perhaps some of them will disappear.

Article Dispersion interactions, electronic absorption spectra of an...

Leaving all my other questions, my main question is only;

2. In the literature, the narrow peaks are called fine structure. I am confused what does it indicae, As per my assumption, it is linked to crystal, narrow peaks show high crystallinity and is thus called fine structures (by its name)?

You are wrong. It called the fine-structure spectra, well resolved vibronic spectra. They are obtained by placing the impurity molecule in a polycrystalline matrix of n-paraffins. For example, a pyrene solution in n-hexane was cooled by placing it in liquid nitrogen (70 K). Thus, single pyrene molecules are embedded in a polycrystalline matrix, and their interaction with the environment (with the matrix) is weak. This interaction is called an electron-phonon interaction. The ordered structure of the hexane crystals allow to significantly reduce the impact of fluctuations of interaction with the environment on the position of the pyrene lines in the spectrum of PL. It is so-called Shpolsky effect.