Calculating the UV/Vis spectrum of perylene
I won't comment on the accuracy or otherwise of you calculation but that does not seem to a problem just now.

In the spectrum you show and in similar ones, the electronic transition energy is at approximately the mid-point of the first absorption and emission peaks, at approx 22800 cm$^{-1}$ in your figure. The different bands you see are due to vibrational transitions from various normal modes 'on top', as it were, of the electronic 0-0 transition. The energy gaps between peaks in the absorption spectrum measure the vibrational frequency in the excited state and vice versa for the fluorescence spectrum. Look up a Jablonski diagram to see generic sketches vibrational levels and transitions.

The number and magnitude of the vibrational transitions depends on the shape of the potential energy surface and is governed by the Franck-Condon factors which are $|\int \psi_e\psi_g|^2$ between the ground (g) and excited state(e).

The width of the lines in solution spectra (such as the one you show) is partly also due to rotational lines  but mainly due to collisions with solvent shifting and broadening energy levels. Consequently if you look up gas/vapour phase spectra at high resolution, such as for benzene as there a many published spectra, you will see many narrow lines corresponding to different vibrational normal modes and if resolution is high enough, even rotational lines.