Calculating the UV/Vis spectrum of perylene

Question

I recently started to do computational chemistry and am now trying to write some basic inputs for important calculations. One, which I guess is quite important to me would be to predict UV/Vis spectra of molecules. So I looked for a basic input file on the net, and although my tutor warned me about using DFT for absorption spectra (it's not a topic of the lecture and therefore he wasn't sure what to use either) the first few simple molecules, mostly long conjugated systems and a few azo-compounds gave really good solutions in comparison to literature values.

Now I wanted to predict a perylene in benzene as solvent as well and gave the structure optimization (HF/VDZ) six cycles, which took forever to calculate before I stopped it. Then I used the geometry at each of the six steps to predict the spectrum and compared the results. What surprises me is that the optimization, while becoming better, moves the first absorption peak at ~435 nm further from experiment. From its position and the direction, it seems to better describe the second peak (~410 nm) instead of the first one.

I am also only getting one peak only but for the other molecules, it had been pretty much the same as well, where one peak was quite big and the rest, although being at the right positions were too small to really see.

Now I know about the quantum mechanics and the theoretical backgrounds of UV/Vis spectroscopy but we never really discussed the effects in real spectra. I know from NMR that peaks can split and multiply in experiment, while your theoretical model only contains one signal.

Is there a reason, perhaps due to the big delocalized system why perhaps the bands shift or multiply in some way or why I am not able to see the first band? Or perhaps my calculation shows the first band and it's really far off?

All UV/Vis calculations were done with Orca using RI-BP86/SV(P) and COSMO for the solven.

Here is the experimental spectrum I am referring to:

Please note: Those are my very first calculations and I am still trying to understand when the simple approaches yield good results and when I need to switch to different approaches.

Answer 1

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.