I am currently working on a machine learning with spectroscopy. I had learnt about the Franck-Condon principle and the vibronic coupling in photochemistry courses in my undergraduate lectures. However, in computational chemistry when electronic spectra (absorption) are calculated with TD-DFT for example, I find the usage of the terms "vertical excitation" and "0-0 transition".
I am struggling to understand what they mean and what their link with the peak in experimental absoroption spectrum is. For example, here is a UV-visible absorption spectrum of BODIPY dye:
Now I used to think that the absorption peak here (498 nm) corresponds closest to results of the "vertical excitation", since the light absorption in experiment is faster than nuclear movement. But recently I saw a paper where they were using "0-0 transitions" to compare against experiment. I had the impression from the photochemistry lectures that the "0-0 transition" is usually not the peak in experimental spectrum due to Franck-Condon effects:
Could someone please help me understand these terms and what their link to the experimental spectrum is?