I am attempting to identify Eg from both theoretical and experimental studies. In UV-Vis method, I calculate the Eg through lambda onset. However, in TD-DFT method, the Eg is picked as the 1st excited state and it is different from the above, although the theoretical UV-Vis graph is nearly identical to the experiment.
When it comes to bandgaps, there are two quantities, the electronic and the optical bandgap, there are very good answers in this previous discussion and the references therein: https://www.researchgate.net/post/What_is_the_difference_between_optical_band_gap_and_electronic_band_gap/1
If you get a different result for the first excited state but it does not affect the final spectrum, it may be that a transition involving the first excited state is symmetry-forbidden or something like that, so that it does not affect the calculated spectrum because the calculated peak intensity is 0.
Finally, while TD-DFT is the most straightforward method for UV-Vis calculation, please always keep in mind that it is not an exact method and that there are partially systematic and asystematic deviations depending on functional and basis set.
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