Hello Kusum Yadav

If you're numbering roots as calculated (regardless of their oscillator strengths), then "Excited State 3" in your output is S3, and "Excited State 4" is S4.

However, suppose you want to assign spectroscopic states (the ones you expect to see in absorption spectra). In that case, it's conventional to assign S1, S2, S3... based on energy ordering and significant oscillator strength, because very dark (low-f) states may not be observed in one-photon absorption at all.

You also might refer to the books (chapter on TDDFT and Excited states):

1. C. J. Cramer, Essentials of Computational Chemistry: Theories and Models, 2nd ed. (Wiley, 2004)

2. Frank Jensen, Introduction to Computational Chemistry, 3rd ed. (Wiley, 2017)

Regards,

Dilawar

Hi Dilawar Singh Sisodiya, Thank you for your response. I am unable to find it in the mentioned books. Could you help me with some research articles where the authors have skipped the very dark states? Especially when someone works on optimizing the excited states to calculate fluorescence and phosphorescence wavelengths.

Hello Kusum Yadav

You might refer to the review article : Article TD-DFT benchmarks: A review

Dark states (low-f or zero-f) may not affect absorption spectra.

However, for excited-state studies, they are essential.

To do a computational study, one needs to consider various things (often with experimental data), such as identifying the target state(s) and their nature, finding relaxation pathways, which can include optimizing the dark and bright state stationary points, etc.

Reading research articles ( and reviews) on computational photochemistry will give you more insights into how to deal with the dark and bright states.

Also, most molecules emit from the lowest excited state (Kasha's rule), S1 for fluorescence or T1 for phosphorescence.

Many exceptions show emission (Anti-Kasha) from higher excited states, S2, T2, etc.

Feel free to reach out.

Regards,

Dilawar