CIS roots changing order during optimization

We are interested in calculating various excited state energies and spectra. I realize that depending upon the root you minimize on, that the root of “most interest” can change order, depending upon the structure being minimized.

What I’d like to know is the following: If I need to effectively run an exited state geometry optimization for each root to find the one I want, what happens if I do the following:

  • Start off with a lower level of theory (rung 2) using simpler basis set to identify all important roots based on strength.

  • Once the most important roots are identified, bump up my level of theory (rung 4) using a better basis set.

If I run the calculations this way, will I get a reliable order of my roots? Or will the order of my excited state roots (CIS_ROOTS) change because I’m using a different level of theory?

I’d really like to save time in identifying the more important exited state roots before spending the computation time on a more sophisticated calculation if possible. The alternative is to run all exited state roots at the level of theory we want to use. And that can be expensive if the root I want is #14, for example.


In principle what you are suggesting can work, if the energy gaps between the states (roots) is sufficiently large. It’s cases where the gaps are small that it’s easy to imagine the order changing from one level of theory to the next. If you can manage to find (and optimize on) the state that you want at the cheaper level of theory, then that optimized geometry is probably a good starting point to re-optimize at a (more expensive) target level of theory.

One caveat, however, is that “14th state” makes me a bit worried. The higher one goes above the ground state, the more likely one is to encounter state crossing (manifesting as root-flipping). If this is TDDFT then it’s possible that some of those are dark states (Rydberg states that might be real or charge-transfer states that might not be, but in both cases are not likely to be states of interest in the vibronic spectroscopy. A range-separated (long-range-corrected) functional, and/or deleting the diffuse functions from the basis set, can be effective strategies to push those states higher in energy, out of the window where the localized valence excited states appear.

Maybe another comment on this: Kasha’s rule states that in almost all cases, the system is going to relax to the S1 minimum within a couple of picoseconds.

There are only rare cases where a molecule might spend a bit longer trapped in an S2 minimum.

I am not aware of any cases where a molecule would actually spend an appreciable amount of time at the S14 minimum.

Thank you both for your comments and insights.

I agree that the “14th state” is very concerning. And I agree that Kasha’s rule means that we drop down to the lowest excited state rapidly. However, experimentally, we do see absorption bands from higher excited states all the time. I think all Kasha’s rule is telling us is that we only expect emission from the lowest energy excited state, not that photons can’t absorb at the higher energy states. And I’m interested in the absorption spectrum across the spectrum, not just at the lowest energy state.

Based on experimental data, this situation where I see the 14th state with significant strength is also at the wavelength range where the actual absorption is or is expected to be. This means that, at least in this calculation, I’m calculating a number of states at much longer wavelengths that pretty much don’t exist or are so low in intensity so as not be measurable. I guess what I’m saying is that I question whether the first 10 states are real even though some of them have strengths greater than 0.

I’m very much leaning towards my doing something wrong in the calculation by not taking something important into account. Q-Chem is so highly customizable that it is difficult for the novice to not make mistakes here and there.