# Which is most reliable excitation energy: LUMO-HOMO energy or TD-DFT excitation energies?

After running a TD-DFT , we can calculate the HOMO-LUMO difference and then calculate the the excitation energy.

Another approach is just simply pick the energies calculated in the TD-DFT and use them.

For me the latter makes more sense as that's the reason we do TD-DFT , otherwise we could access the HOMO-LUMO difference by any other methods but I have seen papers using the first concept. I also have noticed that the energies in second concept are closer to the experimental values.

Also when I run TD-DFT, I can see Oscillator Strength. Should I pick the energy that has the largest Oscillator Strength for calculation of the maximum wavelength ? Here is an example. Should I pick number 8 for maximum wavelength calculation? • I'm curious about the example - the oscillator strengths are very low! – Geoff Hutchison Mar 24 '15 at 1:19
• Why do you need to run TD-DFT to calculate the energy difference of HOMO and LUMO levels? – Greg Apr 13 '15 at 9:11
• >Geoff Hutchinson Sure, they can be forbidden transitions. It depends what OP wants to calculate. – Greg Apr 13 '15 at 9:13

When you can, use TDDFT, in part because of the oscillator strengths

I like to point out to my group that optical excitations consist of two things consistently (e.g., in a UV/Vis spectra). There are the excitation energies (the x-axis) and the intensity or extinction coefficient (the y-axis). To some degree, the peak widths give a bit more information (e.g., into vibrational structure).

The example you give above is a great example. Most of the excitations are forbidden and have no oscillator strength. I'd pick the same excitation, although I'm curious what the molecule is - usually there are much higher oscillator strengths.

You're right that there are papers and groups that use the HOMO and LUMO eigenvalues. While some DFT methods (e.g. optimally tuned range-separated hybrids) do provide HOMO-LUMO energies that correspond nicely with experiments, there's nothing physical about Kohn-Sham orbital eigenvalues. Moreover, in general, unfilled orbitals are not handled well by DFT methods.

It's been a while since I looked for reviews, but general TDDFT excitation energies are ~0.2-0.3 eV from experimental absorption energies after correcting for solvent effects, etc.

In my group, we also do what I call a "consensus" model. That is, when you run a TDDFT calculation, you get the HOMO and LUMO energies anyway. Since there are slightly different random and systematic errors from each approach, you can calibrate both against experiment and use a multivariate linear regression. The result decreases the average error significantly.

• Thanks a lot Geoff, as always your answers are perfect. Actually this molecule was just a scratch I was doing ( I think I was adding multiple explicit solvent molecules to my system) . – Aug Mar 24 '15 at 4:28
• I got really interested in your "consensus model" and I think that is exactly what I need. Have you ever published a paper on it that I can use that model as a citation in my paper ? – Aug Mar 24 '15 at 4:31
• We mention the idea first in this Macromolecules article. We haven't published a paper on the method itself (yet). – Geoff Hutchison Mar 24 '15 at 16:18