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I am working on a project where I have to calculate the TDDFT excitation energies of organic molecules (to compare to the experimental UV/visible i.e. optical absorption spectrum). Now, if I understand correctly, most of the time, the absorption peaks in the UV/vis spectrum correspond to a vertical excitation i.e., the geometry of the molecule stays the same while the electron density shifts quickly (Frank-Condon).

Now I have seen the pictures for excitation from the ground state, like the following [from Wikipedia]: Frank-Condon excitation

The vertical excitation (blue line in picture) happens from the lowest point of the PES of the ground electronic state($E_0$), i.e. from the minimum energy geometry. This seems to suggest that excitation energies (with TDDFT or any other method) should be calculated only using the method/basis set combination in which the geometry is a minimum. So, I should optimise the geometry using the same method that I am using for excitation energies.

However, I have seen research papers where EOM-CCSD excitation energies were calculated on geometries obtained with B3LYP/6-31G* for example. Is this correct? Is there any error in the calculated values if I use different functionals or basis sets for the geometry optimisation and the excited state calculation?

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The question, in some sense, is "how accurate is the geometry?"

Yes, in principal, you should do TD-DFT on a true minimum geometry. However, the diagram also indicates that if you displace the geometry a small amount, the excitation energy won't change "much" (depending on your definition of "small amount" for the displacement and "much" for the $\Delta E$ of the excitation).

In my experience, if you're using a "good" method for the geometry optimization of a molecule (e.g., dispersion-corrected hybrid density functional) the differences in the excitation energies are smaller than the errors in TD-DFT for low-energy excitations like you're describing.

You mention cases with EOM-CCSD excitation energies on B3LYP geometries. There are two reasons for this:

  1. Performing geometry optimizations with CCSD for anything but small molecules is extremely computationally-intensive.

  2. Optimization with B3LYP is fairly standard for organic molecules - it produces fairly good geometries.

Taken together, people usually optimize with RI-MP2 or a good density functional for TD-DFT or an EOM method. These days, I'd probably recommend RI-MP2 or $\omega$B97X-D4 or $\omega$B97M-V.

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From my point of view, it will not affect so much on the excitation energy, but it is preferred to use the same level of functional and basis set unless you will increase the level of theory to get more accurate result.

I did before a B3LYP/6-31G* optimization, and then I did the vertical excitation(CASPT2 with different basis set) using the optimized geometry(B3LYP) and the result is published at an excellent journal with IF=15,34.

In general, You will use TD-DFT just to save time and understand your system, but the result from TD-DFT is not accurate compared to other methods.

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    $\begingroup$ I don't know if I agree with "the result from TD-DFT is not accurate." For low-lying excitations in organic conjugated species, the mean absolute error is often ~0.15-0.25 eV, which is quite good. It often won't do well with some types of excitations (e.g., Rydberg states) but most methods have limitations. $\endgroup$ Commented Dec 22, 2021 at 15:38

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