Is there an example where TD-DFT fails to provide sufficient accuracy for a small system, where RI-CC2 is sufficient?

Question

Time-dependent density functional theory (TD-DFT) is considered to be more efficient (in terms of its accuracy/speed ratio) than alternatives such as the approximate coupled-cluster singles and doubles (CC2), even with resolution of identity which together forms RI-CC2¹.

Piacenza et al. (2008)² highlight that one drawback of TD-DFT is that "for larger conjugated systems the $\sigma\to\pi^\ast$ and $\pi\to\pi^\ast$ transitions can become significantly wrong when calculated with TD-DFT" and so for such systems RI-CC2 should be used despite its taking slower.

However, is it always the case that for small(er) systems that RI-CC2 need not be used as TD-DFT can provide sufficient accuracy, and if not what is an example where the former prevails?

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_References

_{[1] Jacquemin, D. et al. (2015). 0–0 Energies Using Hybrid Schemes: Benchmarks of TD-DFT, CIS(D), ADC(2), CC2, and BSE/GW formalisms for 80 Real-Life Compounds. J Chem Theory Comput. 11(11):5340–5359.}

_{[2] Piacenza, M., Zambianchi, M., Barbarella, G. et al. (2008). Theoretical study on oligothiophene N-succinimidyl esters: size and push–pull effects. Physical Chemistry Chemical Physics. 10(35):5363-5373.}

Answer 1

The question cites a 2008 paper about fairly large molecules (e.g. bithiophene N-succinimidyl esters), in which TD-DFT gave significantly wrong results, so the authors recommended RI-CC2. The question then asks if there's any example where TD-DFT was insufficient for a smaller system. After searching the literature, I have found an example of a small molecule for which TD-DFT gave significantly worse results than RI-CC2: The molecule is C$_2$H$_4$.

Here I will make a condensed version of the relevant energies in their Table II:

\begin{array}{c c c c} \text{State} & \text{TD-DFT} & \text{RI-CC2} & \text{Benchmark}\\ \hline B_{1u} & 7.72 & 8.27 & 8.22\\ B_{1g} & 8.09 & 8.73 & 8.59\\ B_{3u} & 8.11 & 8.84 & 8.75\\ \end{array}

Here's some further explanations about the table:

• All energies are in eV.
• The benchmark was CC3, which the authors say they expect to be within about 0.1 eV of the exact truth (so whatever error is in these benchmarks, is negligible here).
• In every case RI-CC2 was closer to the benchmark by more than 0.5 eV.
• The functional used for TD-DFT was B3LYP. According to this figure one might be able to get 1.5 kcal/mol better by using a double-hybrid such as B2PLYP, but that's only 0.065 eV, which is negligible compared to the fact that the table shows TD-DFT being more than 0.5 eV worse than RI-CC2 in every case.
• I have only included the first 3 states from Table II of the original paper, you're welcome to see the whole table, and the observations above remain the same (in fact the TD-DFT error becomes much worse for some of the other states.

The bottom line is that if you have enough compute power available, coupled-cluster-based approaches will almost always beat DFT, except for multi-reference cases where coupled-cluster is known to fail, such as some molecules containing transition metals (where DFT can have an advantage, especially if the functionals are optimized for transition metal systems, such as some of the functionals that have come out of Don Truhlar's group).

Answer 2

TD-DFT works best for valence-valence excitation energies, but does not very well for charge-transfer excitation (unless xc potentials are constructed to lower delocalization error).

Core-excitation energies are also not described will with TD-DFT.