Iridium complexes and the failure of ADC(2) to describe them

When I started working on iridium complexes two and a half years ago, there was one simple thing I could not explain: The results at the ADC(2) level were more than one eV off from the ADC(3) reference. And that is not good: you would not expect that a correlated ab-initio method would fail so badly. What followed was a two year detour through the world of excited state analysis (seen in some previous posts: [1], [2], [3], [4], [5]). And finally, I feel like I am in a position to discuss the above question properly in our new paper "High-Level Ab Initio Computations of the Absorption Spectra of Organic Iridium Complexes", which just appeared in JPCA.

The first step was to properly quantify the charge transferred using population analysis schemes. This revealed that ADC(2) had a strong bias toward overstabilizing charge transfer states. Usually you would think that this is a problem of TDDFT. But interestingly even TDDFT/B3LYP performed much better with errors only on the order of 0.5 eV.

To quantify the problem of ADC(2) we needed a new tool. For this purpose we took a closer look at the attachment/detachment analysis of Head-Gordon. While it is common to visualize the attachment and detachment densities, there is also an important meaning to the integral over them, the promotion number p. This quantity counts the total number of rearranged electrons and proved as a useful measure for orbital relaxation effects, which are difficult to understand otherwise.

So what happened when we made this analysis? At the ADC(1) level (whose energies and state densities are identical to CIS) p has to be equal to 1 per construction. Then ADC(2) apparently overestimates orbital relaxation effects with p values above 1.5. And only the ADC(3) level is balanced enough to cover some but not too much orbital relaxation.