Visualising electron correlation

How do you visualise the correlation between two particles? One option is to fix one of them at a specific region of space and look at the distribution of the other one. This is the principle behind a new method for visualising excitonic correlation just presented in a paper in ChemPhotoChem: Visualisation of Electronic Excited‐State Correlation in Real Space, and released within the TheoDORE 2.0 code. First, we have to interpret the excited state within the electron-hole picture as explained previously and compute the two-body electron-hole distribution. Then, we can fix one of the quasi-particles in space and observe the distribution of the other one.

Below, I am showing what this analysis looks like for a simple PPV oligomer. I am fixing the hole either at the terminal phenyl, the vinyl or the central phenyl and plot the corresponding electron distribution. In the case of the S₁ state, the electron does not really care about the hole. The electron comfortably rests in the LUMO no matter what the hole does:

But for the S₂ state things look completely differently. The electron now tries to actively avoid the hole as it moves through the system.

S₃, for comparison, has a much more localised structure where the electron is always focussed on the centre.

S₄ has a somewhat more complicated structure:

By the way, I realised that the same type of analysis has been recently performed for periodic computations as well. The difference is that in a periodic system every atom (or symmetry unit) will produce the same picture. In a finite system the picture also changes with the position of the probe.