Wednesday, 22 January 2020

Understanding excitation energies beyond the MO picture

There is a new preprint out, you might want to take a look at: Toward an Understanding of Electronic Excitation Energies Beyond the Molecular Orbital Picture. This is basically a sequel to my previous post HOMO-LUMO gaps and excitation energies, which seems to consistently attract visitors to this blog. In fact the paper started out as a short sequel and then it turned into 19 dense pages. Well, I hope it is worth the effort.

The TOC shows a diagrammatic representation of the exchange repulsion, which is responsible for the difference in energies between singlet and triplet states. The red and blue lines refer to the hole and electron, respectively. The dotted green line is the Coulomb interaction. The diagram is read in the following way: The hole and electron come together on the bra (bottom) and ket (top) side forming the transition density. They interact with each other via the Coulomb interaction. The resulting term can be interpreted as the Coulomb repulsion of the transition density with respect to itself. To represent this, we show the transition density and its electrostatic potential (ESP). The exchange repulsion is now simply an overlap between density and ESP.

The state shown is the first ππ* state of uracil. A closer look at the transition density (upper left) shows the expected π contributions. But why are there also σ contributions? It turns out that the pure ππ* state would have an excessively high exchange repulsion. That is why σ contributions are mixed in to lower the energy. These σ contributions lower the transition moment (shown in green) and, thus, have a direct experimentally observable consequence. They also mean that any description of the state in terms of only n and π orbitals is insufficient, which explains the problems of CASSCF in describing these sorts of states - called ionic states in the valence-bond description.

Wednesday, 18 September 2019

A view at the ESP at varying distance from the nucleus

Just a few more images from my little pymol wrapper qc_pymol. These images show the electrostatic potential (ESP) of the ground state of uracil mapped onto the density using different isovalues. We start out close to the nuclei where the ESP is highly positive (purple). When we move away it becomes less positive (blue). And finally, we have a negative (orange) ESP at the oxygens and positive (blue) around the remaining molecule.

Friday, 13 September 2019

Plotting the electrostatic potential with PyMOL

It has always been my aim to automatise the plotting of densities and orbitals. You can see my previous efforts in the context of VMD and Jmol in some previous posts, and you can find the associated scripts in the TheoDORE distribution. Let's turn to PyMOL now. The nice thing about PyMOL is that it can be scripted with python, which means that it is easy to add functionality in an integrated way. I started creating a toolbox for using PyMOL with quantum chemistry programs: qc_pymol, which you can find on github.

Let's say we have a cube file called es_1_diff.cube and we want to draw isosurface at isovalues of -0.01 and 0.01, then using qc_pymol we just type into the pymol console:
show_dens es_1_diff.cube, -0.01 0.01, cyan orange
And we get the following picture of the density. In this case, this is the difference density of an nπ* state with respect to the ground state (cyan is where the density is taken away, orange where it is added).

We can also map the electrostatic potential (ESP) onto the density if we have both as cube files. In this case, the command is
map_esp es_1_dens.cube, es_1_dens_esp.cube
Here, you can see that we have positive (blue) potential at the oxygen where the electron is taken away, and negative (yellow) potential at the other oxygen and at the carbon atom where electron density is added above.

We can do the same thing for the next three states and get the following combinations of difference densities and ESPs. We get the same trends as before depletion (cyan) in the difference density corresponds to positive ESP (blue), and addition (orange) corresponds to negative ESP (orange).

Monday, 17 June 2019

Visualising electron correlation (2)

Just a quick follow-up on last post. Here are some more pictures of conditional electron/hole densities taken from the computations performed in the original ChemPhotoChem paper but with some extra rendering. To get a better overview, you can check my a newest talk (starting at slide 32). What we are doing here is that we are pulling the hole through the system from left to right and we are observing how the electron behaves. For the S1 state, the adjustment is rather small.

Tuesday, 11 June 2019

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.