Thursday, 5 March 2020

From eV to kJ/mol

What is the conversion factor from eV to kJ/mol? To go from eV to J, you have to multiply with the unit charge (formally speaking you insert the e into eV). To go to J/mol you multiply with Avogadro's number. What is the product of the unit charge and Avogadro's number - the Faraday constant. And if you were treated to Chemistry Olympiad at school then, hopefully, you are still able to blurt out its value even when woken up in the middle of the night: 96 485 C/mol. If we divide this by 1000, we get the desired result 1 eV is 96.485 kJ/mol. Or more broadly speaking, you just have to multiply with a factor of 100 if you want to go from eV to kJ/mol. I have never realised that connection before.

Sunday, 26 January 2020

Negative singlet-triplet gaps

A question that I was wondering about for a while: Are there molecules where the first excited singlet state lies below the first triplet? Apparently there are, as this recent paper in JPCL shows.

In the single-electron picture this is not possible. Singlet and triplet excited states can access the same configuration space and the only difference between singlet and triplet energies is a repulsive exchange term (see my recent post and preprint). This exchange term is always positive and, thus, always pushes up the singlet above the triplet with the same orbital transition. But the situation changes when double excitations come into play. The reason is that only singlets can form the type of double excitations where two electrons are placed in the same orbital and, hence, singlets and triplets have a different accessible configuration space. If a doubly excited state is close enough in energy, it can push the S1 down enough to be lower than T1. This is apparently the case for the cyclazine molecule at its ground-state equilibrium geometry (see DOI: 10.1021/acs.jpclett.9b02333).

Wednesday, 22 January 2020

Understanding excitation energies beyond the MO picture

Is it possible to get an intuitive understanding of electronic excitation energies that truly goes beyond the MO picture? This is what we are discussing in our newest preprint: 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).