Singlet-Triplet Energy Gaps in Planar Organic Chromophores

A new framework for tuning singlet-triplet (S1/T1) gaps based on electrostatic interactions of the transition density is developed. Three widely applicable design rules for maximizing the singlet-triplet gap are derived: minimizing the number of electrons, localizing the excitation, and optimizing through-space interactions.  

 

W. Zeng, C. Zhong, H. Bronstein, F. Plasser
Understanding and Tuning Singlet-Triplet (S1/T1) Energy Gaps in Planar Organic Chromophores
Angew Chemie Int Ed in print (2025), DOI: 10.1002/anie.202502485

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Entanglement Entropy of Electronic Excitations

There is more to excited states than meets the eye. Just looking at the orbitals will not tell you everything there is to know about the many-body wavefunctions. The purpose of my newest paper "Entanglement Entropy of Electronic Excitations," that just appeared in J. Chem. Phys., was to quantify the amount of information that is hidden from view. For this purpse, I used the idea of mutual information from quantum information theory.

The focus of this paper is the eigenvalue spectrum of the natural transition orbital (NTO) decomposition. There is information in the eigenvalue spectrum independent of the orbitals themselves. To illustrate the point, we can look at the first excited singlet state of two interacting ethylene molecules at 6.0 Å

and at 3.5 Å

The orbitals in both cases look similar but the eigenvalues λ₁ and λ₂ are different. For the larger separation both are equal at about 0.45. For the smaller separation, there is one dominant one at 0.86. Clearly, these are different wavefunctions, but what is the significance?

In the paper I am arguing that only the first case is consistent with the idea of a Frenkel exciton, i.e. two coupled local excitations. The second case can be seen as one homogeneous transition. This automatically means that there is admixture of charge transfer, since the orbitals are distributed evenly. And indeed when we apply our charge transfer measures, we find charge resonance character in the second case.

The whole formalism employed is somewhat abstract, unfortunately, and too much for one single blogpost. But the take home message is the following: Quantum and correlation effects appear even for rather simple excited state calculations. In critical cases these may mislead us when interpreting the calculations. Luckily, there is a solution to this conundrum - our wavefunction analysis tools TheoDORE and libwfa :)

Many worlds of Surface Hopping

What happens during a surface hop in Surface Hopping dynamics? Does the wavefunction collapse or do you create a parallel universe?

Imagine the process of vision. We start with retinal in its excited state after it has absorbed a photon. In the next picosecond retinal has several distinct possibilities to hop to the ground state. Once such a hop occurrs, the molecule can isomerize, which can in turn change the configuration of the rhodopsin protein and ultimately trigger vision. In our simulations we need a random number generator to decide when the hop occurs. Why do we need a random number generator to simulate reality?

There are two equally disturbing answers to this question. Answer 1: Random wavefunction collapses happen, or as Einstein put it - God plays dice. Answer 2: The wavefunction never collapses. Everything we know of is just one big wavefunction. That means that for every possible quantum transition both branches are equally real (weighted by the transition probability). Effectively, we spawn a parallel universe with every quantum transition. In one branch of reality the hop occurs at 100 fs and triggers the isomerization, in another branch it happens at 200 fs. In yet another branch the isomerization does not occur and no nerve signal of vision is transmitted. All these branches exist in parallel. But if decoherence occured fast enough they do not know about each other and it seems like the wavefunction collapsed.

If you want to know more about parallel universes, read Max Tegmark's book "Our Mathemtatial Universe".

Looking back, I wrote a similar post before. The topic still captivates me ...