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 :)