Our new paper was just accepted by the Journal of Chemical Theory and Computation. And it is actually already available as a just accepted manuscript (Link). What we are looking at is the analysis of excited states. If an excited state contains several configurations, it is not only tedious to analyze it but a lot of information may be missed by considering the configurations independently. The problem is in particular significant in the case of delocalized states. Here our procedure, which is based on the transition density matrix, can provide a well defined automatized measure for delocalization, which is also independent on the orbital resolution.
Another challenging case is to differentiate between (Frenkel) excitonic and charge resonance transitions. For example if you look at a symmetric dimer: Then you know that there have to be excitonic resonance states and charge resonance states. But because all the orbitals are delocalized, it is not trivial to differentiate between them (unless you use our analysis tools).
In summary, I am kind of proud of it ... :) And interestingly one of my first blog posts about quantum chemistry, which I have not really thought of in the meantime, was concerned with a part of this paper: a singular value decomposition of the transition density matrix yielding the natural transition orbitals. Apparently I had the same taste in things I consider interesting five years ago...
Tolman, “The Principles of Statistical Mechanics, Chapter 1, Part 1

Survey of classical mechanics: Generalized coordinates and momenta.
Lagrangian equations. Derivation of Hamilton’s equations from Lagrangian.
Poisson bra...
2 weeks ago
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