De-excitations

If the electronic ground state of a molecule has double-excitation character and the excited state only single-excitation character, then you can view the molecule as being "de-excited." Electrons are taken from a higher lying orbital and moved into a lower lying orbital. A recent paper tries to formalise this idea by computing an expectation value of the particle-hole permutation operator. We take the two-body exciton wavefunction, switch the electron and hole and see how much it resembles the original wavefunction. If the hole resides purely in the occupied orbitals and the electron purely in the virtual orbitals, this has to yield zero. But with a correlated ground state it does not vanish.

The striking thing is that this expectation value of the particle-hole permutation operator seems to agree between TDDFT and wavefunction based methods in, both, magnitude and sign. This means that de-excitations are a "real thing" rather than just an artifact of TDDFT - not physically observable but a well-defined property of the wavefunction. For more on this, see PCCP 2020, 22, 6058.