Establish whether the QED-BSE residual defines a universal selection rule

Establish whether the observed bright-along-the-cavity-axis and strongly dipolar criterion for a non-negligible QED-BSE kernel residual is a universal selection rule rather than an empirical pattern limited to the molecules and basis sets examined.

Background

The study identifies an empirical pattern: the residual correction to the lowest exciton is appreciable when the excitation is both bright along the cavity polarization and strongly dipolar. This pattern persists for the tested molecules across cc-pVDZ and aug-cc-pVDZ.

The authors explicitly caution that the available data do not establish a universal selection rule. Generalizing the criterion beyond the tested molecular set and determining whether it follows from a more fundamental property of the BSE kernel remain unresolved.

References

The consequence for the central claim is as follows. The bright/dipolar criterion consistently identifies the molecules with a non-negligible kernel residual in the two bases tested, but the present data do not establish a universal selection rule or determine the sign of the total shift.

— GW and Bethe-Salpeter Theory for Molecular Polaritons, Quasiparticles, and Excitons  (2609.00594 - Willow et al., 1 Sep 2026) in Section 3.7, subsection “Basis-set robustness of the channel decomposition”