Determine the basis dependence of the QED-BSE kernel residual

Determine how the residual electron–hole kernel correction remaining after DSE–photon cancellation scales with diffuse basis functions and whether it grows sufficiently to compete with the quasiparticle contribution to the finite-basis exciton-binding shift.

Background

For unbound molecular anions, the quasiparticle contribution to the exciton-binding shift is strongly basis-dependent because diffuse functions substantially alter the electron-attachment channel. The authors observe that the quasiparticle contribution increases dramatically from cc-pVDZ to aug-cc-pVDZ.

By contrast, the kernel residual is a matrix-element effect associated with incomplete cancellation between DSE and photon terms. The available cc-pVDZ data cannot determine whether this residual follows the same basis dependence, leaving unresolved whether diffuse basis functions amplify it enough to compete with the quasiparticle channel.

References

Whether the kernel residual $\delta_\lambda E_b\mathrm{ker}$, a matrix-element effect, grows with it is not something the cc-pVDZ data can answer.

— 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”

Whether the residual overcomes the quasiparticle channel and reverses the net finite-basis shift is a separate, strongly basis-sensitive question, as discussed in Sec.~\ref{sec:exciton-basis}.

— GW and Bethe-Salpeter Theory for Molecular Polaritons, Quasiparticles, and Excitons  (2609.00594 - Willow et al., 1 Sep 2026) in Section 3.6, subsection “Cavity-kernel transparency and an empirical polarization criterion”