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Relativistic Linear Response in Quantum-Electrodynamical Density Functional Theory

Lukas Konecny*

Valeriia P. Kosheleva†, Heiko Appel‡, and Michael Ruggenthaler§

Angel Rubio∥

  • *Contact author: lukas.konecny@uit.no
  • †Contact author: valeriia.kosheleva@mpsd.mpg.de
  • ‡Contact author: heiko.appel@mpsd.mpg.de
  • §Contact author: michael.ruggenthaler@mpsd.mpg.de
  • ∥Contact author: angel.rubio@mpsd.mpg.de
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Phys. Rev. X 15, 031052 – Published 25 August, 2025

DOI: https://doi.org/10.1103/ttc3-867m

Abstract

We present the theoretical derivation and numerical implementation of the linear-response equations for relativistic quantum-electrodynamical density functional theory (QEDFT). In contrast to previous works based on the Pauli-Fierz Hamiltonian, our approach describes electrons interacting with photonic cavity modes at the four-component Dirac-Kohn-Sham level, derived from fully relativistic QED through a series of established approximations. Moreover, we show that a new type of spin-orbit-like (SO) cavity-mediated interaction appears under the relativistic description of the coupling of matter with quantized cavity modes. Benchmark calculations performed for atoms of group 12 elements (Zn, Cd, Hg) demonstrate how a relativistic treatment enables the description of exciton polaritons that arise from the hybridization of formally forbidden singlet-triplet transitions with cavity modes. For atoms in cavities tuned on resonance with a singlet-triplet transition, we discover a significant interplay between SO effects and coupling to an off-resonant intense singlet-singlet transition. This dynamic relationship highlights the crucial role of ab initio approaches in understanding cavity quantum electrodynamics. Finally, using the mercury porphyrin complex as an example, we show that relativistic linear-response QEDFT provides computationally feasible first-principles calculations of polaritonic states in large heavy-element-containing molecules of chemical interest.

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Popular Summary

Cavity-materials engineering has emerged as a powerful method for modifying the physical and chemical properties of atoms, molecules, and solids. Inside optical cavities, confinement modifies vacuum photon modes, enabling us to change the photon vacuum in a way that selectively alters specific features, such as electronic transitions, of a material placed inside. Of special interest is the manipulation of relativistic effects such as spin-orbit interactions and singlet-triplet transitions. However, no theoretical method has been able to treat both strong light-matter coupling and relativistic quantum effects at the same time. In this study, we extend quantum electrodynamical density functional theory to the relativistic realm. We derive the theory from first principles and show that a new type of spin-orbit-like, cavity-mediated interaction emerges under the relativistic description of light-matter coupling in cavities.

Using a computer implementation of our theory, we show in benchmark calculations that when group 12 atoms—zinc, cadmium, and mercury—inside optical cavities interact with cavity photons, singlet-triplet transitions, which are spin forbidden in nonrelativistic theories, can mix into polaritonic states. For atoms in cavities tuned on resonance with a singlet-triplet transition we discover a significant interplay between spin-orbit effects and coupling to an off-resonant intense singlet-singlet transition.

Our results show that relativistic quantum electrodynamical density functional theory is both accurate and computationally practical for systems involving heavy elements and strong light-matter interactions. By capturing effects that nonrelativistic methods miss, this framework provides a solid foundation for future studies in cavity-controlled chemistry and materials science.

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Phys. Rev. X 15, 031052– Published 25 August, 2025
  • Received 5 July 2024
  • Revised 22 April 2025
  • Accepted 4 June 2025
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