Dataset for "Relativistic linear response in quantum-electrodynamical density functional theory"

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 which 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.我们报道了相对论量子电动力学密度泛函理论（QEDFT）的线性响应方程的理论推导与数值实现。与此前基于泡利-菲泽哈密顿量的研究不同，我们的方法从完全相对论性量子电动力学出发，通过一系列已确立的近似，在四分量狄拉克-科恩-沙姆层面描述了电子与光子腔模的相互作用。此外，我们发现，在物质与量子化腔模耦合的相对论性描述框架下，会出现一种新型的类自旋轨道（SO）腔介导相互作用。针对第12族元素（锌Zn、镉Cd、汞Hg）原子的基准计算表明，相对论性处理能够实现对激子极化激元的描述——这类极化激元由形式上禁阻的单重态-三重态跃迁与腔模杂化产生。对于腔被调谐至与单重态-三重态跃迁共振的原子体系，我们发现自旋轨道效应与非共振强单重态-单重态跃迁耦合之间存在显著的相互作用。这种动态关联凸显了从头算方法在理解腔量子电动力学中的关键作用。最后，以汞卟啉配合物为例，我们证明相对论性线性响应QEDFT可在计算上实现对具有化学研究价值的含重元素大型分子的极化激元态的第一性原理计算。