Quantum-Electrodynamical Time-Dependent Density Functional Theory Description of Molecules in Optical Cavities

We introduce a quantum-electrodynamical time-dependent density functional theory with a tensor-product representation (QED-TDDFT-TP) to model molecules strongly coupled to quantized cavity fields. By combining real-space electronic wave functions with truncated Fock-space photon states, the method captures light-matter correlations at a computational cost close to standard DFT. Benchmark calculations show good agreement with QED-FCI and QED-CASCI for ground-state energies and polaritonic spectra. Applications to weakly bound dimers─including (H₂)₂, Ar₂, (H₂O)₂, and HF─demonstrate that cavity confinement can significantly alter binding energies and geometries in a polarization-dependent manner. The framework provides an accurate and scalable tool for studying cavity-modified molecular structure and interactions.