Development of Real-Time TDDFT Program with k-Point Sampling and DFT + U in a Gaussian and Plane Waves Framework

We developed a k-point sampling real-time TDDFT (RT-TDDFT) program within the Gaussian and plane waves (GPW) framework of the CP2K software suite. In addition to standard real-time propagation of time-dependent Kohn–Sham orbitals, we make use of symmetry-based k-point reduction and k-point parallelization schemes so that our RT-TDDFT program in the GPW framework is feasible for practical large-scale calculations. We also implemented DFT + U as a relevant extension for real-time simulations of systems with strong electron correlations. In particular, we extended the "tensorial" subspace representation approach for DFT + U, following the formulation in [Chai, Z., et al. J. Chem. Theory Comput., 2024, 20, 8984], to k-point sampling RT-TDDFT. Our extension, which is, to our knowledge, the first application of the "tensorial" subspace representation approach to k-point sampling RT-TDDFT, is found to be robust and efficient with small additional costs owing to the locality of Gaussian basis functions, indicating that it is a promising approach to RT-TDDFT + U for solids. We show details of our implementation in CP2K and the results of our benchmark calculations.