SALMON 2.3: Implementation of divide-and-conquer ground-state initialization for large-scale real-time TDDFT

In large-scale real-time time-dependent density functional theory (TDDFT) simulations, preparing the ground-state electronic structure can demand more computation than the subsequent time propagation. This creates a major bottleneck for simulations of non-equilibrium electron dynamics. This limitation is particularly severe for realistic systems, such as disordered materials, liquids, nanostructures, and heterogeneous condensed-matter systems, that contain thousands to tens of thousands of atoms. Real-time TDDFT provides a powerful framework for describing nonlinear and strong-field phenomena, including high-harmonic generation and light-induced phase transitions. However, its application to large-scale systems is hindered by the computational cost of conventional ground-state density functional theory (DFT) calculations.SALMON is an open-source first-principles code for light-matter interaction simulations based on real-time TDDFT on real-space grids. It supports massively parallel calculations that combined message passing interface (MPI) with OpenMP or GPU acceleration. In SALMON 2.3, a new stable version of the code, we implement a divide-and-conquer density functional theory (DC-DFT) scheme. We combine this scheme with a postprocessing method that reconstructs spatially extended Kohn--Sham orbitals of the entire system. These reconstructed global orbitals serve directly as initial states for the real-time TDDFT module of SALMON. This establishes a practical workflow that connects efficient ground-state preparation based on DC-DFT to the standard real-time, real-space TDDFT framework. Therefore, nonequilibrium and nonlinear phenomena in large-scale systems can be simulated at a realistic computational cost.The present approach combines the efficiency of DC-DFT for ground-state preparation with the robustness and general applicability of conventional real-time TDDFT in SALMON. In particular, the self-consistent-field procedure based on DC-DFT exhibits linear scaling with system size. This directly addresses a major bottleneck in large-scale electron-dynamics simulations. We describe the computational procedure, parallelization strategy, and input/output design of the implementation. Weak-scaling measurements using Si supercells on Fugaku confirm the linear-scaling behavior of the DC-DFT implementation. We assess the accuracy of DC-initialized real-time TDDFT for a 512-atom amorphous Si system and a bulk H2O liquid system containing 4134 atoms. These results demonstrate that the present workflow provides a practical route toward large-scale simulations of nonequilibrium electron dynamics by combining linear-scaling ground-state preparation with the established real-space, real-time TDDFT framework of SALMON.