A Large-scale Parallel Implementation of Quasi-Four-Component Relativistic Density Functional Theory with Numeric Atom-centered Orbitals

We present a large-scale parallel implementation of quasi-four-component (Q4C) relativistic density-functional theory with numeric atom-centered orbital basis sets for both molecules and periodic solids in the all-electron code FHI-aims. Our approach employs a domain decomposition method on non-uniform real space integration grids, which enables order-N integration of the Q4C Hamiltonian matrix elements using efficient, distributed-memory and compute-parallel real space operations. Next, we build the Hamiltonian and overlap matrices in a two-dimensional block-cyclic distribution layout. The resulting generalized eigenvalue problems are solved with the massively parallel ELPA eigenvalue solver library. We benchmark memory usage, parallel efficiency, and scalability across multiple MPI tasks and compute nodes. This algorithm extends the reach of fully relativistic DFT simulations for periodic solids well beyond 1,000 atoms per unit cell. As a demonstration, we calculate the fully relativistic band structure for a 1,504 atom-per-unit-cell doped hybrid organic-inorganic perovskite, (PEA)₂(Pb_1-xBi_x)I₄ (PEA=phenethylammonium), showing the scalability and accuracy of this approach.