An efficient implementation of two-component relativistic density functional theory with torque-free auxiliary variables

An integration and assembly strategy for efficient evaluation of the exchange correlation term in relativistic density functional theory within two-component Kohn- Sham framework is presented. Working equations that both take into account all the components of the spin magnetization and can exploit parallelism, optimized cache utilization, and micro-architecture specific-floating point operations are discussed in detail in this work. The presented assembly of the exchange correlation potential, suitable for both open and closed shell systems, uses spinor density and a set of auxiliary variables, ensuring easy retro fitting of existing density functionals designed for collinear density. The used auxiliary variables in this paper, based on the scalar and non-collinear density, can preserve non-zero exchange correlation magnetic field local torque, without violating the required overall zero torque, even for GGA functionals. This is mandatory to obtain accurate spin dynamics and proper time evolution of the magnetization. Spin frustrated hydrogen rings are used to validate the current implementation and phenoxy radicals of different sizes are used to monitor the performance. This approach is a step towards extending the applicability of relativistic two-component DFT to systems of large size (> 100 atoms).