Treecode-accelerated Green iteration for Kohn-Sham density functional theory

We present a real-space computational method called treecode-accelerated Green Iteration (TAGI) for all-electron Kohn-Sham Density Functional Theory. TAGI is based on reformulation of the equations in which eigenvalue problem differential form converted into fixed-point integral by convolution with modified Helmholtz Green's function. In each self-consistent field (SCF) iteration, fixed-points are computed Iteration, where discrete sums efficiently evaluated GPU-accelerated barycentric Lagrange treecode. Other techniques used include a-priori adaptive mesh refinement, Fejér quadrature, singularity subtraction, gradient-free update, and Anderson mixing to accelerate convergence SCF Iterations. Ground state energy computations several atoms (Li, Be, O) small molecules (H2, CO, C6H6) demonstrate TAGI's ability achieve chemical accuracy.