An Orthogonalization-Free Parallelizable Framework for All-Electron Calculations in Density Functional Theory

All-electron calculations play an important role in density functional theory, which improving computational efficiency is one of the most needed and challenging tasks. In model formulations, both nonlinear eigenvalue problem total energy minimization pursue orthogonal solutions. Most existing algorithms for solving these two models invoke orthogonalization process either explicitly or implicitly each iteration. Their suffers from this view its cubic complexity low parallel scalability terms number electrons large scale systems. To break through bottleneck, we propose orthogonalization-free algorithm framework based on problem. It shown that desired orthogonality can be gradually achieved without invoking Moreover, fully consists BLAS operations thus naturally parallelized. The global convergence proposed established. We also present a preconditioning technique dramatically accelerate algorithm. numerical experiments all-electron show effectiveness high