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All-electron calculations play an important role in density functionaltheory, in which improving computational efficiency is one of the most neededand challenging tasks. In the model formulations, both nonlinear eigenvalueproblem and total energy minimization problem pursue orthogonal solutions. Mostexisting algorithms for solving these two models invoke orthogonalizationprocess either explicitly or implicitly in each iteration. Their efficiencysuffers from this process in view of its cubic complexity and low parallelscalability in terms of the number of electrons for large scale systems. Tobreak through this bottleneck, we propose an orthogonalization-free algorithmframework based on the total energy minimization problem. It is shown that thedesired orthogonality can be gradually achieved without invokingorthogonalization in each iteration. Moreover, this framework fully consists ofBasic Linear Algebra Subprograms (BLAS) operations and thus can be naturallyparallelized. The global convergence of the proposed algorithm is established.We also present a precondition technique which can dramatically accelerate theconvergence of the algorithm. The numerical experiments on all-electroncalculations show the efficiency and high scalability of the proposedalgorithm.

An orthogonalization-free parallelizable framework for all-electron calculations in density functional theory