Abstract
One of the fundamental problems in electronic structure calculations is to determine the electron density associated with the minimum total energy of a molecular or bulk system. The total energy minimization problem is often formulated as a nonlinear eigenvalue problem. The most widely used algorithm for solving this type of problem is the self-consistent field (SCF) iteration accelerated by Direct Inversion on the Iterative Subspace (SCF-DIIS), in which a linearly constrained least-squares problem is embedded. We will examine and compare the numerical stability of three different ways to solve this least-squares problem.
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