A Linearly Constrained Least-squares Problem in Electronic Structure Computations

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 Anderson acceleration (SCF-AA), 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.