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Asymptotics-based configuration-interaction (CI) methods [G. Friesecke and B.D. Goddard, Multiscale Model. Simul. 7, 1876 (2009)] are a class of CI methodsfor atoms which reproduce, at fixed finite subspace dimension, the exactSchr\"odinger eigenstates in the limit of fixed electron number and largenuclear charge. Here we develop, implement, and apply to 3d transition metalatoms an efficient and accurate algorithm for asymptotics-based CI.  Efficiency gains come from exact (symbolic) decomposition of the CI spaceinto irreducible symmetry subspaces at essentially linear computational cost inthe number of radial subshells with fixed angular momentum, use of reduceddensity matrices in order to avoid having to store wavefunctions, and use ofSlater-type orbitals (STO's). The required Coulomb integrals for STO's areevaluated in closed form, with the help of Hankel matrices, Fourier analysis,and residue calculus.  Applications to 3d transition metal atoms are in good agreement withexperimental data. In particular we reproduce the anomalous magnetic moment andorbital filling of Chromium in the otherwise regular series Ca, Sc, Ti, V, Cr.

Efficient Algorithm for Asymptotics-Based Configuration-Interaction Methods and Electronic Structure of Transition Metal Atoms