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

TL;DR

This paper presents an efficient algorithm for asymptotics-based configuration-interaction methods, enabling accurate electronic structure calculations of transition metal atoms with improved computational efficiency and agreement with experimental data.

Contribution

The authors develop and implement a novel, efficient algorithm for asymptotics-based CI that leverages symbolic decomposition, reduced density matrices, and closed-form Coulomb integrals.

Findings

Accurately reproduces experimental data for 3d transition metal atoms.

Successfully captures the anomalous magnetic moment of Chromium.

Achieves linear computational scaling with the number of radial subshells.

Abstract

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