Efficient $6j$ symbol evaluations for atomic calculations

TL;DR

This paper introduces a new, efficient tabulation scheme for evaluating $6j$ symbols, optimized for atomic calculations involving coupled-cluster methods, especially in perturbed scenarios, leveraging symmetry and triangular conditions.

Contribution

The paper presents a novel tabulation scheme that improves the efficiency of $6j$ symbol evaluations in atomic coupled-cluster calculations, including perturbed cases.

Findings

Significantly reduces computational time for $6j$ evaluations.

Applicable to perturbed coupled-cluster calculations with additional perturbations.

Utilizes symmetry and triangular conditions to optimize evaluations.

Abstract

We have developed an efficient tabulation scheme to evaluate $6j$ symbol for atomic calculations. The scheme is appropriate for coupled-cluster based calculations. In particular, for perturbed coupled-clusters calculations, which has another perturbation in addition to the residual Coulomb interaction. The scheme relies on the symmetry of the $6j$ symbol and the triangular conditions.