Reducing the computational load - atomic multiconfiguration calculations based on configuration state function generators

In configuration interaction (CI) calculations the atomic wave functions are given as expansions over configuration state functions (CSFs) built on relativistic one-electron orbitals. The expansion coefficients of the configuration state functions are obtained by constructing and diagonalizing the Hamiltonian matrix. Here we show how a regrouping of the configuration state functions and the introduction of configuration state function generators (CSFGs) allow for a substantial reduction of the computational load in relativistic CI calculations. The computational methodology based on configuration state function generators, recently implemented in the General Relativistic Atomic Structure package (Grasp2018, Froese Fischer et al. (2019) [16]), is applied to a number of atomic systems and correlation models with increasing sets of oneelectron orbitals. We demonstrate a reduction of the CPU time with factors between 10 and 14 for the largest CI calculations. The inclusion of the Breit interaction into the calculations is time consuming. By applying restrictions on the Breit integrals we show that it is possible to further reduce the CPU times with factors between 2 and 3, with negligible changes to the computed excitation energies. We also demonstrate that the introduction of configuration state function generators allows for efficient a priori condensation techniques, with reductions of the expansions sizes with factors between 1.5 and 2.5 and the CPU time with factors between 2.5 and 4.5, again with negligible changes to the excitation energies. In total we demonstrate reductions of the CPU time with factors up to 68 for CI calculations based on configuration state function generators, restrictions on the Breit integrals and with a priori condensed expansions compared to ordinary CI calculations without restrictions on the Breit integrals and with full expansions. Further perspectives of the new methodology based on configuration state function generators are given. (c) 2022 Published by Elsevier B.V.

Automated summary

This study demonstrates a computational method based on configuration state function generators (CSFGs) that significantly reduces the computational load in relativistic calculations and further reduces the CPU time by limiting the Breit integrals.