A Partitioned Correlation Function Interaction approach for describing electron correlation in atoms

TL;DR

The paper introduces the partitioned correlation function interaction (PCFI) method, which relaxes the orthonormality restriction in atomic calculations, enabling parallel, smaller-scale computations that improve convergence and accuracy over traditional methods.

Contribution

It presents a novel PCFI approach that breaks down large atomic correlation calculations into smaller, parallelizable parts using non-orthogonal orbitals, enhancing efficiency and precision.

Findings

PCFI converges faster than traditional MCHF and CI methods.

Applying PCFI improves hyperfine parameter convergence in Li I.

The method achieves lower total energies with manageable computational complexity.

Abstract

Traditional multiconfiguration Hartree-Fock (MCHF) and configuration interaction (CI) methods are based on a single orthonormal orbital basis (OB). For atoms with complicated shell structures, a large OB is needed to saturate all the electron correlation effects. The large OB leads to massive configuration state function (CSF) expansions that are difficult to handle. We show that it is possible to relax the orthonormality restriction on the OB and break down the originally large calculations to a set of smaller ones that can be run in parallel. Each calculation determines a partitioned correlation function (PCF) that accounts for a specific correlation effect. The PCFs are built on optimally localized orbital sets and are added to a zero-order multireference (MR) function to form a total wave function. The mixing coefficients of the PCFs are fixed from a small generalized eigenvalue problem. The required matrices are computed using a biorthonormal transformation technique. The new method, called partitioned correlation function interaction (PCFI), converges rapidly and gives total energies that are lower than the ordinary ones (MCHF and CI). Considering Li I, we show that by dedicating a PCF to the single excitations from the core highly improves the convergence patterns of the hyperfine parameters. Collecting the optimized PCFs to correct the MR function, the variational degrees of freedom in the relative mixing coefficients of the CSFs building the PCFs are inhibited. These constraints lead to small off-sets in computed properties other than total energy, with respect to the correct values. By (partially) deconstraining the mixing coefficients one converges to the correct limits and keeps the important advantage in the convergence rates. Reducing ultimately each PCF to a single CSF with its own OB leads to a non-orthogonal CI approach. Various perspectives of the new method are given.