Hierarchy Configuration Interaction: Combining Seniority Number and Excitation Degree

TL;DR

This paper introduces hierarchy configuration interaction (hCI), a new method combining excitation degree and seniority number to improve electronic structure calculations, showing competitive performance with traditional CI methods.

Contribution

The paper proposes a novel partitioning of the Hilbert space called hierarchy configuration interaction (hCI), combining excitation degree and seniority number in a single hierarchy parameter.

Findings

hCI generally outperforms or matches excitation-based CI.

Orbital optimization offers limited benefits at higher CI orders.

Orbital-optimized CI with singles effectively describes bond breaking.

Abstract

We propose a novel partitioning of the Hilbert space, hierarchy configuration interaction (hCI), where the excitation degree (with respect to a given reference determinant) and the seniority number (i.e., the number of unpaired electrons) are combined in a single hierarchy parameter. The key appealing feature of hCI is that each hierarchy level accounts for all classes of determinants whose number share the same scaling with system size. By surveying the dissociation of multiple molecular systems, we found that the overall performance of hCI usually exceeds or, at least, parallels that of excitation-based CI. For higher orders of hCI and excitation-based CI, the additional computational burden related to orbital optimization usually do not compensate the marginal improvements compared with results obtained with Hartree-Fock orbitals. The exception is orbital-optimized CI with single excitations, a minimally correlated model displaying the qualitatively correct description of single bond breaking, at a very modest computational cost.