Quasipinning and selection rules for excitations in atoms and molecules

TL;DR

This paper explores how saturation of certain inequalities related to natural occupation numbers can inform selection rules in electronic structure calculations, potentially reducing computational costs in atomic and molecular systems.

Contribution

It demonstrates that saturation of inequalities constrains dominant configurations, offering a new approach to simplify configuration interaction expansions.

Findings

Saturation of inequalities leads to specific selection rules.

Application to atomic and molecular systems reduces computational complexity.

Provides insights into the structure of natural occupation numbers.

Abstract

Postulated by Pauli to explain the electronic structure of atoms and molecules, the exclusion principle establishes an upper bound of 1 for the fermionic natural occupation numbers $\{n_i\}$. A recent analysis of the pure $N$-representability problem provides a wide set of inequalities for the $\{n_i\}$, leading to constraints on these numbers. This has a strong potential impact on reduced density matrix functional theory as we know it. In this work we continue our study the nature of these inequalities for some atomic and molecular systems. The results indicate that (quasi)saturation of some of them leads to selection rules for the dominant configurations in configuration interaction expansions, in favorable cases providing means for significantly reducing their computational requirements.