Structure of the first order Reduced Density Matrix in three electron systems: A Generalized Pauli Constraints assisted study

TL;DR

This paper analyzes the structure of the one-body reduced density matrix in three-electron systems, exploring spin dependence, occupation number ordering, and the effects of generalized Pauli constraints using CI expansions.

Contribution

It introduces a measure for spin dependence of natural orbitals and examines the implications of nearly pinned generalized Pauli constraints in three-electron systems.

Findings

Natural orbitals are generally spin dependent except in maximally polarized systems.

The spin dependence measure varies significantly across different systems.

Ordering of occupation numbers impacts RDMFT minimization and CI expansion formulations.

Abstract

We investigate the structure of the one-body Reduced Density Matrix (1RDM) of three electron systems, i.e. doublet and quadruplet spin configurations, corresponding to the smallest interacting system with an open-shell ground state. To this end, we use Configuration Interaction (CI) expansions of the exact wave function in Slater determinants built from natural orbitals in a finite dimensional Hilbert space. With the exception of maximally polarized systems, the natural orbitals of spin eigenstates are generally spin dependent, i.e. the spatial parts of the up and down natural orbitals form two different sets. A measure to quantify this spin dependence is introduced and it is shown that it varies by several orders of magnitude depending on the system. We also study the ordering issue of the spin-dependent occupation numbers which has practical implications in Reduced Density Matrix Functional Theory minimization schemes when Generalized Pauli Constraints are imposed and in the form of the CI expansion in terms of the natural orbitals. Finally, we discuss the aforementioned CI expansion when there are GPCs that are almost "pinned".