# Natural orbital functional for spin-polarized periodic systems

## TL;DR

This paper extends natural orbital functional theory to spin-polarized periodic systems, enabling accurate modeling of strong electron correlation in systems like Hubbard models and hydrogen rings.

## Contribution

It introduces an extension of the PNOF5 and PNOF7 models to describe spin-uncompensated systems with explicit handling of high-spin cases.

## Key findings

- PNOF7 accurately describes strong correlation in hydrogen rings.
- The reconstructed two-particle density matrix maintains N-representability and spin conservation.
- Model results agree well with exact solutions for test systems.

## Abstract

Natural orbital functional theory is considered for systems with one or more unpaired electrons. An extension of the Piris natural orbital functional (PNOF) based on electron pairing approach is presented, specifically, we extend the independent pair model, PNOF5, and the interactive pair model PNOF7 to describe spin-uncompensated systems. An explicit form for the two-electron cumulant of high-spin cases is only taken into account, so that singly occupied orbitals with the same spin are solely considered. The rest of electron pairs with opposite spins remain paired. The reconstructed two-particle reduced density matrix fulfills certain N-representability necessary conditions, as well as guarantees the conservation of the total spin. The theory is applied to model systems with strong non-dynamic (static) electron correlation, namely, the one-dimensional Hubbard model with periodic boundary conditions and hydrogen rings. For the latter, PNOF7 compares well with exact diagonalization results so the model presented here is able to provide a correct description of the strong-correlation effects.