H$_4$: A Challenging System For Natural Orbital Functional Approximations

TL;DR

This paper investigates the challenge of accurately describing nondynamic correlation in the H$_4$ molecule's potential energy surface, demonstrating that interpair nondynamic correlation is crucial for correct, cusp-free results using natural orbital functional methods.

Contribution

It shows that incorporating interpair nondynamic correlation in PNOF6 yields a smooth, accurate PES for H$_4$, improving upon previous single-reference and geminal-based approaches.

Findings

PNOF6 avoids PES cusps near equilibrium.

Interpair nondynamic correlation is key for correct PES.

PNOF6 accurately predicts spin and delocalization properties.

Abstract

The correct description of nondynamic correlation by electronic structure methods not belonging to the multireference family is a challenging issue. The transition of $D_{2h}$ to $D_{4h}$ symmetry in H$_4$ molecule is among the most simple archetypal examples to illustrate the consequences of missing nondynamic correlation effects. The resurge of interest in density matrix functional methods has brought several new methods including the family of Piris Natural Orbital Functionals (PNOF). In this work we compare PNOF5 and PNOF6, which include nondynamic electron correlation effects to some extent, with other standard ab initio methods in the H$_4$ $D_{4h}/D_{2h}$ potential energy surface. Thus far, the wrongful behavior of single-reference methods at the $D_{2h}-D_{4h}$ transition of H$_4$ has been attributed to wrong account of nondynamic correlation effects, whereas in geminal-based approaches it has been assigned to a wrong coupling of spins and the localized nature of the orbitals. We will show that actually $\textit{interpair}$ nondynamic correlation is the key to a cusp-free qualitatively correct description of H$_4$ PES. By introducing $\textit{interpair}$ nondynamic correlation, PNOF6 is shown to avoid cusps and provide the correct smooth PES features at distances close to equilibrium, total and local spin properties along with the correct electron delocalization, as reflected by natural orbitals and multicenter delocalization indices.