# 5- and 6‑Membered Rings: A Natural Orbital Functional Study

## TL;DR

This paper evaluates a new method for calculating electron correlation in ring-shaped molecules, showing it works well for capturing dynamic effects.

## Contribution

The study introduces and validates a modified version of the GNOF functional for capturing dynamic correlation in ring systems.

## Key findings

- GNOFm shows small but consistent improvements over the original GNOF in describing 5- and 6-membered rings.
- Both GNOF and GNOFm deliver accurate correlation energies comparable to CCSD(T) benchmarks.
- The results confirm the GNOF family's reliability for dynamic correlation in complex molecular systems.

## Abstract

The Global Natural Orbital Functional (GNOF) provides
a straightforward
approach to capture most electron correlation effects without needing
perturbative corrections or limited active spaces selection. In this
work, we evaluate both the original GNOF and its modified variant,
GNOFm, on a set of twelve 5- and 6-membered molecular rings, systems
characterized primarily by dynamic correlation. This reference set
is vital as it comprises essential substructures of more complex molecules.
We report complete-basis-set limit correlation energies for GNOF,
GNOFm, and the benchmark CCSD­(T) method. Across the Dunning basis
sets, both functionals deliver a balanced and accurate description
of the molecular set, with GNOFm showing small but systematic improvements
while preserving the overall robustness of the original formulation.
These results confirm the reliability of the GNOF family and its ability
to capture dynamic correlation effects.