Global Natural Orbital Functional: Towards the Complete Description of the Electron Correlation

TL;DR

This paper introduces a new global natural orbital functional (GNOF) that accurately describes electron correlation in systems with any spin, improving the understanding of multi-configurational and excited states in molecules and atoms.

Contribution

The paper presents a novel GNOF functional that captures complete intrapair and interorbital electron correlation, including static and dynamic effects, for any spin state and external potential.

Findings

Accurately predicts total energies and energy differences for atoms from H to Ne.

Successfully models ionization potentials of first-row transition metals.

Reproduces energies of molecular systems and dissociation processes consistent with high-level theories.

Abstract

The current work presents a natural orbital functional (NOF) for electronic systems with any spin value independent of the external potential being considered, that is, a global NOF (GNOF). It is based on a new two-index reconstruction of the two-particle reduced density matrix for spin multiplets. The emergent functional describes the complete intrapair electron correlation, and the correlation between orbitals that make up both the pairs and the individual electrons. The interorbital correlation is composed of static and dynamic terms. The concept of dynamic part of the occupation numbers is introduced. To evaluate the accuracy achieved with GNOF, calculation of a variety of properties is presented. They include the total energies and energy differences between the ground state and the lowest-lying excited state with different spin of atoms from H to Ne, ionization potentials of the first-row transition-metal atoms (Sc-Zn), and the total energies of a selected set of 55 molecular systems in different spin states. GNOF is also applied to the homolytic dissociation of selected diatomic molecules in different spin states and to the rotation barrier of ethylene, both paradigmatic cases of systems with significant multi-configurational character. The values obtained agree with those reported at high level of theory and experimental data.