# Natural orbital functional for multiplets

## TL;DR

This paper introduces a new natural orbital functional tailored for electronic multiplet states, accurately capturing electron correlation effects and conserving total spin, with promising results for transition-metal ionization potentials.

## Contribution

A novel natural orbital functional for multiplets based on a new 2RDM reconstruction that preserves spin and captures electron correlation.

## Key findings

- Accurately predicts ionization potentials of transition metals.
- Fulfills (2,2)-positivity and spin conservation.
- Matches high-level theoretical and experimental data.

## Abstract

A natural orbital functional for electronic systems with any value of the spin is proposed. This energy functional is based on a new reconstruction for the two-particle reduced density matrix (2RDM) of the multiplet, that is, of the mixed quantum state that allows all possible spin projections. The mixed states of maximum spin multiplicity are considered. This approach differs from the methods routinely used in electronic structure calculations that focus on the high-spin component or break the spin symmetry. In the ensemble, there are no interactions between electrons with opposite spins in singly occupied orbitals, as well as new inter-pair alpha-beta-contributions are proposed in the 2RDM. The proposed 2RDM fulfills (2,2)-positivity necessary N-representability conditions and guarantees the conservation of the total spin. The NOF for multiplets is able to recover the non-dynamic and the intrapair dynamic electron correlation. The missing dynamic correlation is recovered by the NOF-MP2 method. Calculation of ionization potentials of the first-row transition-metal atoms is presented as test case. The values obtained agree with those reported at the coupled cluster singles and doubles level of theory with perturbative triples and experimental data.