# Is there a physical meaning of the natural orbitals? Analysis of exactly solvable models

## TL;DR

This paper examines whether natural orbitals have a meaningful physical interpretation by analyzing their effectiveness in describing various many-body excited states in exactly solvable models.

## Contribution

It provides a detailed analysis of the applicability of natural orbitals for different excited states and clarifies their role compared to fractional occupation numbers in reduced density-matrix functional theory.

## Key findings

- Natural orbitals can effectively describe some bound and ionized excited states.
- The success of reduced density-matrix functional theory relies more on fractional occupations than on natural orbitals.
- The physical meaning of natural orbitals varies depending on the specific excited state.

## Abstract

We investigate the suitability of natural orbitals as a basis for describing many-body excitations. We analyze to which extend the natural orbitals describe both bound as well as ionized excited states and show that depending on the specifics of the excited state the ground-state natural orbitals yield a good approximation or not. We show that the success of reduced density-matrix functional theory in describing molecular dissociation lies in the flexibility provided by fractional occupation numbers while the role of the natural orbitals is minor.