Charge-transfer steps in Density Functional Theory from the perspective of the Exact Electron Factorization

TL;DR

This paper explains the origin of step structures in density functional theory during molecular dissociation using the exact electron factorization, linking electron entanglement to charge transfer and improving modeling approaches.

Contribution

It introduces an exact mapping via the electron factorization to elucidate the physical origin of steps in DFT potentials during dissociation.

Findings

Steps are caused by spatial electron entanglement and charge transfer.

Step height can be deduced from the mechanism of electron entanglement.

Two approximate methods for reproducing potentials are proposed.

Abstract

When a molecule dissociates, the exact Kohn-Sham (KS) and Pauli potentials may form step structures. Reproducing these steps correctly is central for the description of dissociation and charge-transfer processes in density functional theory (DFT): The steps align the KS eigenvalues of the dissociating subsystems relative to each other and determine where electrons localize. While the step height can be calculated from the asymptotic behavior of the KS orbitals, this provides limited insight into what causes the steps. We give an explanation of the steps with an exact mapping of the many-electron problem to a one-electron problem, the exact electron factorizaton (EEF). The potentials appearing in the EEF have a clear physical meaning that translates to the DFT potentials by replacing the interacting many-electron system with the KS system. With a simple model of a diatomic, we illustrate that the steps are a consequence of spatial electron entanglement and are the result of a charge transfer. From this mechanism, the step height can immediately be deduced. Moreover, two methods to approximately reproduce the potentials during dissociation suggest themselves. One is based on the states of the dissociated system, while the other one is based on an analogy to the Born-Oppenheimer treatment of a molecule. The latter method also shows that the steps connect adiabatic potential energy surfaces. The view of DFT from the EEF thus provides a better understanding of how many-electron effects are encoded in a one-electron theory and how they can be modeled.