Exploring the role of mean-field potentials and short-range wave function behavior in the adiabatic connection

TL;DR

This paper investigates how mean-field potentials and short-range wave function behavior influence the construction of Hamiltonians with long-range interactions, revealing that corrections based on short-range behavior are crucial and that mean fields do not always improve accuracy.

Contribution

It introduces a parameter-dependent potential approach to analyze adiabatic connections and demonstrates the limited benefit of mean-field potentials compared to short-range corrections in two-electron systems.

Findings

Mean-field potentials improve Hamiltonian expectation values but not energy accuracy within chemical bounds.

Short-range wave function behavior provides universal corrections that diminish mean-field advantages.

Energy errors within chemical accuracy are not significantly improved by mean-field potentials.

Abstract

In this article, we explore the construction of Hamiltonians with long-range interactions and their corrections using the short-range behavior of the wave function. A key aspect of our investigation is the examination of the one-particle potential, kept constant in our previous work, and the effects of its optimization on the adiabatic connection. Our methodology involves the use of a parameter-dependent potential dependent on a single parameter to facilitate practical computations. We analyze the energy errors and densities in a two-electron system (harmonium) under various conditions, employing different confinement potentials and interaction parameters. The study reveals that while the mean-field potential improves the expectation value of the physical Hamiltonian, it does not necessarily improve the energy of the system within the bounds of chemical accuracy. We also delve into the impact of density variations in adiabatic connections, challenging the common assumption that a mean field improves results. Our findings indicate that as long as energy errors remain within chemical accuracy, the mean field does not significantly outperform a bare potential. This observation is attributed to the effectiveness of corrections based on the short-range behavior of the wave function, a universal characteristic that diminishes the distinction between using a mean field or not.