A two-density approach to the general many-body problem and a proof of principle for small atoms and molecules

TL;DR

This paper introduces a two-density extended electron model that simplifies many-body electronic calculations, proves the Hohenberg-Kohn theorems for it, and demonstrates its accuracy on small atoms and molecules, promising more efficient quantum simulations.

Contribution

It proves the Hohenberg-Kohn theorems for a novel density model and provides a practical implementation that matches the accuracy of existing methods.

Findings

The model reproduces experimental results of quantum mechanics.

The approach is computationally more efficient than traditional methods.

It accurately predicts properties of small atomic systems.

Abstract

An extended electron model fully recovers many of the experimental results of quantum mechanics while it avoids many of the pitfalls and remains generally free of paradoxes. The formulation of the many-body electronic problem here resembles the Kohn-Sham formulation of standard density functional theory. However, rather than referring electronic properties to a large set of single electron orbitals, the extended electron model uses only mass density and field components, leading to a substantial increase in computational efficiency. To date, the Hohenberg-Kohn theorems have not been proved for a model of this type, nor has a universal energy functional been presented. In this paper, we address these problems and show that the Hohenberg-Kohn theorems do also hold for a density model of this type. We then present a proof-of-concept practical implementation of this method and show that it reproduces the accuracy of more widely used methods on a test-set of small atomic systems, thus paving the way for the development of fast, efficient and accurate codes on this basis.