Abstract
In the present work, we introduce a self-consistent density-functional embedding technique, which leaves the realm of standard energy-functional approaches in density functional theory and targets directly the density-to-potential mapping that lies at its heart. Inspired by the density matrix embedding theory, we project the full system onto a set of small interacting fragments that can be solved accurately. Based on the rigorous relation of density and potential in density functional theory, we then invert the fragment densities to local potentials. Combining these results in a continuous manner provides an update for the Kohn–Sham potential of the full system, which is then used to update the projection. We benchmark our approach for molecular bond stretching in one and two dimensions and show that, in these cases, the scheme converges to accurate approximations for densities and Kohn–Sham potentials. We demonstrate that the known steps and peaks of the exact exchange-correlation potential are reproduced by our method with remarkable accuracy.
Highlights
Over the past decades, density functional theory (DFT) has become a well-established and successful method that is able to accurately describe molecular and condensed matter systems.One reason for its success can be attributed to its computational efficiency as all physical observables of interest are functionals of the ground-state density n(r).[1]
The self-consistent density-functional embedding (SDE) algorithm can be improved by increasing the fragment size, and it converges to the exact solution
Our numerical results are limited to 1D and 2D model systems, we still discuss cases that are notoriously difficult to capture for standard KS DFT
Summary
Density functional theory (DFT) has become a well-established and successful method that is able to accurately describe molecular and condensed matter systems. One reason for its success can be attributed to its computational efficiency as all physical observables of interest are functionals of the ground-state density n(r).[1] The most popular technique to find the density of the system accurately is the Kohn−Sham (KS) DFT, where the density of the full interacting system is computed via an auxiliary noninteracting system.[2] All interactions and correlations of the interacting system are mimicked by the so-called exchange-correlation (xc) potential, which is usually determined as the derivative of the xc energy fpurnaccttiiocen.a2l−E6xc[An]. That is unknown and has to be remaining challenge is to approximated in find functional approximations describing other wanted observables O[n]. The dissociation limit of the H2 molecule is a good example for a simple system that is not easy to describe with commonly used approximate
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