Generalized local potential functional embedding theory of localized orbitals

TL;DR

This paper introduces a generalized local potential functional embedding theory (gLPFET) that combines elements of density functional theory and density matrix embedding, improving accuracy in strongly correlated electron systems.

Contribution

It develops a generalized embedding framework that incorporates non-local exchange and local correlation potentials, enhancing the accuracy over previous methods like DMET and LPFET.

Findings

High accuracy in strongly correlated regimes

Fixes flaws of previous LPFET in weak correlation regimes

Numerical validation on model systems

Abstract

In this work we introduce a generalized flavor, in the sense of generalized Kohn-Sham density functional theory (gKS-DFT), of the recently derived local potential functional embedding theory (LPFET) [J. Chem. Theory Comput. 2025, 21, 20, 10293], where the in-principle exact formalism of DFT is combined with that of density matrix embedding theory (DMET). In generalized LPFET (gLPFET), the embedding clusters are designed from a full-size gKS system where the (in-principle non-local) Hartree-Fock exchange potential is combined with a local (in the localized orbital representation) correlation potential. The latter is optimized self-consistently such that gKS and local embedding cluster's densities match. Unlike in DMET, which uses the same (global) chemical potential value in all clusters, each embedded orbital has its own chemical potential in gLPFET. We show analytically that, when electron correlation is strongly local, the latter potential becomes a simple functional of the correlation potential. Numerical calculations on model systems confirm the high accuracy of gLPFET in this regime, in contrast to DMET. Moreover, we show that gLPFET completely fixes the flaw of LPFET in weaker correlation regimes, through its appropriate description of the Hartree-exchange potential.