Generalized local potential functional embedding theory of localized orbitals

TL;DR

This work introduces generalized LPFET (gLPFET), a lattice embedding theory that combines a generalized KS-DFT reference with density matrix embedding concepts. By using a non-local Hartree–Fock exchange in the full-reference Hamiltonian and a local correlation potential, gLPFET yields impurity potentials that vary by embedded orbital, with the impurity chemical potential becoming a simple functional of the local correlation potential in the regime of strong local correlation, $\mu^{(i)}_{\rm imp} \approx \sum_{k} \langle b^{(i)}|\chi_k\rangle^2 \, v^{\rm c}_k$. The theory is implemented via an inner gKS-SCF loop and an outer density-matching loop that optimizes $\mathbf{v}^{\rm c}$ to reproduce the full system density across test cases, including a non-uniform Hubbard ring and an ab initio H$_6$ chain. Numerical results show gLPFET cures the weak-correlation failures of LPFET, improves upon gDET in certain regimes, and preserves accuracy in strongly correlated cases, highlighting its potential as a robust, scalable embedding framework with a formal link to in-principle exact lattice DFET formulations. The approach provides a practical route to accurate, locally correlated embedding across a range of electronic structure problems and paves the way for further theoretical and methodological developments in lattice-DFT embedding.

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.

Figures (7)

• Figure 1: Density profile of the half-filled six-site Hubbard ring obtained for different interaction strengths $U/t$ with (g)LPFET and (g)DET embedding methods. Comparison is made with the exact FCI results.
• Figure 2: Same as Fig. \ref{['fig:comparison']} for generalized embedding methods only and other interaction strengths.
• Figure 3: Full Hxc potential on-site values evaluated with respect to that of site 0 at the gLPFET and gDET levels of embedding, for different interaction strengths. Comparison is made with the exact reverse engineered Hxc potential obtained from the FCI density profile.
• Figure 4: Impurity chemical potential values obtained on each embedded site at the gLPFET and gDET levels of embedding, for various interaction strengths. Comparison is made with the exact reverse engineered values (from the FCI density profile) and those computed from the gLPFET ansatz of Eq. (\ref{['eq:ind_LPFET_chem_pot']}) with the exact correlation potential.
• Figure 5: Total energy of the half-filled six-site Hubbard ring computed as a function of the interaction strength $U/t$ with the various embedding methods. Comparison is made with FCI.