Why Projection-Based DMRG-in-DFT Cannot Be Exact, Even with the Exact Exchange-Correlation Functional

TL;DR

This paper reveals fundamental limitations of projection-based DMRG-in-DFT embedding, showing that even with exact exchange-correlation functionals, inherent errors persist due to nonvariational functionals and self-interaction effects.

Contribution

It establishes the theoretical basis for embedding wave functions in DFT environments and analyzes the sources of errors in projection-based DMRG-in-DFT with approximate functionals.

Findings

The embedding functional is inherently nonvariational and bounded from above by the true ground-state energy.

The primary error source is the nonadditive exchange-correlation energy at the subsystem interface.

Using pair-density functionals does not eliminate errors caused by self-interaction effects.

Abstract

We establish the theoretical foundations for embedding a correlated wave function in an environment formed by Kohn-Sham orbitals. We show that introducing an approximation which equates two, in principle distinct, kinetic-energy functionals yields an embedding functional identical to the projection-based wavefunction-in-DFT formulation of Miller and co-workers. We demonstrate that this functional is inherently nonvariational: its minimum is not guaranteed to coincide with the exact ground-state energy and remains bounded from above by it. Building on this formal framework, we analyze the dominant sources of error in projection-based DMRG-in-DFT embedding with approximate exchange-correlation (xc) functionals. Using molecules with dissociating covalent bonds as a diagnostic example, we demonstrate that the primary source of error is the nonadditive exchange-correlation energy describing the nonclassical coupling between the active subsystem and its environment. Eliminating the fractional-spin error by employing a pair-density xc functional (PDFT) instead of a semilocal GGA does not remedy this deficiency, because the inaccuracy stems from self-interaction effects at the subsystem-environment interface.