Projection-based DMRG-in-DFT embedding corrected by non-additive exchange-correlation

TL;DR

This work targets inaccuracies in projection-based DMRG-in-DFT embedding caused by nonadditive exchange–correlation (XC) errors. It introduces two corrections: an exact nonadditive exchange term $E_{xx}^{\text{nadd}}$ and a multireference AC0-based nonadditive correlation term $E_{c}^{\text{AC0,nadd}}$ that vanish at dissociation, improving the description of strongly correlated fragments coupled to environments. Benchmarking on H$_{20}$ chain dissociation and CN bond cleavage in propionitrile shows substantial reductions in embedding errors, achieving near chemical accuracy with modest active spaces. The approach enhances the practicality of WF-in-DFT embedding for large, strongly correlated systems and points to efficient implementations, including truncation and fractional-spin functional strategies for future work.

Abstract

The projection-based wave function (WF)-in-DFT embedding enables an efficient description of both the energetics and properties of large and complex chemical systems, with accuracy exceeding that of pure DFT. Recently, we have proposed using the density matrix renormalization group (DMRG) as the WF method for molecules containing strongly correlated fragments [Beran, P. et al. J. Phys. Chem. Lett. 2023, 14, 3, 716-722]. In this work, we demonstrate that the accuracy of the DMRG-in-DFT approach is primarily limited by the approximate treatment of the coupling between the active component and its environment through nonadditive exchange-correlation functionals. To address this issue, we combine exact exchange to reduce the nonadditive exchange error with a multireference adiabatic connection (AC) scheme to recover nonadditive correlation. The performance of the improved DMRG-in-DFT embedding is illustrated on two prototypical strongly correlated systems: the dissociation of the H20 chain and the cleavage of a triple CN bond in propionitrile.

Figures (7)

• Figure 1: Benchmark problems investigated in this work: (a) H$_{20}$ chain with the central active fragment (A) composed of four hydrogen atoms, where the interatomic distances ($R$) are varied, (b) triple bond stretching in propionitrile (CH$_3$CH$_2$CN) with the active fragment defined as the $-$CN group.
• Figure 2: Relative energy error (kcal$\cdot$mol$^{-1}$) for the H$_{20}$ chain comparing self-consistent DMRG-in-B3LYP and standard DMRG-in-B3LYP, using a four-atom active fragment. Errors are referenced to full-system DMRG energies with the 6-31G basis set.
• Figure 3: Relative energy error (in kcal/mol) of DMRG-in-B3LYP for the H$_{20}$ chain with 4 atoms in the active fragment, compared to full-system DMRG, using the 6-31G basis set. The labels "full", $n=0$, $n=1$, and $n=2$ denote the calculations without concentric localization, and with the first, second, and third CL shells, respectively.
• Figure 4: Relative energy errors (in kcal/mol) of DMRG-in-B3LYP and DMRG-in-B3LYP with the non-additive exchange ($\Delta_x^{\text{nadd}}$), correlation ($\Delta_c^{\text{nadd}}$), and exchange–correlation ($\Delta_{xc}^{\text{nadd}}$) corrections, for H$_{20}$ chain with (a) 4-atom active fragment and (b) 8-atom active fragment, benchmarked against full-system DMRG with the cc-pVDZ basis set.
• Figure 5: Relative energy errors (in kcal/mol) of CAS-in-B3LYP, AC0(A)-CAS-in-B3LYP, and AC0(A)-CAS-in-B3LYP with the non-additive exchange ($\Delta_x^{\text{nadd}}$), correlation ($\Delta_c^{\text{nadd}}$), and exchange–correlation ($\Delta_{xc}^{\text{nadd}}$) corrections, for H$_{20}$ chain with (a) 4-atom active fragment and (b) 8-atom active fragment, benchmarked against full-system DMRG with the cc-pVDZ basis set.