Kohn-Sham density encoding rescues coupled cluster theory for strongly correlated molecules

Abstract

Coupled cluster theory with a Kohn-Sham reference (KS-CC) can dramatically outperform its Hartree-Fock counterpart for strongly correlated systems, but the origin of these improvements has remained unclear. Here we demonstrate that these improvements arise from differences in the one-particle density matrix that are encoded into the non-canonical Fock matrix and not from the nature of the KS orbitals, as is commonly assumed. Equipped with this insight, KS-CCSD(T) can be leveraged to achieve near-chemical-accuracy for electronic and thermochemical properties of transition-metal dimers and main-group compounds. Most strikingly, KS-CCSD(T) qualitatively recovers the entire Cr$_2$ potential energy surface, a notorious failure case for HF-CCSD(T) and single-reference density functional theory. We further introduce a density difference diagnostic that identifies multireference character and guides practitioners toward rational selections of optimal references at mean-field cost. These results establish KS-CCSD(T) as a practical route to treat strong correlation within the "gold standard" framework, and this has immediate implications for machine learning potential development and materials research, areas that heavily rely on KS-DFT for model-parameter fitting.

Figures (6)

• Figure 1: MO eigenvalue changes with increasing %HFX for HF, B3LYP, and B3LYP after semi-canonicalization. The percent exchange of the DFA is adjusted in proportion to the exact exchange. The vertical dashed lines represent the standard %HFX in the DFA. Highest occupied (HOMO) and lowest unoccupied (LUMO) MO energies are obtained with the cc-pVTZ and aug-cc-pVTZ basis sets respectively.
• Figure 2: Benchmark comparison of density functional and coupled cluster methods for transition metal–ligand bond dissociation energies. Mean absolute errors (MAE) in bond dissociation energies for first-row transition metal compounds across four bond classes: a, metal–oxygen (M-O); b, metal–chlorine (M-Cl); c, metal–hydrogen (M-H); and d, over all bonds. Blue bars represent density functional methods (KS-DFT), orange bars represent CCSD(T)/CBS calculations using different reference determinants (CC-X denotes CCSD(T)/CBS with densities from method X), and the green bar represents phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) results from Ref.Shee2019. CC-Best denotes the optimal reference selection either from HF or DFT for each system, and QMC-Best denotes the optimal reference when using MP2, CC, or TZ/QZ extrapolation in ph-AFQMC. The subtle gray shading indicates the chemical accuracy threshold (0--3 kcal/mol $\approx$$0$--$0.13$ eV).
• Figure 3: Performance of density functional and coupled cluster methods for metal hydride cations and bimetallic bond dissociation energies. Mean absolute errors (MAE) in bond dissociation energies for: a, metal hydride cations (M-H+); b, homonuclear metal–metal dimers (M-M); and c, overall performance. Blue bars represent density functional methods (KS-DFT) and orange bars represent CCSD(T)/CBS with different reference determinants. CC-Best denotes the optimal reference selection (HF or DFT) for each system. The subtle gray shading indicates the chemical accuracy threshold (0--3 kcal/mol $\approx$$0$--$0.13$ eV).
• Figure 4: Potential energy curve of the antiferromagnetic state of Cr2 dimer computed with UCCSD(T)/CBS using different reference densities. Binding energy as a function of bond length for Cr2, the prototypical multireference transition metal dimer. Plot depicts UCCSD(T)/CBS calculations with reference orbitals from Hartree–Fock (UCC-HF), SVWN5 (UCC-SVWN5), PBE (UCC-PBE), PW91 (UCC-PW91), R²SCAN (UCC-R²SCAN), and PBE0 (UCC-PBE0). The experimental curve (Exp, black) and the best theoretical estimate from state-of-the-art multireference calculations (BTE, crimson) from Ref.Larsson2022 provide comparison.
• Figure 5: Singlet-triplet gaps (STGs) for BN and $\mathbf{{CH}_{2}}$ computed with CCSD(T)/cc-pVTZ with HF and KS-DFT determinants. The solid and dashed horizontal orange line represent the reference theoretical estimate and experimental value, respectively.