Size-Consistent Adiabatic Connection Functionals via Orbital-Based Matrix Interpolation

TL;DR

The paper tackles the long-standing issue of size-consistency in adiabatic-connection functionals by introducing orbital-based size-consistent matrix interpolation (OSMI) for ACPT2. By forming correlation-energy matrices in the space of occupied KS orbitals and integrating over α with a matrix-valued interpolation (including a matrix modISI form), the authors achieve both size-consistency and orbital-invariance, while enabling a simple nonempirical AC and a one-parameter strong-interaction limit. They demonstrate that OSMI-ACPT2 accurately reproduces uniform electron gas correlation across densities, improves dissociation curves in molecular systems, and delivers competitive GMTKN55 performance—outperforming MP2, κ-MP2, and several nonempirical functionals, and closely approaching state-of-the-art hybrids for barrier heights and self-interaction-sensitive reactions. The approach shows promise for heterogeneous chemical systems and surfaces, offering a framework that preserves fundamental physics while enabling broader applicability of AC-based functionals.

Abstract

We introduce a size-consistent and orbital-invariant formalism for constructing correlation functionals based on the adiabatic connection for density functional theory (DFT). By constructing correlation energy matrices for the weak and strong correlation limits in the space of occupied orbitals, our method, which we call orbital-based size-consistent matrix interpolation (OSMI), avoids previous difficulties in the construction of size-consistent adiabatic connection functionals. We design a simple, nonempirical adiabatic connection and a one-parameter strong-interaction limit functional, and we show that the resulting method reproduces the correlation energy of the uniform electron gas over a wide range of densities. When applied to subsets of the GMTKN55 thermochemistry database, OSMI is more accurate on average than MP2 and nonempirical density functionals. Most notably, OSMI provides excellent predictions of the barrier heights we tested, with average errors of less than 2 kcal mol$^{-1}$. Finally, we find that OSMI improves the trade-off between fractional spin and fractional charge errors for bond dissociation curves compared to DFT and MP2. The fact that OSMI provides a good description of molecular systems and the uniform electron gas, while also maintaining low self-interaction error and size-consistency, suggests that it could provide a framework for studying heterogeneous chemical systems.

Figures (4)

• Figure 1: Spin-restricted dissociation curves of (a) the hydrogen molecule with and without an argon "spectator atom" 100 Å away and of (b) the nitrogen molecule. "NSC" is the non-size-consistent approach of eq \ref{['eq:adiabatic_connection']}, and "OSMI" is our size-consistent model (eq \ref{['eq:osmi_acmp2_xc']}). The hydrogen dissociation curves with and without argon match for OSMI but not NSC. Energies are referenced to the spin-unrestricted dissociation limit for each method.
• Figure 2: Correlation energy per electron $\epsilon_\text{c}$ of the uniform electron gas (UEG) for $\kappa$-MP2, non-size-consistent ACPT2 (NSC-ACPT2), and size-consistent OSMI-ACPT2. The exact result was calculated using the modified PW92 LDA functional perdewAccurateSimpleAnalytic1992 (LDA_C_PW_MOD in libxc lehtolaRecentDevelopmentsLibxc2018), which interpolates over quantum Monte Carlo results for the correlation energy of the UEG. ceperleyGroundStateElectron1980
• Figure 3: Mean absolute errors (MAEs) of density functionals and MP2/GL2 variants for selected subsets of the GMTKN55 database. The subsets are separated based on type of property: (a) reaction energies, ionization potentials, and electron affinities, (b) barrier heights, (c) noncovalent interactions, and (d) noncovalent interactions excluding IDISP, to make the energy scale more readable.
• Figure 4: Spin-restricted dissociation curves of (a) the hydrogen molecule and (b) the nitrogen molecule with different methods, as well as doublet dissociation curves of (c) the H2+ molecular ion and (d) the He2+ molecular ion. Energies are referenced to the open-shell dissociation limit for each method. The "exact" result for H2 was obtained from CCSD in the aug-cc-pVQZ basis dunningGaussianBasisSets1989kendallElectronAffinitiesFirstrow1992woonGaussianBasisSets1993, while for nitrogen it was taken from Gdanitz gdanitzAccuratelySolvingElectronic1998, which used multi-reference coupled-cluster theory. The "exact" result for H2+ was obtained from Hartree-Fock, while for He2+ it was obtained from CCSD(T), with both methods using the aug-cc-pVQZ basis. MP2 and $\kappa$-MP2 are not shown for H2+ because they are exact for 1-electron systems. For He2+, MP2, $\kappa$-MP2, and OSMI-ACPT2 produce very similar dissociation curves.