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

TL;DR

This paper presents OSMI, a size-consistent, orbital-invariant correlation functional for DFT that accurately predicts energies, barrier heights, and dissociation curves, improving upon existing methods by combining uniform electron gas and molecular system descriptions.

Contribution

The authors develop a novel size-consistent, orbital-based matrix interpolation method for adiabatic connection functionals, enhancing accuracy and applicability in DFT calculations.

Findings

OSMI accurately reproduces the uniform electron gas correlation energy.

OSMI outperforms MP2 and nonempirical functionals on the GMTKN55 database.

OSMI predicts barrier heights with less than 2 kcal/mol error.

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.