xDH double hybrid functionals can be qualitatively incorrect for non-equilibrium geometries: Dipole moment inversion and barriers to radical-radical association using XYG3 and XYGJ-OS

TL;DR

This paper reveals that xDH double hybrid functionals XYG3 and XYGJ-OS can produce unphysical results for non-equilibrium geometries, such as dipole moment inversion and incorrect energy barriers, due to orbital mismatch issues.

Contribution

It demonstrates that commonly used xDH functionals can be qualitatively incorrect for stretched bonds, highlighting limitations in their applicability beyond equilibrium geometries.

Findings

XYG3 and XYGJ-OS predict unphysical dipole moments in stretched molecules.

Failures are due to orbital mismatch, not PT2 effects.

These functionals can produce inaccurate energy barriers for radical-radical associations.

Abstract

Double hybrid (DH) density functionals are amongst the most accurate density functional approximations developed so far, largely due to incorporation of correlation effects from unoccupied orbitals via second order perturbation theory (PT2). The xDH family of DH functionals calculate energy directly from orbitals optimized by a lower level approach like B3LYP, without self-consistent optimization. XYG3 and XYGJ-OS are two widely used xDH functionals that are known to be quite accurate at equilibrium geometries. Here, we show that the XYG3 and XYGJ-OS functionals can be ill behaved for stretched bonds well beyond the Coulson-Fischer point, predicting unphysical dipole moments and humps in potential energy curves for some simple systems like the HF molecule. Numerical experiments and analysis show these failures are not due to PT2. Instead, a large mismatch at stretched bond-lengths between the reference B3LYP orbitals and the optimized orbitals associated with the non-PT2 part of XYG3 lead to an unphysically large non-Hellman-Feynman contribution to first order properties like forces and electron densities.