  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.
