Double hybrid density-functional theory using the Coulomb-attenuating method

A double hybrid approximation using the Coulomb-attenuating method (CAM-DH) is derived within range-separated density-functional perturbation theory, in the spirit of a recent work by Cornaton {\it et al.} [Phys. Rev. A 88, 022516 (2013)]. The energy expression recovered through second order is linear in the parameters $\alpha$ and $\beta$ that control the Coulomb attenuation. The method has been tested within the local density approximation on a small test set consisting of rare-gas and alkaline-earth-metal dimers as well as diatomics with single, double and triple bonds. In this context, the semi-empirical $\alpha=0.19$ and $\beta=0.46$ parameters, that were optimized for the hybrid CAM-B3LYP functional, do not provide accurate interaction and total energies. Using semi-local functionals with density scaling, that was neglected in this work, may lead to different conclusions. Calibration studies on a larger test set would be necessary at this point. This is left for future work. Finally, we propose as a perspective an alternative CAM-DH approach that relies on the perturbation expansion of a partially long-range interacting wavefunction. In this case the energy is not linear anymore in $\alpha$ and $\beta$. Work is in progress in this direction.