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.Comment: 36 pages, 6 figure

N-centered ensemble density-functional theory for open systems

Two (so-called left and right) variants of N-centered ensemble density-functional theory (DFT) [Senjean and Fromager, Phys. Rev. A 98, 022513 (2018)] are presented. Unlike the original formulation of the theory, these variants allow for the description of systems with a fractional electron number. While conventional DFT for open systems uses only the true electron density as basic variable, left/right N-centered ensemble DFT relies instead on (i) a fictitious ensemble density that integrates to a central (integral) number N of electrons, and (ii) a grand canonical ensemble weight $\alpha$ which is equal to the deviation of the true electron number from N. Within such a formalism, the infamous derivative discontinuity that appears when crossing an integral number of electrons is described exactly through the dependence in $\alpha$ of the left and right N-centered ensemble Hartree-exchange-correlation density functionals. Incorporating N-centered ensembles into existing density-functional embedding theories is expected to pave the way towards the in-principle-exact description of an open fragment by means of a pure-state N-electron many-body wavefunction. Work is currently in progress in this directionComment: 15 pages, 4 figures, 1 tabl