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We extend to strongly correlated molecular systems the recently introducedbasis-set incompleteness correction based on density-functional theory (DFT)[E. Giner et al., J. Chem. Phys. 149, 194301 (2018)]. This basis-set correctionrelies on a mapping between wave-function calculations in a finite basis setand range-separated DFT (RSDFT) through the definition of an effectivenon-divergent interaction corresponding to the electron-electron Coulombinteraction projected in the finite basis set. This enables the use ofRSDFT-type complementary density functionals to recover the dominant part ofthe short-range correlation effects missing in this finite basis set. To studyboth weak and strong correlation regimes we consider the potential energycurves of the H10, N2, O2, and F2 molecules up to the dissociation limit, andwe explore various approximations of complementary functionals fulfilling twokey properties: spin-multiplet degeneracy (i.e., independence of the energywith respect to the spin projection Sz) and size consistency. Specifically, weinvestigate the dependence of the functional on different types of on-top pairdensities and spin polarizations. The key result of this study is that theexplicit dependence on the on-top pair density allows one to completely removethe dependence on any form of spin polarization without any significant loss ofaccuracy. Quantitatively, we show that the basis-set correction reacheschemical accuracy on atomization energies with triple-zeta quality basis setsfor most of the systems studied here. Also, the present basis-setincompleteness correction provides smooth potential energy curves along thewhole range of internuclear distances.

A basis-set error correction based on density-functional theory for strongly correlated molecular systems