A recently proposed series of corrections to the earliest JK-only functionals has considerably improved the prospects of density matrix functional theory ͑DMFT͒. Still, the most advanced of these functionals ͑correction C3͒ requires a preselection of the terms in the pair density ⌫͑r 1 , r 2 ͒ involving the bonding and antibonding natural orbitals ͑NOs͒ belonging to an electron pair bond. Ideally, a DMFT functional should only depend on the NOs and their occupation numbers, and we propose a

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... tional with an occupation number driven weighing of terms in the pair density. These are formulated as "damping" for certain ranges of occupation numbers of the two-electron cumulant that arises in the expansion of the two-particle density matrix of the paradigmatic two-electron system. This automatic version of C3, which we denote AC3, provides the correct dissociation limit for electron pair bonds and it excellently reproduces the potential energy curves of the multireference configuration interaction ͑MRCI͒ method for the dissociation of the electron pair bond in the series of the ten-electron hydrides CH 4 , NH 3 , H 2 O, and HF. AC3 reproduces closely the experimental equilibrium distances and at R e it yields correlation energies of the ten-electron systems with an average error in the absolute values of only 3.3% compared to the MRCI values. We stress the importance of treatment of strong correlation cases ͑NO occupation numbers differing significantly from 2.0 and 0.0͒ by appropriate terms in the cumulant. 2 ͵ ⌫͓͑␥͔;r 1 ,r 2 ͒ ͉r 1 − r 2 ͉ dr 1 dr 2 , ͑1.4͒ energies ͑we use atomic units͒. In Eq. ͑1.3͒ ͑r 1 ͒ is the electron density ͑diagonal of the one-matrix͒ and v ext ͑r 1 ͒ is the external potential. The exact pair-density functional ⌫͓␥͔ is not known. We use the usual partitioning in Coulomb, exchange, and a rest term ͑"correlation"͒, ⌫͓͑␥͔;r 1 ,r 2 ͒ = ͑r 1 ͒͑r 2 ͒ − 1 2 ͉␥͑r 1 ,r 2 ͉͒ 2 + C͓͑␥͔;r 1 ,r 2 ͒. ͑1.5͒ When in the exchange term the exact one-matrix ␥ is used, as we will do, instead of the Hartree-Fock density matrix ␥ HF ; the correlation part of the two-electron energy ͑1 / 2͒͐C͑r 1 , r 2 ͒dr 1 dr 2 / r 12 is differently defined than in the usual definition of correlation as the energy difference with respect to the Hartree-Fock energy. The partitioning of the energy according to Eq. ͑1.5͒ has often been used, 11,16-18 although it has the disadvantage that the sum rule for the exchange hole that it integrates to −1 now no longer holds. ͑This can be remedied by working with the best idempotent approximant to ␥, see Kutzelnigg 19 ͒. It is natural to use Eq. ͑1.5͒ when the Hartree-Fock model is not taken as a starting point, but the one-matrix is targeted directly, as in this paper. The correlation term C͓␥͔͑r 1 , r 2 ͒ is in fact the two-particle cumulant in the well-known cumulant expansion of the twoparticle density matrix ͑two-matrix͒, and although we will not make any essential use of the cumulant expansion as such ͑i.e., to higher orders͒, we will conveniently denote it as the two-electron cumulant henceforth. The two-electron cumulant can be written as a͒ Electronic mail: baerends@chem.vu.nl.