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New advances in NOF theory: paving the way towards chemical accuracy

The energy functional of the one-particle reduced density matrix (1- RDM) is called natural orbital functional (NOF) when it is based upon the spectral expansion of the 1-RDM. A detailed account of the state of the art of NOF theory until 2006 can be found in Ref. [1]. In this presentation, the spin-conserving density matrix functional theory is outlined. The reconstruction functional PNOF, which is based on an explicit ansatz of the two-particle cumulant λ(Δ,Π) satisfying necessary positivity conditions for the two-particle reduced density matrix (2-RDM), is considered to reconstruct the latter. New approachs4 to Π and Δ are examined. The theory is applied to the first- and second-row atoms (H-Ne), and selected molecules formed with them. The energy differences between the ground state and the lowest-lying excited state with different spin for these atoms, and the atomization energies of the considered molecules are presented. Several reactions are also investigated to illustrate the potentiality of NOF theory to yield the correct topology of potential energy surfaces that are sensible to electron correlation. The recent proposed algorithm which yields the natural orbitals by iterative diagonalization of a generalized Hermitian matrix is used. The values we have obtained are very accurate comparing with the CCSD(T,full) method and the experimental data ​
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