Natural orbital functional for spin-polarized periodic systems

Abstract

Natural orbital functional theory is considered for systems with one or more unpaired electrons. An extension of the Piris natural orbital functional (PNOF) based on electron pairing approach is presented, specifically, we extend the independent pair model, PNOF5, and the interactive pair model PNOF7 to describe spin-uncompensated systems. An explicit form for the two-electron cumulant of high-spin cases is only taken into account, so that singly occupied orbitals with the same spin are solely considered. The rest of electron pairs with opposite spins remain paired. The reconstructed two-particle reduced density matrix fulfills certain N-representability necessary conditions, as well as guarantees the conservation of the total spin. The theory is applied to model systems with strong non-dynamic (static) electron correlation, namely, the one-dimensional Hubbard model with periodic boundary conditions and hydrogen rings. For the latter, PNOF7 compares well with exact diagonalization results so the model presented here is able to provide a correct description of the strong-correlation effects.

Electron Correlation in the Iron(II) Porphyrin by Natural Orbital Functional Approximations

“…The reformulation 61 of NOF-MP2 based on the static part of PNOF7 (PNOF7s) and the orbital-invariant MP2 allowed us to prevent reference ONs and NOs from being spuriously influenced by nondynamic correlation in dynamic correlation domains and extend the NOF-MP2 method to any type of orbitals, including localized ones, respectively. NOF-MP2 has been shown to provide quantitative agreement for dissociation energies, with performance comparable to that of the accurate complete active space second-order perturbation theory in hydrogen abstraction reactions, 19 and is highly reliable for accurate chemical reaction mechanistic studies in elementary reactions of transition metal compounds. 31 A canonicalization procedure applied to the NOs gave us the possibility to combine any many-body perturbation method, 62 like random-phase approximation or coupled-cluster singles and doubles, with a NOF.…”

“…Recent developments − show that NOF theory has become an active field of research. Nowadays, an open-source implementation of NOF-based methods is available (github.com/DoNOF) to the scientific community.…”

Natural orbital functional for multiplets

“…Within NOF approximations, spin-dependent formalisms have been also proposed [9,10], which do not conserve spin. NOFs that correctly reproduce the expectation values of spin operators have been reported [11][12][13][14], however, only for the high-spin component of the multiplet.…”

Symmetry-adapted formulation of the hybrid treatment resulting from the G-particle-hole Hypervirial equation and equations of motion methods: a procedure for modeling solids

“…In section four we analyze the results obtained for a set of small-to-mediumsized cyclic one-dimensional hydrogen chains showing the performance and efficiency of this new formulation. This kind of systems has been widely used as prototype model to describe solids in quantum chemistry, condensed matter, and solid state physics [23][24][25][26][27]; they present some interesting features that are essential for testing the suitability of theoretical methods to describe real systems, as the presence of strong correlation of diverse nature depending on the H-H distance. Finally, in the last section, we report the conclusions of this work.…”