Towards a formal definition of static and dynamic electronic correlations

Abstract

Some of the most spectacular failures of density-functional and Hartree-Fock theories are related to an incorrect description of the so-called static electron correlation. Motivated by recent progress on the N-representability problem of the one-body density matrix for pure states, we propose a way to quantify the static contribution to the electronic correlation. By studying several molecular systems we show that our proposal correlates well with our intuition of static and dynamic electron correlation. Our results bring out the paramount importance of the occupancy of the highest occupied natural spin-orbital in such quantification.PACS numbers: 31.15. V-, 31.15.xr, 31.70.-f

Symmetry in Multiple Self-Consistent-Field Solutions of Transition-Metal Complexes

“…The purpose of this paper is therefore twofold: firstly, to demonstrate that symmetry-broken HF solutions are not unphysical and should not be discarded as they can be assigned definitively to actual electronic terms after their symmetry has been restored; and secondly, to show that NOCI using symmetrybroken HF solutions yields wavefunction descriptions of both ground and excited electronic states that recover a decent amount of static correlation missed out by HF single determinants. 31 We hope that the results presented here shed some light on the nature and properties of multiple SCF solutions in TM complexes and any other strongly correlated systems involving unpaired electrons, and that this understanding can better inform the choice of reference for excited-state calculations.…”

On the time evolution of fermionic occupation numbers

“…(6) by the corresponding particle number operators. The importance of this result lies on the fact that it provides an important selection rule for the Slater determinants that can appear in the configurationinteraction expansion of wave functions 38 . Indeed, a wave function whose spectrum is pinned to one of the polytope's facets P j = {n|D j (n) = 0} (see Fig.…”

“…1) can be written as a linear superposition of the Slater determinants which belong to the zero-eigenspace of the operatorD j . This selection rule can be used to systematically produce ansätzen for ground states in the form of sparse wave functions, which, instead of using the full Hilbert space, can be expanded in the basis of the natural orbitals (the eigenvalues of γ) with a few Slater determinants 38,39 . Apart from the simplification of the wave function, there is another advantage in using natural orbitals that is worth mentioning here: it is known that the basis of natural orbitals is typically quite good to convergence the full wave function.…”

“…Thus, ground states can be viewed as functionals of such reduced densities (say, Ψ gs [γ]) 6 . Since γ accounts for fractional natural occupation numbers (i.e., its eigenvalues), employing this matrix as the main object leads to a theory able to capture quite well strong (static) electron correlations [7][8][9][10] . For instance, unlike density functional theory, such a densitymatrix functional theory correctly predicts the insulating behavior of Mott-type insulators 11,12 .…”

Static correlated functionals for reduced density matrix functional theory

“…For pure quantum systems the occupation numbers meet also additional requirements with tremendous physical implications [4][5][6][7][8][9][10][11][12][13]. This so-called generalized Pauli exclusion principle provides a (large) set of constraints on the natural occupation numbers.…”