Chemical verification of variational second-order density matrix based potential energy surfaces for the N2 isoelectronic series

Aggelen, Helen van; Verstichel, Brecht; Bultinck, Patrick; Neck, Dimitri Van; Ayers, Paul W.; Cooper, David L.

doi:10.1063/1.3354910

Cited by 36 publications

(35 citation statements)

References 31 publications

(34 reference statements)

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“…The decrease in energy upon dissociation is so strong that the optimal F − 3 geometry is only a local minimum in the DM2 potential energy surface. The cause of this problem is clear from previous work on diatomic molecules [9]: the dependence of the DM2(PQG) energy on the number of electrons is strictly convex in most atoms, so the dissociating system may reach a lower energy by allowing a fractional number of electrons on both atoms. Unless the decrease in energy caused by allowing a fractional charge on one atom is countered by a bigger increase in energy for the corresponding fractional charge on the other atom, the molecule will incorrectly dissociate into fractionally charged atoms.…”

Section: Resultsmentioning

confidence: 95%

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Variational second order density matrix study of $\mathrm{F_3^-}$F3−: Importance of subspace constraints for size-consistency

Aggelen

Verstichel²,

Bultinck³

et al. 2011

The Journal of Chemical Physics

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Variational second order density matrix theory under '2-positivity' tends to dissociate molecules into unphysical fractionally charged products with too low energies. We aim to construct a qualitatively correct potential energy surface for F − 3 by applying subspace energy constraints on mono-and diatomic subspaces of the molecular basis space. Mono-atomic subspace constraints do not guarantee correct dissociation: the constraints are thus geometry dependent. Furthermore, the number of subspace constraints needed for correct dissociation does not grow linearly with the number of atoms. The subspace constraints do impose correct chemical properties in the dissociation limit and size-consistency, but the structure of the resulting DM2 does not exactly correspond to a system of non-interacting units.

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Section: Resultsmentioning

confidence: 95%

“…The objective will therefore be to minimize the molecular energy subject to (3)- (9). Obviously, generally holding constraints must be based on the lowest energy ensemble of states with weights x i that corresponds to a total number of electrons N A .…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Variational second order density matrix study of $\mathrm{F_3^-}$F3−: Importance of subspace constraints for size-consistency

Aggelen

Verstichel²,

Bultinck³

et al. 2011

The Journal of Chemical Physics

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“…36 Note that, as already mentioned, a variational method using the 2-RDM while applying only the P, Q and G conditions as N-representability conditions is not size-consistent. [21][22][23][24] First, let us consider the subsystems: 1-and 2-RDM of subsystems A (γ A , A ) and B (γ B and B ) are defined using a set of one-particle basis allocated in each subsystem A or B from the whole system as follows: where i 1 , i 2 , j 1 , j 2 correspond to the one-particle basis of B.…”

Section: A the Definition Of Size-consistency For The Rdm Methods Andmentioning

confidence: 99%

“…22 This treatment requires applying (a subset of) the fractional N-representability conditions to the subsystems. 23,24 This is only a sufficient condition in this very specific case, and we discuss a sufficient condition for size-consistency in general.…”

Section: Introductionmentioning

confidence: 99%

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On the size-consistency of the reduced-density-matrix method and the unitary invariant diagonal N-representability conditions

Nakata¹,

Anderson²

2012

AIP Advances

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Variational calculation of the ground state energy and its properties using the second-order reduced density matrix (2-RDM) is a promising approach for quantum chemistry. A major obstacle with this approach is that the N -representability conditions are too difficult in general. Therefore, we usually employ some approximations such as the P , Q, G, T 1 and T 2 ′ conditions, for realistic calculations. The results of using these approximations and conditions in 2-RDM are comparable to those of CCSD(T). However, these conditions do not incorporate an important property; sizeconsistency. Size-consistency requires that energies E(A), E(B) and E(A • • • B) for two infinitely separated systems A, B, and their respective combined systemIn this study, we show that the size-consistency can be satisfied if 2-RDM satisfies the following conditions: (i) 2-RDM is unitary invariant diagonal N -representable; (ii) 2-RDM corresponding to each subsystem is the eigenstate of the number of corresponding electrons; and (iii) 2-RDM satisfies at least one of the P , Q, G, T 1 and T 2 ′ conditions.

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Twenty‐four‐month postradiation prostate biopsies are strongly predictive of 7‐year disease‐free survival

Crook

Malone

Perry

et al. 2009

Cancer

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The cumulant expansion gives rise to an useful decomposition of the two‐matrix in which the pair correlated matrix (cumulant) is disconnected from the antisymmetric product of the one‐matrices. The cumulant can be approximated in terms of two matrices, Δ and Π, which are explicit functions of the occupation numbers of the natural orbitals. It produces a natural orbital functional (NOF) that reduces to the exact expression for the total energy in two‐electron systems. The N‐representability positivity necessary conditions of the two‐matrix impose several bounds on the matrices Δ and Π. Appropriate forms of these matrices lead to different implementations of the NOF known in the literature as PNOFi (i = 1–5). The basic features of these functionals are reviewed here. The strengths and weaknesses of the different PNOFs are assessed. © 2012 Wiley Periodicals, Inc.

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Chemical verification of variational second-order density matrix based potential energy surfaces for the N2 isoelectronic series

Abstract: To refer to or to cite this work, please use the citation to the published version: Van

Cited by 36 publications

References 31 publications

Variational second order density matrix study of $\mathrm{F_3^-}$F3−: Importance of subspace constraints for size-consistency

Variational second order density matrix study of $\mathrm{F_3^-}$F3−: Importance of subspace constraints for size-consistency

On the size-consistency of the reduced-density-matrix method and the unitary invariant diagonal N-representability conditions

Twenty‐four‐month postradiation prostate biopsies are strongly predictive of 7‐year disease‐free survival

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