Incorrect diatomic dissociation in variational reduced density matrix theory arises from the flawed description of fractionally charged atoms

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

doi:10.1039/b907624g

Cited by 47 publications

(55 citation statements)

References 23 publications

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“…43 The analysis here will establish an interpretation for the LUMO, as rigorous as that of the HOMO. Our approach, based on the fractional charge and fractional spin perspectives 19,44,45 is general and applicable not only to DFT but also any method whose basic variable is not the wavefunction, such as reduced density matrix theory 46 or theories of the many-body Green function. 47 …”

Section: Introductionmentioning

confidence: 99%

Derivative discontinuity, bandgap and lowest unoccupied molecular orbital in density functional theory

Yang

Cohen

Mori‐Sánchez

2012

The Journal of Chemical Physics

172

178

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The conventional analysis of Perdew and Levy, and Sham and Schlüter shows that the functional derivative discontinuity of the exchange-correlation density functional plays a critical role in the correct prediction of bandgaps, or the chemical hardness. In a recent work by the present authors, explicit expressions for bandgap prediction with all common types of exchange-correlation functionals have been derived without invoking the concept of exchange-correlation energy functional derivative discontinuity at all. We here analyze the two approaches and establish their connection and difference. The present analysis further leads to several important results: (1) The lowest unoccupied molecular orbital (LUMO) in DFT has as much meaning in describing electron addition as the highest occupied molecular orbital (HOMO) in describing electron removal. (2) Every term in the total energy functional contributes to the energy gap because of the discontinuity of the derivative of the density (or density matrix) with respect to the number of electrons, ((∂ρ s (r , r))/∂N ) v s , at integers. (3) Consistent with the Perdew-Levy-Sham-Schlüter conclusion that the exact Kohn-Sham energy gap differs from the fundamental bandgap by a finite correction due to the functional derivative discontinuity of the exchange-correlation energy, we show that the exchange-correlation functional cannot be an explicit and differentiable functional of the electron density, either local or nonlocal. The last result is further strengthened when we consider Mott insulators. There, the exact exchange-correlation functional needs to have an explicitly discontinuous (nondifferentiable) dependence on the density or the density matrix. (4) We obtain exact conditions on the derivatives of total energy with respect to the spin-up and spin-down number of electrons.

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Section: Introductionmentioning

confidence: 99%

Derivative discontinuity, bandgap and lowest unoccupied molecular orbital in density functional theory

Yang

Cohen

Mori‐Sánchez

2012

The Journal of Chemical Physics

172

178

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“…These constraints were inspired by the observation of fractionally charged dissociation products in heteronuclear diatomics [8]. Their fractional charge almost coincided with the minimum of the the strictly convex relationship between the sum of the atomic energies and the charge on one of the atoms, for a fixed total number of electrons.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…The assumption of convexity of the set of energies is reasonable; we have never encountered a violation. Consequently, only two indices i=N and i=N+1 in equations (7)- (9) non-zero, expressions (8) and (9) are bounded. In summary, under the above assumptions, the constraint reduces to…”

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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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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“…However, in 2009, Van Aggelen et al reported a dramatic failure in the dissociation limits of some molecules. 21 They observed that with fractionally charged atoms that the P, Q and G conditions were insufficient to guarantee size-consistency. For example, at the dissociation limit of CN − , the Mulliken population of C and N − were 6.60 and 7.40, respectively.…”

Section: Introductionmentioning

confidence: 99%

“…Additionally, the assumption that each subsystem being an eigenstate of the number of electrons is not trivial as it is often violated in practice. 21 However, choice of subsystem is arbitrary and does not need to be known before hand like previous approache. 21 Despite these difficulties this sufficient condition can, in principal, be implemented into a semidefinite programming code (though it would be computationally demanding thus have limited utility).…”

Section: Introductionmentioning

confidence: 99%

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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Incorrect diatomic dissociation in variational reduced density matrix theory arises from the flawed description of fractionally charged atoms

Cited by 47 publications

References 23 publications

Derivative discontinuity, bandgap and lowest unoccupied molecular orbital in density functional theory

Derivative discontinuity, bandgap and lowest unoccupied molecular orbital in density functional theory

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

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