Water molecule by the self-consistent atomic deformation method

Ossowski, M.; Boyer, L. L.; Mehl, Michael J.; Pederson, Mark R.

doi:10.1103/physrevb.68.245107

Cited by 16 publications

(18 citation statements)

References 31 publications

(19 reference statements)

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“…[51]. The LiF molecular potential energy curve provides a good example of this problem [51][52][53]. In this case, LSDA total energies as functions of charge on the separated systems predict that the ground state of a separate Li and separated F has approximately 2.3 units of charge on the Li and 9.7 units of charge on the F (this result depends slightly on choice of functional).…”

Section: Resultsmentioning

confidence: 99%

“…However, in many cases, systems composed of two fragments are found to be electronically unstable for either two neutral separated fragments or two oppositely charged cation/anion fragment pairs [45][46][47][48][49][50], and rare cases where this is not a qualitative problem have been demonstrated in Ref. [51]. The LiF molecular potential energy curve provides a good example of this problem [51][52][53].…”

Section: Resultsmentioning

confidence: 99%

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Full self-consistency in the Fermi-orbital self-interaction correction

2017

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The Perdew-Zunger self-interaction correction cures many common problems associated with semilocal density functionals, but suffers from a size-extensivity problem when Kohn-Sham orbitals are used in the correction. Fermi-Löwdin-orbital self-interaction correction (FLOSIC) solves the size-extensivity problem, allowing its use in periodic systems and resulting in better accuracy in finite systems. Although the previously published FLOSIC algorithm [J. Chem. Phys. 140, 121103 (2014)] appears to work well in many cases, it is not fully self-consistent. This would be particularly problematic for systems where the occupied manifold is strongly changed by the correction. In this paper we demonstrate a new algorithm for FLOSIC to achieve full self-consistency with only marginal increase of computational cost. The resulting total energies are found to be lower than previously reported non-self-consistent results.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Full self-consistency in the Fermi-orbital self-interaction correction

2017

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“…1 below). This failure has been discovered as early as 1982 by Perdew et al [17], for an infinitely stretched LiH molecule treated within the local density approximation, and has since been found in various molecules with different DFAs [16,[18][19][20][21][22][23][24][25]46]. Perdew et al [17] have shown that this would not have happened had the atomic energy curves, and as a result the molecular energy curve, been exactly piecewise linear.…”

Section: Introductionmentioning

confidence: 99%

“…This fundamental principle is not reproduced by many DFAs. Instead, one finds that a system of two well-separated atoms often reaches its energy minimum when the number of electrons on each of the atoms is fractional: N 0 A + q electrons on atom A and N 0 B − q electrons on atom B, with q ∈ (−1, 1) [16][17][18][19][20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Elimination of the asymptotic fractional dissociation problem in Kohn-Sham density-functional theory using the ensemble-generalization approach

Kraisler

Kronik

2015

Phys. Rev. A

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Many approximations within density-functional theory spuriously predict that a many-electron system can dissociate into fractionally charged fragments. Here, we revisit the case of dissociated diatomic molecules, known to exhibit this problem when studied within standard approaches, including the local spin-density approximation (LSDA). By employing our recently proposed [E. Kraisler and L. Kronik, Phys. Rev. Lett. 110, 126403 (2013)] ensemble-generalization we find that asymptotic fractional dissociation is eliminated in all systems examined, even if the underlying exchangecorrelation (xc) is still the LSDA. Furthermore, as a result of the ensemble generalization procedure, the Kohn-Sham potential develops a spatial step between the dissociated atoms, reflecting the emergence of the derivative discontinuity in the xc energy functional. This step, predicted in the past for the exact Kohn-Sham potential and observed in some of its more advanced approximate forms, is a desired feature that prevents any fractional charge transfer between the system's fragments. It is usually believed that simple xc approximations such as the LSDA cannot develop this step. Our findings show, however, that ensemble generalization to fractional electron densities automatically introduces the desired step even to the most simple approximate xc functionals and correctly predicts asymptotic integer dissociation.

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“…For example, this is not possible in general without the ensemble definition of Eq. (8), which produces the correct self-consistent occupations (unlike, e.g., the self-consistent atomic deformation method [20,21], where this choice leads to a basis set dependence [22]) . We also never freeze the total density [23,24,25], but only ever consider it as a sum of fragment densities.…”

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confidence: 99%

Partition density-functional theory

et al. 2010

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Partition density functional theory is a formally exact procedure for calculating molecular properties from Kohn-Sham calculations on isolated fragments, interacting via a global partition potential that is a functional of the fragment densities. An example is given and consequences discussed. PACS numbers:Kohn-Sham density functional theory (KS-DFT) [1,2] is an efficient and usefully accurate electronic structure method, because it replaces the interacting Schrödinger equation with a set of single-particle orbital equations. Calculations with several hundred atoms are now routine, but there is always interest in much larger systems. Many such systems are treated by a lower-level method, such as molecular mechanics, but a fragment in which a chemical reaction occurs must still be treated quantum mechanically. A plethora of such QM/MM approaches have been tried and tested, with varying degrees of success [3]. These are often combined with attempts at orbital-free DFT, which avoids the KS equations, but at the cost of higher error and unreliability.On the other hand, partition theory (PT) [4,5] combines the simplicity of functional minimization with a density optimization to define fragments (such as atoms) within molecules, overcoming limitations of earlier approaches to reactivity theory [6,7]. While there are now many definitions of, e.g., charges on atoms, none have the generality of PT and the associated promise of unifying disparate chemical concepts. However, previous work on PT has been either formal [4,5] or for two atom systems [8,9].In this paper, we unite KS-DFT with PT to produce an algorithm that allows a KS calculation for a molecule to be performed via a self-consistent loop over isolated fragments. Such a fragment calculation exactly reproduces the result of a standard KS calculation of the entire molecule. We demonstrate its convergence on a 12-atom example. This also shows that fragments can be calculated 'on the fly', as part of solving any KS molecular problem.Thus we present a formally exact framework within which existing practical approximations can be analyzed and, for smaller systems, compared with exact quantities. In practical terms, our method suggests new approximations that can, by construction, scale linearly[10] with the number of fragments (so-called O(N )), and allow embedding of KS calculations within cruder force-field calculations (QM/MM). It also suggests ways to improve XC approximations so as to produce correct dissociation of molecules [11].To understand the relation between DFT and PT, recall that the Hohenberg-Kohn theorem proves that for a given electron-electron interaction and statistics, the external (one-body) potential v(r) is a unique functional of the density n(r). The total energy can be written as:where F [n] is a universal functional, defined by the LevyLieb constrained search [12] over all antisymmetric wavefunctions Ψ yielding density n(r):whereT andV ee are the kinetic energy and Coulomb repulsion operators respectively. The KS equations are single-particle...

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Water molecule by the self-consistent atomic deformation method

Cited by 16 publications

References 31 publications

Full self-consistency in the Fermi-orbital self-interaction correction

Full self-consistency in the Fermi-orbital self-interaction correction

Elimination of the asymptotic fractional dissociation problem in Kohn-Sham density-functional theory using the ensemble-generalization approach

Partition density-functional theory

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