Single-point kinetic energy density functionals: A pointwise kinetic energy density analysis and numerical convergence investigation

Xia, Junchao; Carter, Emily A.

doi:10.1103/physrevb.91.045124

Cited by 54 publications

(87 citation statements)

References 83 publications

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“…On the other hand, the proposed procedure provides a method how to obtain fast and reliable convergence, a frequently encountered problem for this kind of differential equations. [4,34] Usually, the desired stability of the process is introduced by mixing the solutions of two consecutive steps. [39,40] This method will fail here, as iteratively solving…”

Section: Numerical Detailsmentioning

confidence: 99%

A simple approximation for the Pauli potential yielding self-consistent electron densities exhibiting proper atomic shell structure

Finzel

2015

Int. J. Quantum Chem.

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Section: Numerical Detailsmentioning

confidence: 99%

A simple approximation for the Pauli potential yielding self-consistent electron densities exhibiting proper atomic shell structure

Finzel

2015

Int. J. Quantum Chem.

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“…Furthermore almost all semilocal approximations fail to converge in self-consistent calculations. [XC15] The focus should be on improving the functional derivative rather than the energy itself, and the measure of improvement should be the reduction of the density-driven error.…”

Section: Pure Dftmentioning

confidence: 99%

The Importance of Being Inconsistent

Wasserman

Nafziger

Jiang

et al. 2017

Annu. Rev. Phys. Chem.

116

156

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We review the role of self-consistency in density functional theory. We apply a recent analysis to both Kohn-Sham and orbital-free DFT, as well as to Partition-DFT, which generalizes all aspects of standard DFT. In each case, the analysis distinguishes between errors in approximate functionals versus errors in the self-consistent density. This yields insights into the origins of many errors in DFT calculations, especially those often attributed to self-interaction or delocalization error. In many classes of problems, errors can be substantially reduced by using 'better' densities. We review the history of these approaches, many of their applications, and give simple pedagogical examples.

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“…6 in Ref. 2). It will be interesting to do a similar analysis in all-electron Kohn-Sham (KS) density functional theory (DFT), where we suspect the multi-valuedness also exists because any artifacts due to pseudopotentials will be confined to near-nucleus regions.…”

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confidence: 99%

“…In S. B. Trickey, V. V. Karasiev, and D. Chakraborty's interesting comment 1 on our previous paper, 2 two major issues are discussed: the multi-valuedness of the G factor versus the reduced gradient (s) 2 and the numerical stability of the VT84F 3 kinetic energy density functional (KEDF). On one hand, we still believe in the existence and significance of G-s multi-valuedness, despite possible pseudopotential artifacts and the global kinetic energy upper bound.…”

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Reply to “Comment on ‘Single-point kinetic energy density functionals: A pointwise kinetic energy density analysis and numerical convergence investigation’ ”

Xia

Carter

2015

Phys. Rev. B

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We find that the multi-valued character of the G factor as a function of the reduced gradient (s) still exists after accounting for pseudopotential artifacts and the kinetic energy global upper bound. We also find that the VT84F functional indeed exhibits stable convergence and more reasonable results for self-consistent bulk properties compared to other generalized gradient approximation (GGA) kinetic energy density functionals (KEDFs) that we tested earlier.However, VT84F generally yields overestimated equilibrium volumes, which may result from its inability (as with all GGAs) to reproduce the G-s multi-valued character. The analogous failure to predict the multi-valued character of G as a function of the reduced density (d) is also likely to be responsible for the inaccuracy of our vWGTF functionals reported earlier.Our multi-valuedness analysis therefore does not impugn any particular GGA KEDF. Instead, it merely confirms the importance of pointwise analysis for improving KEDFs, by emphasizing the need to resolve the multi-valuedness of G with respect to various density variables. 2In S. B. Trickey, V. V. Karasiev, and D. Chakraborty's interesting comment 1 on our previous paper, 2 two major issues are discussed: the multi-valuedness of the G factor versus the reduced gradient (s) 2 and the numerical stability of the VT84F 3 kinetic energy density functional (KEDF). On one hand, we still believe in the existence and significance of G-s multi-valuedness, despite possible pseudopotential artifacts and the global kinetic energy upper bound. 1 On the other hand, we are pleased to see the improved convergence of the VT84F KEDF and further perform a series of tests on it, as presented below.First, we agree that using pseudopotentials may introduce artifacts in the G distribution, especially around nuclei. The electron pseudodensities are generally very small around nuclei, which then lead to large G values (see analysis in all-electron Kohn-Sham (KS) density functional theory (DFT), where we suspect the multi-valuedness also exists because any artifacts due to pseudopotentials will be confined to near-nucleus regions. It is possible that in all-electron cases, the multi-valuedness of G versus s will be lessened but it awaits more studies and data to confirm.Second, we agree it is important to consider exact requirements when constructing KEDFs. However, we disagree that the data points with G>1 can be cut out or ignored due to the kinetic energy upper bound 4,5 of the Thomas-Fermi 6-8 plus von Weizsäcker KEDF. 9 As also mentioned in Ref. 1, the upper bound only applies to the total kinetic energy, while the corresponding pointwise upper bound for local kinetic energy density is only sufficient but 3 not necessary. In the Appendix, we provide a proof for the vWGTF1 KEDF proposed in our original paper, 2 which always satisfies the global upper bound but not the pointwise one, for any periodic or finite-volume system. The proof does not hold for isolated systems with infinite volumes where the average density...

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Single-point kinetic energy density functionals: A pointwise kinetic energy density analysis and numerical convergence investigation

Cited by 54 publications

References 83 publications

A simple approximation for the Pauli potential yielding self-consistent electron densities exhibiting proper atomic shell structure

A simple approximation for the Pauli potential yielding self-consistent electron densities exhibiting proper atomic shell structure

The Importance of Being Inconsistent

Reply to “Comment on ‘Single-point kinetic energy density functionals: A pointwise kinetic energy density analysis and numerical convergence investigation’ ”

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