Localizing electron density errors in density functional theory

Laplaza, Rubén; Polo, Víctor; Contreras‐García, Julia

doi:10.1039/c9cp02806d

Cited by 12 publications

(11 citation statements)

References 41 publications

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“…However, some caution is needed when looking at these plots. It has been observed 27 that the density error is localized differently for different density functional approximations. Hence, our observation is valid at least for B3LYP but perhaps not for other functionals.…”

Section: Resultsmentioning

confidence: 99%

“…It has been already pointed out that many possible error measures can be devised since the density is a function. 23 Furthermore, some authors, while studying the realspace localization of the density errors, have advised against the use of global descriptors, 27 which tend to show a bias toward core electrons.…”

Section: Introductionmentioning

confidence: 99%

“…33,41,42 Another key aspect concerning the study of density errors is the selection of the benchmark or reference systems. Often, the studied systems are atoms or small molecules where the DFT computations can be directly compared to high-quality ab initio ones or even a direct comparison with the exact densities, such as CC 12,13,16,18,27 or even full-CI 43 ones. Such a comparison limits the choice of reference systems to the ones that can be accurately calculated by these methods.…”

Section: Introductionmentioning

confidence: 99%

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On the Use of Normalized Metrics for Density Sensitivity Analysis in DFT

Martín-Fernández

Harvey

2021

J. Phys. Chem. A

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In the past years there has been a discussion about how the errors in Density Functional Theory might be related to errors in the self-consistent densities obtained from different density functional approximations. This, in turn, brings up the discussion about the different ways in which we can measure such errors and develop metrics that assess the sensitivity of calculated energies to changes in the density. It is important to realize that there cannot be a unique metric in order to look at this density sensitivity, simultaneously needing size-extensive and size-intensive metrics.In this study we report two metrics that are widely applicable to any density functional approximation. We also show how they can be used to classify different chemical systems of interest with respect to their sensitivity to small variations in the density.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the Use of Normalized Metrics for Density Sensitivity Analysis in DFT

Martín-Fernández

Harvey

2021

J. Phys. Chem. A

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“…The use of machine learning techniques is also a strongly raising field, not only in terms of new functionals forms but also for the accurate prediction of chemical properties [53]. Moreover, it has been also shown how localizing electronic density errors in real-space can contribute to further chemical insights [54].…”

Section: Summary Of Some Emerging Dft Methodsmentioning

confidence: 99%

Emerging DFT Methods and Their Importance for Challenging Molecular Systems with Orbital Degeneracy

Maroto

Sancho‐García

2019

Computation

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We briefly present some of the most modern and outstanding non-conventional density-functional theory (DFT) methods, which have largely broadened the field of applications with respect to more traditional calculations. The results of these ongoing efforts reveal that a DFT-inspired solution always exists even for pathological cases. Among the set of emerging methods, we specifically mention FT-DFT, OO-DFT, RSX-DFT, MC-PDFT, and FLOSIC-DFT, complementing the last generation of existing density functionals, such as local hybrid and double-hybrid expressions.

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“…DFT's popularity stems from the accuracy and computational efficiency of commonly used approximations to the exchange-correlation (xc) energy, such as the local density [1] and the generalized gradient [6] approximation. However, these popular approximations are unreliable for molecules with strong electron localization [7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Exact expressions for the height of the interatomic step in the exchange-correlation potential from the derivative discontinuity of the energy

Hodgson

2021

Preprint

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Popular approximations to the exchange-correlation (xc) energy of density functional theory do not yield the spatial 'step' structures in the exact xc potential which are necessary to describe dissociation and electron excitation with the Kohn-Sham (KS) system. Via the discontinuity in the derivative of the xc energy as a function of electron number I derive exact analytic expressions in terms of the KS single-particle energies for the height of the step in the xc potential between a variety of open-and closed-shell atoms within stretched molecules.

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Localizing electron density errors in density functional theory

Abstract: The accuracy of different density functional approximations is assessed through the use of quantum chemical topology on molecular electron densities.

Cited by 12 publications

References 41 publications

On the Use of Normalized Metrics for Density Sensitivity Analysis in DFT

On the Use of Normalized Metrics for Density Sensitivity Analysis in DFT

Emerging DFT Methods and Their Importance for Challenging Molecular Systems with Orbital Degeneracy

Exact expressions for the height of the interatomic step in the exchange-correlation potential from the derivative discontinuity of the energy

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