Analysis of atomic Pauli potentials and their large-Z limit

Redd, Jeremy; Cancio, Antonio C.

doi:10.1063/5.0059283

Cited by 3 publications

(2 citation statements)

References 79 publications

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“…44 Thus, DC-DFT allows one to balance improvements in the approximate potential (and therefore the density) relative to those of the KS kinetic energy functional itself, such as whether exact conditions on the potential are relevant to the energies. 116 This is an area with great potential applications. In the light of DC-DFT, another way to view the genius of KS is that it (usually) reduces density-driven errors to negligible amounts.…”

Section: ■ Challengesmentioning

confidence: 99%

“…When the KS kinetic energy is approximated, even if very accurately, even small imperfections in the derivative will yield large errors in the density . Thus, DC-DFT allows one to balance improvements in the approximate potential (and therefore the density) relative to those of the KS kinetic energy functional itself, such as whether exact conditions on the potential are relevant to the energies . This is an area with great potential applications.…”

Section: Challengesmentioning

confidence: 99%

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Improving Results by Improving Densities: Density-Corrected Density Functional Theory

et al. 2022

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Density functional theory (DFT) calculations have become widespread in both chemistry and materials, because they usually provide useful accuracy at much lower computational cost than wavefunction-based methods. All practical DFT calculations require an approximation to the unknown exchange-correlation energy, which is then used self-consistently in the Kohn−Sham scheme to produce an approximate energy from an approximate density. Density-corrected DFT is simply the study of the relative contributions to the total energy error. In the vast majority of DFT calculations, the error due to the approximate density is negligible. But with certain classes of functionals applied to certain classes of problems, the density error is sufficiently large as to contribute to the energy noticeably, and its removal leads to much better results. These problems include reaction barriers, torsional barriers involving π-conjugation, halogen bonds, radicals and anions, most stretched bonds, etc. In all such cases, use of a more accurate density significantly improves performance, and often the simple expedient of using the Hartree−Fock density is enough. This Perspective explains what DC-DFT is, where it is likely to improve results, and how DC-DFT can produce more accurate functionals. We also outline challenges and prospects for the field.

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Section: ■ Challengesmentioning

confidence: 99%

Section: Challengesmentioning

confidence: 99%

Improving Results by Improving Densities: Density-Corrected Density Functional Theory

et al. 2022

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Neural network learned Pauli potential for the advancement of orbital-free density functional theory

Gangwar,

Bulusu,

Banerjee

2023

The Journal of Chemical Physics

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The Pauli kinetic energy functional and its functional derivative, termed Pauli potential, play a crucial role in the successful implementation of orbital-free density functional theory for electronic structure calculations. However, the exact forms of these two quantities are not known. Therefore, perforce, one employs the approximate forms for the Pauli functional or Pauli potential for performing orbital-free density functional calculations. In the present study, we developed a feed-forward neural network-based representation for the Pauli potential using a 1-dimensional (1-D) model system. We expanded density in terms of basis functions, and the coefficients of the expansion were used as input to a feed-forward neural network. Using the neural network-based representation of the Pauli potential, we calculated the ground-state densities of the 1-D model system by solving the Euler equation. We calculated the Pauli kinetic energy using the neural network-based Pauli potential employing the exact relation between the Pauli kinetic energy functional and the potential. The sum of the neural network-based Pauli kinetic energy and the von Weizsäcker kinetic energy resulted in an accurate estimation of the total kinetic energy. The approach presented in this paper can be employed for the calculation of Pauli potential and Pauli kinetic energy, obviating the need for a functional derivative. The present study is an important step in the advancement of application of machine learning-based techniques toward the orbital-free density functional theory-based methods.

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Investigations of the exchange energy of neutral atoms in the large-Z limit

Redd,

Cancio,

Argaman

et al. 2024

The Journal of Chemical Physics

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The non-relativistic large-Z expansion of the exchange energy of neutral atoms provides an important input to modern non-empirical density functional approximations. Recent works report results of fitting the terms beyond the dominant term, given by the local density approximation (LDA), leading to an anomalous Z ln Z term that cannot be predicted from naïve scaling arguments. Here, we provide much more detailed data analysis of the mostly smooth asymptotic trend describing the difference between exact and LDA exchange energy, the nature of oscillations across rows of the Periodic Table, and the behavior of the LDA contribution itself. Special emphasis is given to the successes and difficulties in reproducing the exchange energy and its asymptotics with existing density functional approximations.

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Analysis of atomic Pauli potentials and their large-Z limit

Cited by 3 publications

References 79 publications

Improving Results by Improving Densities: Density-Corrected Density Functional Theory

Improving Results by Improving Densities: Density-Corrected Density Functional Theory

Neural network learned Pauli potential for the advancement of orbital-free density functional theory

Investigations of the exchange energy of neutral atoms in the large-Z limit

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