Bypassing the Energy Functional in Density Functional Theory: Direct Calculation of Electronic Energies from Conditional Probability Densities

McCarty, Ryan J.; Perchak, Dennis; Pederson, Ryan; Evans, Robert; Qiu, Yiheng; White, Steven R.; Burke, Kieron

doi:10.1103/physrevlett.125.266401

Cited by 13 publications

(15 citation statements)

References 50 publications

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“…We next show how this difficulty was overcome in Ref [11]. First, the pure blue electron approximation was shown to violate the electron-electron cusp condition by a factor of 2.…”

Section: Introductionmentioning

confidence: 95%

“…A simple LDA to this potential yields surprisingly accurate results for systems as disparate as the binding energy curve of H 2 and the uniform gas. This approximation automatically has no self-interaction error for one-electron systems [6], correctly dissociates the H 2 singlet into two separate H atoms [12], and its accuracy does not deteriorate as the temperature is raised in a uniform gas [11].…”

Section: Introductionmentioning

confidence: 99%

“…Recently, it was pointed out that, for any electronic system, one could extract the unknown XC energy by a sequence of Kohn-Sham DFT (KS-DFT) calculations (one for each point on a grid in the system) if a well-defined but unknown potential, the conditional probability potential, were known [11]. A simple LDA to this potential yields surprisingly accurate results for systems as disparate as the binding energy curve of H 2 and the uniform gas.…”

Section: Introductionmentioning

confidence: 99%

“…As this does not require any manybody calculation, this is deemed acceptable. But it was also necessary to smoothly turn this Gaussian off as a function of increasing r s , a somewhat empirical procedure, but one which yields the high accuracy presented in Ref [11].…”

Section: Introductionmentioning

confidence: 99%

“…Recently, CP-DFT, an alternative approach to electronic structure calculation, was suggested [11]. This takes advantage of the well-known expression for the XC energy in terms of the (coupling-constant averaged) XC hole, which in turn is simply related to the conditional probability density for finding an electron at r , given an electron at r. Knowledge of this function (or in fact just some particular integrals over it) determines E XC exactly.…”

Section: Introductionmentioning

confidence: 99%

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Correlation energy of the uniform gas determined by ground state conditional probability density functional theory

Perchak,

McCarty,

Burke

2022

Preprint

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Conditional-probability density functional theory (CP-DFT) is a formally exact method for finding correlation energies from Kohn-Sham DFT without evaluating an explicit energy functional. We present details on how to generate accurate exchange-correlation energies for the ground-state uniform gas. We also use the exchange hole in a CP antiparallel spin calculation to extract the high-density limit. We give a highly accurate analytic solution to the Thomas-Fermi model for this problem, showing its performance relative to Kohn-Sham and may be useful at high temperatures. We explore several approximations to the CP potential. Results are compared to accurate parameterizations for both exchange-correlation energies and holes.

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“…We next show how this difficulty was overcome in Ref [11]. First, the pure blue electron approximation was shown to violate the electron-electron cusp condition by a factor of 2.…”

Section: Introductionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Correlation energy of the uniform gas determined by ground state conditional probability density functional theory

Perchak,

McCarty,

Burke

2022

Preprint

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Orbital-Free Density Functional Theory: An Attractive Electronic Structure Method for Large-Scale First-Principles Simulations

Mi,

Luo,

Trickey

et al. 2023

Chem. Rev.

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Kohn−Sham Density Functional Theory (KSDFT) is the most widely used electronic structure method in chemistry, physics, and materials science, with thousands of calculations cited annually. This ubiquity is rooted in the favorable accuracy vs cost balance of KSDFT. Nonetheless, the ambitions and expectations of researchers for use of KSDFT in predictive simulations of large, complicated molecular systems are confronted with an intrinsic computational cost-scaling challenge. Particularly evident in the context of firstprinciples molecular dynamics, the challenge is the high cost-scaling associated with the computation of the Kohn−Sham orbitals. Orbital-free DFT (OFDFT), as the name suggests, circumvents entirely the explicit use of those orbitals. Without them, the structural and algorithmic complexity of KSDFT simplifies dramatically and near-linear scaling with system size irrespective of system state is achievable. Thus, much larger system sizes and longer simulation time scales (compared to conventional KSDFT) become accessible; hence, new chemical phenomena and new materials can be explored. In this review, we introduce the historical contexts of OFDFT, its theoretical basis, and the challenge of realizing its promise via approximate kinetic energy density functionals (KEDFs). We review recent progress on that challenge for an array of KEDFs, such as one-point, twopoint, and machine-learnt, as well as some less explored forms. We emphasize use of exact constraints and the inevitability of design choices. Then, we survey the associated numerical techniques and implemented algorithms specific to OFDFT. We conclude with an illustrative sample of applications to showcase the power of OFDFT in materials science, chemistry, and physics.

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Ab Initio Calculation of Coupling-Constant Averaged Exchange–Correlation Holes for Spherically Symmetric Atoms

Hou,

Irons,

Wang

et al. 2024

J. Phys. Chem. A

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Accurate approximation of the exchange−correlation (XC) energy in density functional theory (DFT) calculations is essential for reliably modeling electronic systems. Many such approximations are developed from models of the XC hole; accurate reference XC holes for real electronic systems are crucial for evaluating the accuracy of these models however the availability of reliable reference data is limited to a few systems. In this study, we employ the Lieb optimization with a coupled cluster singles and doubles (CCSD) reference to construct accurate coupling-constant averaged XC holes, resolved into individual exchange and correlation components, for five spherically symmetric atoms: He, Li, Be, N, and Ne. Alongside providing a new set of reference data for the construction and evaluation of model XC holes, we compare our data against the exchange and correlation hole models of the established local density approximation (LDA) and Perdew−Burke−Ernzerhof (PBE) density functional approximations. Our analysis confirms the established rationalization for the limitations of LDA and the improvement observed with PBE in terms of the hole depth and its long-range decay, which is demonstrated in real-space for this series of spherically symmetric atoms.

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Bypassing the Energy Functional in Density Functional Theory: Direct Calculation of Electronic Energies from Conditional Probability Densities

Cited by 13 publications

References 50 publications

Correlation energy of the uniform gas determined by ground state conditional probability density functional theory

Correlation energy of the uniform gas determined by ground state conditional probability density functional theory

Orbital-Free Density Functional Theory: An Attractive Electronic Structure Method for Large-Scale First-Principles Simulations

Ab Initio Calculation of Coupling-Constant Averaged Exchange–Correlation Holes for Spherically Symmetric Atoms

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