DFT: A Theory Full of Holes?
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A rough, quirky overview of both the history and present state of the art of density functional theory can be found in this article, where the authors focus on the underlying exact theory, the origin of approximations, and the tension between empirical and non-empirical approaches.Abstract:
This article is a rough, quirky overview of both the history and present state of the art of density functional theory. The field is so huge that no attempt to be comprehensive is made. We focus on the underlying exact theory, the origin of approximations, and the tension between empirical and nonempirical approaches. Many ideas are illustrated on the exchange energy and hole. Features unique to this article include how approximations can be systematically derived in a nonempirical fashion and a survey of warm dense matter.read more
Citations
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Bypassing the Kohn-Sham equations with machine learning
Felix Brockherde,Felix Brockherde,Leslie Vogt,Li Li,Mark E. Tuckerman,Mark E. Tuckerman,Kieron Burke,Klaus-Robert Müller,Klaus-Robert Müller,Klaus-Robert Müller +9 more
TL;DR: The first molecular dynamics simulation with a machine-learned density functional on malonaldehyde is performed and the authors are able to capture the intramolecular proton transfer process.
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By-passing the Kohn-Sham equations with machine learning
TL;DR: In this paper, the density potential and energy density maps for test systems and various molecules are learned via examples, bypassing the need to solve the Kohn-Sham equations.
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The uniform electron gas at warm dense matter conditions
TL;DR: For the first time, thorough benchmarks of important approximation schemes regarding various quantities such as different energies, in particular the exchange-correlation free energy, and the static structure factor are possible.
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Quantum chemical accuracy from density functional approximations via machine learning.
Mihail Bogojeski,Leslie Vogt-Maranto,Mark E. Tuckerman,Mark E. Tuckerman,Klaus-Robert Müller,Klaus-Robert Müller,Klaus-Robert Müller,Kieron Burke +7 more
TL;DR: In this paper, the authors leverage machine learning to calculate coupled-cluster energies from DFT densities, reaching quantum chemical accuracy (errors below 1 kcal/mol-1) on test data.
References
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Generalized Gradient Approximation Made Simple
TL;DR: A simple derivation of a simple GGA is presented, in which all parameters (other than those in LSD) are fundamental constants, and only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked.
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Density‐functional thermochemistry. III. The role of exact exchange
TL;DR: In this article, a semi-empirical exchange correlation functional with local spin density, gradient, and exact exchange terms was proposed. But this functional performed significantly better than previous functionals with gradient corrections only, and fits experimental atomization energies with an impressively small average absolute deviation of 2.4 kcal/mol.
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Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density
TL;DR: Numerical calculations on a number of atoms, positive ions, and molecules, of both open- and closed-shell type, show that density-functional formulas for the correlation energy and correlation potential give correlation energies within a few percent.
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Self-Consistent Equations Including Exchange and Correlation Effects
Walter Kohn,L. J. Sham +1 more
TL;DR: In this paper, the Hartree and Hartree-Fock equations are applied to a uniform electron gas, where the exchange and correlation portions of the chemical potential of the gas are used as additional effective potentials.
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Density-functional exchange-energy approximation with correct asymptotic behavior.
TL;DR: This work reports a gradient-corrected exchange-energy functional, containing only one parameter, that fits the exact Hartree-Fock exchange energies of a wide variety of atomic systems with remarkable accuracy, surpassing the performance of previous functionals containing two parameters or more.