scholarly journals Weight dependence of local exchange–correlation functionals in ensemble density-functional theory: double excitations in two-electron systems

2020 ◽  
Vol 224 ◽  
pp. 402-423 ◽  
Author(s):  
Clotilde Marut ◽  
Bruno Senjean ◽  
Emmanuel Fromager ◽  
Pierre-François Loos
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Electron Systems ◽  
Local Exchange ◽  
Functional Theory ◽  
Exchange Correlation

We discuss the construction of first-rung weight-dependent exchange–correlation density-functional approximations for He and H2 specifically designed for the computation of double excitations within Gross–Oliveira–Kohn-DFT.

scholarly journals Asymptotic Behavior of the Exchange-Correlation Energy Density and the Kohn-Sham Potential in Density Functional Theory: Exact Results and Strategy for Approximations

2019 ◽  
Author(s):  
Eli Kraisler
Keyword(s):  
Density Functional Theory ◽  
Asymptotic Behavior ◽  
Energy Density ◽  
Density Functional ◽  
Correlation Energy ◽  
Electron Systems ◽  
Functional Theory ◽  
Exchange Correlation ◽  
Exact Exchange ◽  
Exact Factorization

The present work is a review of two analytical properties of the exact exchange-correlation (xc) functional in density-functional theory. These properties are the asymptotic behavior of the xc energy density per particle and the asymptotic behavior of the Kohn-Sham potential, in finite many-electron systems. The derivation of the asymptotic forms for both quantities is reviewed, employing the concepts of the adiabatic connection and of the xc hole with relation to the first quantity and the electron exact factorization approach for the second one. Furthermore, it is shown that the correct asymptotic behavior of one of the aforementioned quantities does not guarantee a correct behavior of the other. In this process, a new quantity, the xc hole response function, is defined and its exact exchange part is analytically derived. The extent to which existing xc approximations satisfy the named exact properties is reviewed and the relationship between correct asymptotics and freedom from one-electron self-interaction in DFT is discussed. Finally, a strategy for development of advanced approximations for exchange and correlation with a correct asymptotic behavior is suggested.<br>

scholarly journals Machine learning the derivative discontinuity of density-functional theory

2021 ◽  
Author(s):  
Johannes Gedeon ◽  
Jonathan Schmidt ◽  
Matthew Hodgson ◽  
Jack Wetherel ◽  
Carlos Benavides-Riveros ◽  
...  
Keyword(s):  
Machine Learning ◽  
Density Functional Theory ◽  
Density Functional ◽  
Correlation Energy ◽  
Integer Number ◽  
Local Exchange ◽  
Functional Theory ◽  
Exchange Correlation ◽  
Derivative Discontinuity ◽  
Number Of Particles

Abstract Machine learning is a powerful tool to design accurate, highly non-local, exchange-correlation functionals for density functional theory. So far, most of those machine learned functionals are trained for systems with an integer number of particles. As such, they are unable to reproduce some crucial and fundamental aspects, such as the explicit dependency of the functionals on the particle number or the infamous derivative discontinuity at integer particle numbers. Here we propose a solution to these problems by training a neural network as the universal functional of density-functional theory that (i) depends explicitly on the number of particles with a piece-wise linearity between the integer numbers and (ii) reproduces the derivative discontinuity of the exchange-correlation energy. This is achieved by using an ensemble formalism, a training set containing fractional densities, and an explicitly discontinuous formulation.

scholarly journals Asymptotic Behavior of the Exchange-Correlation Energy Density and the Kohn-Sham Potential in Density Functional Theory: Exact Results and Strategy for Approximations

2019 ◽  
Author(s):  
Eli Kraisler
Keyword(s):  
Density Functional Theory ◽  
Asymptotic Behavior ◽  
Energy Density ◽  
Density Functional ◽  
Correlation Energy ◽  
Electron Systems ◽  
Functional Theory ◽  
Exchange Correlation ◽  
Exact Exchange ◽  
Exact Factorization

The present work is a review of two analytical properties of the exact exchange-correlation (xc) functional in density-functional theory. These properties are the asymptotic behavior of the xc energy density per particle and the asymptotic behavior of the Kohn-Sham potential, in finite many-electron systems. The derivation of the asymptotic forms for both quantities is reviewed, employing the concepts of the adiabatic connection and of the xc hole with relation to the first quantity and the electron exact factorization approach for the second one. Furthermore, it is shown that the correct asymptotic behavior of one of the aforementioned quantities does not guarantee a correct behavior of the other. In this process, a new quantity, the xc hole response function, is defined and its exact exchange part is analytically derived. The extent to which existing xc approximations satisfy the named exact properties is reviewed and the relationship between correct asymptotics and freedom from one-electron self-interaction in DFT is discussed. Finally, a strategy for development of advanced approximations for exchange and correlation with a correct asymptotic behavior is suggested.<br>

Exchange-Correlation Energy Densities and Response Potentials: Connection Between Two Definitions and Analytical Model for the Strong-Coupling Limit of a Stretched Bond

2019 ◽  
Author(s):  
S. Giarrusso ◽  
Paola Gori-Giorgi
Keyword(s):  
Density Functional Theory ◽  
Strong Coupling ◽  
Density Functional ◽  
Correlation Energy ◽  
Order Term ◽  
Strong Coupling Limit ◽  
Local Form ◽  
Coupling Constant ◽  
Functional Theory ◽  
Exchange Correlation

We analyze in depth two widely used definitions (from the theory of conditional probablity amplitudes and from the adiabatic connection formalism) of the exchange-correlation energy density and of the response potential of Kohn-Sham density functional theory. We introduce a local form of the coupling-constant-dependent Hohenberg-Kohn functional, showing that the difference between the two definitions is due to a corresponding local first-order term in the coupling constant, which disappears globally (when integrated over all space), but not locally. We also design an analytic representation for the response potential in the strong-coupling limit of density functional theory for a model single stretched bond.<br>

scholarly journals Application of time-dependent current-density-functional theory to nonlocal exchange-correlation effects in polymers

2003 ◽  
Vol 118 (3) ◽  
pp. 1044-1053 ◽  
Author(s):  
M. van Faassen ◽  
P. L. de Boeij ◽  
R. van Leeuwen ◽  
J. A. Berger ◽  
J. G. Snijders
Keyword(s):  
Density Functional Theory ◽  
Current Density ◽  
Density Functional ◽  
Time Dependent ◽  
Correlation Effects ◽  
Functional Theory ◽  
Exchange Correlation

EXCHANGE–CORRELATION KERNEL IN TIME-DEPENDENT DENSITY FUNCTIONAL THEORY DERIVED FROM MANY-BODY THEORY

2004 ◽  
Vol 18 (07) ◽  
pp. 1055-1067 ◽  
Author(s):  
K. KARLSSON ◽  
F. ARYASETIAWAN
Keyword(s):  
Density Functional Theory ◽  
Optical Absorption ◽  
Density Functional ◽  
Time Dependent ◽  
Many Body ◽  
Functional Theory ◽  
Correlation Kernel ◽  
Exchange Correlation ◽  
Many Body Theory ◽  
Dependent Density

We derive a simplified Bethe–Salpeter equation for calculating optical absorption based on the assumption of a local electron–hole interaction. The original four-point equation for the kernel is reduced to a two-point one. A connection to the exchange–correlation kernel in time-dependent density functional theory can be established. The resulting fxc is found to be -W/2 where W contains only the short-range (local) part of the Coulomb screened interaction. This simple approximation was successfully applied to optical absorption spectra of some excitonic crystals, reproducing not only the continuum excitons but also the bound ones.

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