scholarly journals Exact thermal density functional theory for a model system: Correlation components and accuracy of the zero-temperature exchange-correlation approximation

2016 ◽  
Vol 93 (24) ◽  
Author(s):  
J. C. Smith ◽  
A. Pribram-Jones ◽  
K. Burke
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Model System ◽  
Zero Temperature ◽  
Functional Theory ◽  
Exchange Correlation ◽  
Temperature Exchange ◽  
Correlation Approximation

scholarly journals Approximate bounds and temperature dependence of adiabatic connection integrands for the uniform electron gas

2021 ◽  
Author(s):  
Brittany P. Harding ◽  
Zachary Mauri ◽  
Aurora Pribram-Jones
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Correlation Energy ◽  
Electron Gas ◽  
High Energy ◽  
Zero Temperature ◽  
Temperature Dependent ◽  
Functional Theory ◽  
Exchange Correlation ◽  
Uniform Electron Gas

Thermal density functional theory is commonly used in simulations of warm dense matter, a highly energetic phase characterized by substantial thermal effects and by correlated electrons demanding quantum mechanical treatment. The numerous approximations for the exchange-correlation energy component in zero-temperature density functional theory, though often used in these high-energy-density simulations with Fermi-weighted electronic densities, are known to miss temperature-dependent effects in the electronic structure of these systems. In this work, the temperature-dependent adiabatic connection is demonstrated and analyzed using a well-known parameterization of the uniform electron gas free energy. Useful tools based on this formalism for analyzing and constraining approximations of the exchange-correlation at zero temperature are leveraged for the finite-temperature case. Inspired by the Lieb-Oxford inequality, which provides a lower bound for the ground-state exchange-correlation energy, bounds for the exchange-correlation at finite-temperatures are approximated for various degrees of electronic correlation.

scholarly journals Approximate bounds and temperature dependence of adiabatic connection integrands for the uniform electron gas

2021 ◽  
Author(s):  
Brittany P. Harding ◽  
Zachary Mauri ◽  
Aurora Pribram-Jones
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Correlation Energy ◽  
Electron Gas ◽  
High Energy ◽  
Zero Temperature ◽  
Temperature Dependent ◽  
Functional Theory ◽  
Exchange Correlation ◽  
Uniform Electron Gas

Thermal density functional theory is commonly used in simulations of warm dense matter, a highly energetic phase characterized by substantial thermal effects and by correlated electrons demanding quantum mechanical treatment. The numerous approximations for the exchange-correlation energy component in zero-temperature density functional theory, though often used in these high-energy-density simulations with Fermi-weighted electronic densities, are known to miss temperature-dependent effects in the electronic structure of these systems. In this work, the temperature-dependent adiabatic connection is demonstrated and analyzed using a well-known parameterization of the uniform electron gas free energy. Useful tools based on this formalism for analyzing and constraining approximations of the exchange-correlation at zero temperature are leveraged for the finite-temperature case. Inspired by the Lieb-Oxford inequality, which provides a lower bound for the ground-state exchange-correlation energy, bounds for the exchange-correlation at finite temperatures are approximated for various degrees of electronic correlation.

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.

On the role of steric and exchange–correlation effects in halogenated complexes

2021 ◽  
Author(s):  
Mojtaba Alipour ◽  
Parisa Fallahzadeh
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Energy Partitioning ◽  
Correlation Effects ◽  
Functional Theory ◽  
Exchange Correlation

Density functional theory formalisms of energy partitioning schemes are utilized to find out what energetic components govern interactions in halogenated complexes.

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