Short-range exchange-correlation energy of a uniform electron gas with modified electron-electron interaction

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.

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

10.26434/chemrxiv-2021-j8030 ◽

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.

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Simple model of the static exchange-correlation kernel of a uniform electron gas with long-range electron-electron interaction

Physical Review B ◽

10.1103/physrevb.72.035117 ◽

2005 ◽

Vol 72 (3) ◽

Cited By ~ 15

Author(s):

Julien Toulouse

Keyword(s):

Simple Model ◽

Long Range ◽

Electron Gas ◽

Electron Interaction ◽

Correlation Kernel ◽

Exchange Correlation ◽

Uniform Electron Gas

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Spin-resolved second-order correlation energy of the two-dimensional uniform electron gas

Physical Review B ◽

10.1103/physrevb.70.073101 ◽

2004 ◽

Vol 70 (7) ◽

Cited By ~ 11

Author(s):

Michael Seidl

Keyword(s):

Correlation Energy ◽

Electron Gas ◽

Second Order ◽

Two Dimensional ◽

Uniform Electron Gas

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Relativistic AB Initio calculations of the properties of ionic solids

Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences ◽

10.1098/rsta.1986.0106 ◽

1986 ◽

Vol 320 (1553) ◽

pp. 107-158 ◽

Cited By ~ 63

Keyword(s):

Ab Initio ◽

Short Range ◽

Correlation Energy ◽

Electron Gas ◽

Empirical Method ◽

Coulombic Interactions ◽

Ionic Solids ◽

Electron Correlation Energy ◽

Crystal Properties ◽

Semi Empirical

Relativistic ab initio calculations of inter-ionic potential energies are used to develop a reliable non-empirical method for predicting the properties of ionic solids containing the heaviest ions. A physically realistic method for describing the non-negligible differences between free and in-crystal ion wavefunctions is described. Functions are presented for describing the partial quenching, arising from ion wavefunction overlap, of the standard long-range form of the inter-ionic dispersive attractions. These attractions are shown to be distinct from the contributions to the inter-ionic potentials that arise from that portion of the electron correlation energy which is nonzero solely because of overlap of the ion wavefunctions. The results presented for NaCl, MgO and the fluorides of Li, Na, Ag and Pb show that these modifications overcome the deficiencies of previous calculations. Ab initio predictions of the closest cation-cation and anion-anion short-range interactions, which are not available from semi-empirical fits to experimental data, are presented. The non-point coulombic interactions between pairs of anions, derived by adding the dispersive attractions to the short-range interactions, are compared with previous semi-empirical and approximate ab initio results. The uncorrelated short-range inter-ionic potentials computed exactly are compared with those predicted from electron-gas theory. The use of the electron-gas approximation to describe any of these potentials degrades the quality of the predicted crystal properties.

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