Approximate bounds and temperature dependence of adiabatic connection integrands for the 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. Methods that account for temperature dependence, such as Mermin-Kohn-Sham finite-temperature density functional theory and free energy density functional theory, are now employed with more regularity and available in many standard code packages. However, approximations from zero-temperature density functional theory are still often used in temperature-dependent simulations using thermally weighted electronic densities as an input to exchange-correlation functional approximations, a practice known to miss temperature-dependent effects in the exchange-correlation free energy 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.& nbsp;Published under an exclusive license by AIP Publishing.

Automated summary

Thermal density functional theory is commonly used to simulate warm dense matter, taking into account temperature-dependent effects. However, current methods often approximate temperature-dependent simulations using zero-temperature density functional theory, missing out on the temperature-dependent effects in the exchange-correlation free energy. This study demonstrates and analyzes the temperature-dependent adiabatic connection, leveraging tools based on the approximation of exchange-correlation at zero temperature for finite-temperature cases.