Temperature-dependent behavior of confined many-electron systems in the Hartree-Fock approximation

Abstract

Many-electron systems confined at substantial finite temperatures and densities present a major challenge to density functional theory. In particular, there is comparatively little systematic knowledge about the behavior of free-energy density functionals for temperatures and pressures of interest, for example, in the study of warm dense matter. As with ground-state functionals, development of approximate free-energy functionals is faced with significant needs for reliable assessment and calibration data. Here we address, in part, this need for detailed results on well-characterized systems. We present results on a comparatively simple, well-defined, computationally feasible but previously unexplored model, the thermal Hartree-Fock approximation. We discuss the main technical tasks (defining a suitable basis and evaluation of the required matrix elements) and give an illustrative initial application which probes both the content of the model and the solution techniques: a system of eight one-electron atoms with nuclei at fixed, arbitrary positions in a hard-walled box. Even this simple system produces physical behavior different from that produced by simple ground state density functionals used at finite temperature (a common approximation in the study of WDM).

Role of exact exchange in thermally-assisted-occupation density functional theory: A proposal of new hybrid schemes

“…In particular, the FermiDirac distribution, which appears in finite-temperature DFT [49] and finite-temperature HF schemes [72,[76][77][78][79][80][81][82][83], has been a popular distribution function for the FON-related schemes.…”

“…(7)) can be achieved with the finite-temperature exact-exchange and related schemes [88], the resulting scheme can be computationally demanding. To reduce the computational complexity, in this work, the electronic energy for a global hybrid functional in TAO-DFT is minimized with respect to the 1-RDM γ TAO σ (as is usual in the finitetemperature HF (FT-HF) and related schemes [72,[76][77][78][79][80][81][82][83]). The resulting self-consistent equations for the σ-spin electrons can be expressed as…”

Accurate Homogeneous Electron Gas Exchange-Correlation Free Energy for Local Spin-Density Calculations

“…This gives only the implicit T -dependence provided by n(r, T ). However, there is substantial evidence from both finite-T Hartree-Fock [12,15] and finite-T exact exchange calculations [16,17] of non-negligible T -dependence in exchange itself.Addressing that T -dependence until now has been hampered by lack of an accurate, simulation-based LDA for F xc . …”

Comprehensive Study on Piezo-Phototronic Effect: Way Forward for Ferrite Based Solar Cells

“…To understand the basic physics of any phenomenon, it is essential to understand its temperature dependence [120][121][122][123]. Various devices were investigated, and it was observed that with the decrease in temperature from room temperature to low temperature, the width of the depletion region increases [124][125][126].…”

“…Under compressive strain with UV illumination, shown in (c2), the increase and decrease of photocurrent simultaneously take place [127]. The decrease in free mobile charges with the decrease in temperature gives the freeze out effect [123,128] and due to this, the free electrons get trapped in the narrow impurity centres which can be easily activated by the incident UV photon [129,130]. Now for thermally activated transport, the conductivity can be expressed as [52], 0 ( ) exp…”