Analysis of Finite-Temperature Thomas-Fermi Theory in One Dimension

In recent decades, finite-temperature Density Functional Theory has proven very useful in its direct application to warm dense matter simulations. These Kohn-Sham calculations typically make use of a standard Generalized Gradient Approximation, ignoring any temperature-dependent exchange-correlation corrections. Much is still unknown about the temperature-dependence of local and semilocal approximations in DFT. Thomas-Fermi (TF) theory applied to Kohn-Sham electrons offers a natural starting point for analysis, yielding a first look at the temperature-dependent errors. We utilize model systems both to analyze and discuss the performance of finite-temperature TF theory, giving insight into the temperature-dependence of its various errors. A simple correction to the finite-temperature TF energy is proposed, using simple one-dimensional systems as illustrative examples.