Capturing Thermal Effects Beyond the Zero‐Temperature Approximation Using the Uniform Electron Gas

Density functional theory at finite temperatures often relies on the zero‐temperature approximation, which uses a ground‐state exchange‐correlation functional with thermalized densities. This approach, however, neglects the explicit temperature dependence of the exchange‐correlation free energy—a key factor in regimes such as warm dense matter, where both electronic and thermal effects are significant. In this work, we introduce the entropy‐corrected zero‐temperature approach, in which the exchange‐correlation entropy is extracted using the generalized thermal adiabatic connection formula to construct a thermal correction to the standard zero‐temperature approximation. Using a uniform electron gas parametrization, we compare this approach to the finite‐temperature adiabatic connection and demonstrate that it performs best at lower densities. This provides a useful complement to zero‐temperature density functional approximations, which generally perform better at moderate‐to‐large densities. We further identify a density‐dependent intersection between the adiabatic connection curves, revealing a dependence on the ground‐state correlation energy and correlation potential. Additionally, the extension of the entropy‐corrected approach applied as a local density approximation–like temperature correction to the zero‐temperature approximation is discussed.