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Abstract By summarizing the constraint-based development of orbital-free free-energy density functional approximations, we provide a perspective on progress over the last 15 years, the limitations of existing functionals, and the challenges awaiting resolution. We outline the chronology of the development of non-interacting and exchange-correlation free-energy orbital-free functionals and summarize the theoretical basis of existing local density approximation (LDA), second-order approximation, generalized gradient approximation (GGA), and meta-GGAs. We discuss limitations and challenges such as problems with thermodynamic derivatives, free-energy nonadditivity and the closely related issue of all-electron versus valence-only local pseudo-potential performance. 

Abstract Recently, room temperature superconductivity was measured in a carbonaceous sulfur hydride material whose identity remains unknown. Herein, first-principles calculations are performed to provide a chemical basis for structural candidates derived by doping H₃S with low levels of carbon. Pressure stabilizes unusual bonding configurations about the carbon atoms, which can be six-fold coordinated as CH₆entities within the cubic H₃S framework, or four-fold coordinated as methane intercalated into the H-S lattice, with or without an additional hydrogen in the framework. The doping breaks degenerate bands, lowering the density of states at the Fermi level (N_F), and localizing electrons in C-H bonds. Low levels of CH₄doping do not increaseN_Fto values as high as those calculated for$$Im\bar{3}m$$ $Im\overline{3}m$-H₃S, but they can yield a larger logarithmic average phonon frequency, and an electron–phonon coupling parameter comparable to that ofR3m-H₃S. The implications of carbon doping on the superconducting properties are discussed.