**The Superconducting Transition Temperatures of C-S-H Based on Inter-Sublattice S–H _{4}-Tetrahedron Electronic Interactions**, D. R. Harshman and A. T. Fiory [arXiv_v1]

Significant characteristics of the superconducting transitions reported for carbonaceous sulfur hydride [Snider et al., Nature **585**, 373 (2020)] are the exceptionally abrupt onset temperatures and their marked increase toward room temperature at high pressure. Theoretical and experimental studies addressing the superconducting composition and structure have thus far returned mixed results. One possibility, consistent with the experimentally suggested stoichiometry of CSH_{x}, is the theoretically-discovered compressed *I*43*m* CSH_{7} structure [Sun et al., Phys. Rev. B **101**, 174102 (2020)], which comprises a sublattice similar to *Im*3*m* H_{3}S with CH_{4} intercalates. Positing an electronic genesis of the superconductivity, a model is presented in analogy with earlier work on superconductivity in *Im*3*m* H_{3}S, in which pairing is induced via purely electronic Coulomb interactions across the mean distance ζ between the S and H_{4} tetrahedra enclosing C. Theoretical superconducting transition temperatures for *I*43*m* CSH_{7} are derived as *T*_{C0} = (2/3)^{1/2}σ^{1/2}β/*a*ζ, where β = 1247.4 Å^{2}K is a universal constant, σ is the participating charge fraction, and *a* is the lattice parameter. Analysis suggests persistent bulk superconductivity with a pressure-dependent σ, increasing from σ = 3.5, determined previously for *Im*3*m* H_{3}S, to σ = 7.5 at high pressure owing to additionally participating C-H bond electrons. With a and ζ determined by theoretical structure, *T*_{C0} = 283.6 ± 3.5 K is predicted at 267 ± 10 GPa, in excellent agreement (within uncertainty) with the corresponding experimental *T*_{C} = 287.7 ± 1.2 K. Pressure-induced variations in σ combined with experimental uncertainties in pressure yield overall average (*T*_{C} − *T*_{C0}) = (−0.8 ± 3.5).

Dale R. Harshman and Anthony T. Fiory, Journal of Applied Physics **131**, 015105 (2022).