Quantitative Impact of Occupation Smearing Methods on Conventional Superconductivity: from Electronic Structure through Lattice Dynamics to Electron-Phonon Coupling

Abstract

In first-principles calculations of metallic systems, the discrete electronic mesh in the Brillouin zone necessitates a smearing function and its width (e.g., the widely used 0.02 Ry Methfessel-Paxton scheme) to enforce continuity of energy and occupation at the Fermi surface. However, the quantitative impact of such empirical parameters on phonon-mediated superconductivity has long been overlooked, leading to their habitual selection by mere convention. Here, using hexahydride CsH6 as a benchmark, we systematically investigate the magnitude and propagation mechanism of smearing-induced errors against the parameter-free optimized tetrahedron method. Long-tailed smearing delocalizes the occupation window, causing substantial Fermi-level shifts, flattening of the density of states, and hardening phonon modes, thereby weakening electron-phonon coupling. Conversely, short-tailed smearing suffers from insufficient sampling, producing density-of-states oscillations and enhanced Fermi-surface nesting; via amplified electronic screening and Peierls instabilities, this softens acoustic modes and generates imaginary frequencies, causing CsH6 to be dynamically unstable and discarded. However, the optimized tetrahedron method reveals that CsH6 is dynamically stable under ambient pressure with a remarkable superconducting transition temperature of 121 K. To prevent subjective empirical parameters from obscuring theoretically promising high-temperature superconductors, we derive a simple scaling relation for the smearing width, applicable to different smearing functions, from the free-electron-gas model, offering an objective, precise, and efficient protocol for parameter selection in high-throughput screening.