Shear viscosity of liquid Sb and Bi from pseudopotential theory: the temperature-insensitive soft-tail component

Liquid Sb and Bi are two pnictogens whose structure factors show the Friedel shoulder characteristic of nonsimple liquid metals. We compute their shear viscosity with a static, pairwise pipeline, a Bretonnet–Silbert (BS) pseudopotential with Rice–Allnatt transport theory. The main result is component resolved: the soft-tail contribution accounts for 54–59% of the viscosity yet supplies little of its measured temperature dependence. The calculation runs from each melting point to at least 500 K above it, uses five local-field corrections and the Zahid parameters, and resolves the temperature gradient |dη/dT| into kinetic, hard-core, and soft-tail components. The calculated gradient is systematically too weak: η is underestimated at the melting point (−16% for Sb, −32% for Bi) and overestimated at high temperature. Because η_s is an integral over g(r), replacing the hard-sphere form g^HS(r) with a modified hypernetted-chain (MHNC) one changes η_s by −2 to +21%, but does not recover the gradient; nor does varying the pseudopotential parameters across the BS physical window, so no single tested ingredient accounts for it. The local-field correction changes η by only 3–4%, an order of magnitude less than the spread from the non-unique BS parameters; the ab initio molecular-dynamics data are too sparse to test the gradient. These results delimit the static, pairwise framework for Sb and Bi and identify the component that such dynamic, many-body, or screening extensions need to address.