What Does Miedema's Boundary Electron Density Measure? Valence Electron Delocalization as the Physical Origin of nws

Surface tension of liquid metals varies by over an order of magnitude across the periodic table. Density functional theory (DFT) can compute these values numerically, and Miedema's semi-empirical model achieves +/-10-20% accuracy using the Wigner-Seitz boundary electron density nws, but neither provides an electronic-structure descriptor that explains why metals with similar bulk densities (e. g. , Al and Zn, Delta rₛ = 2. 4%, Delta gamma = 46%) have vastly different surface tensions. Here we propose that the inverse participation ratio (IPR) of Kohn-Sham orbitals -- an existing quantity widely used in Anderson localization analysis -- provides this missing link when reinterpreted as a unified descriptor for interfacial properties. DFT calculations on 15 metal dimers show that a valence-only IPR-based delocalization index correlates with interatomic midpoint electron density at r = 0. 89 (p Fe (d6: 0. 37) > Cu (d10: 0. 33) is consistent with Friedel's model of d-band narrowing with filling. Maximally localized Wannier function (MLWF) calculations independently confirm this hierarchy. These results establish that Miedema's nws is a proxy for valence electron delocalization, answering the question raised by Williams, Gelatt, and Moruzzi (PRL 44, 429, 1980) regarding the physical meaning of nws.