Classical turning surfaces in solids: When do they occur, and what do they mean?

TL;DR

This paper investigates the occurrence and significance of classical turning surfaces in solids, revealing their dependence on material type and structural changes, and confirming classical conduction models through computational analysis.

Contribution

It provides the first systematic calculation of classical turning surfaces in various solids, linking their presence to material properties and structural modifications.

Findings

CFRs are absent in metals but common in ionic and molecular crystals.

CFRs appear or grow with uniform expansion of internuclear distances.

All materials become metallic without CFRs under extreme compression.

Abstract

Classical turning surfaces of Kohn-Sham potentials, separating classically-allowed regions (CARs) from classically-forbidden regions (CFRs), provide a useful and rigorous approach to understanding many chemical properties of molecules. Here we calculate such surfaces for several paradigmatic solids. Our study of perfect crystals at equilibrium geometries suggests that CFRs are absent in metals, rare in covalent semiconductors, but common in ionic and molecular crystals. A CFR can appear at a monovacancy in a metal. In all materials, CFRs appear or grow as the internuclear distances are uniformly expanded. Calculations with several approximate density functionals and codes confirm these behaviors. A classical picture of conduction suggests that CARs should be connected in metals, and disconnected in wide-gap insulators. This classical picture is confirmed in the limits of extreme uniform compression of the internuclear distances, where all materials become metals without CFRs, and extreme expansion, where all materials become insulators with disconnected and widely-separated CARs around the atoms.