Slow long-range decay of bound Hartree-Fock orbitals and enhancement of the exchange interaction and tunneling

TL;DR

This paper investigates how exchange interactions alter the decay of localized electron orbitals, leading to slower, power-law decay instead of exponential, which enhances exchange effects and tunneling in various systems.

Contribution

It reveals the long-range power-law decay of Hartree-Fock orbitals and its impact on exchange interactions and tunneling phenomena in molecules and solids.

Findings

Inner orbital decay inside molecules is proportional to 1/r^2.

In macroscopic systems, decay follows cos(k_f r)/r^n with n=3, 3.5, 4 for 1D, 2D, 3D.

Slow decay enhances exchange interactions and makes tunneling coefficients temperature-dependent.

Abstract

Exchange interaction strongly influences the long-range behaviour of localised electron orbitals. It violates the oscillation theorem (creates extra nodes) and produces a power-law decay instead of the usual exponential decrease at large distances. For inner orbitals inside molecules decay is 1/r^2, for macroscopic systems cos(k_f r)/r^n, where k_f is the Fermi momentum and n=3 for 1D, n=3.5 for 2D and n=4 for 3D crystal. Slow decay increases the exchange interaction between localised spins and the under-barrier tunneling amplitude.The under-barrier transmission coefficients in solids (e.g. for point contacts) become temperature-dependent.