Decay Properties of Spatial Molecular Orbitals

TL;DR

This paper proves that certain molecular orbitals in Hartree-Fock theory decay to zero at infinity if they are integrable, using Fourier transform properties, which has implications for understanding orbital behavior.

Contribution

It establishes a rigorous, elementary proof that $L_1$ molecular orbitals in Hartree-Fock decay at infinity, linking integrability to decay properties.

Findings

Orbitals in $L_1$ decay to zero at infinity.

Positive eigenvalue occupied orbitals in $L_1$ also decay.

The proof is rigorous, elementary, and concise.

Abstract

Using properties of the Fourier transform we prove that if a Hartree-Fock molecular spatial orbital is in $L_1(\mathbb{R}^3)$, then it decays to zero as its argument diverges to infinity. The proof is rigorous, elementary, and short. Our result implies that occupied orbitals with positive eigenvalues will decay to zero provided they are in $L_1$.