Origin of Antiferromagnetism in Molecular and Periodic Systems in the Original Kohn–Sham Local Density Approximation

Abstract

This study presents a solution to an issue which became prominent due to the discovery of copper (Cu) oxides in 1986, namely, whether LDA (local density approximation) can describe antiferromagnetism. From an early stage, many LDA band structure calculations failed to reproduce the insulating antiferromagnetic state. The Hubbard model predicts antiferromagnetism in a system under appropriate conditions. The author’s LDA calculations were performed for elongated hydrogen molecules comprising multiple atoms using the discrete variational (DV) molecular orbital method. The LDA employed is the original Kohn–Sham formalism, since the magnetic properties by GGA (generalized gradient approximation) are closer to the original Kohn–Sham results than those obtained by VWN (Vosko–Wilk–Nusair) approximation. The DV method, with a basis set of numerically calculated atomic orbitals, derived the antiferromagnetic state for hydrogen molecules at long interatomic separations but, when used for Cu oxide molecules, was seemingly unable to describe antiferromagnetism, where a well potential with a usual depth of about −1 Eh within an ionic radius was added solely to the potential for generating basis atomic orbitals of O²⁻. However, the author finally achieved the antiferromagnetism description via a reduced well potential depth following long parameter surveys. The calculation was generalized to a periodic system CaCuO₂ using a method employing Bloch-type linear combinations of atomic orbitals with all electrons. Furthermore, we determined a spherically averaged well potential depth having originated from the Coulomb potential by the nucleus and electron clouds around O²⁻ in a solid. The system revealed antiferromagnetic ordering due to a shallow well depth, and since the well for the anionic basis set is induced by the Coulomb potential in general, this method is applied to molecular orbital calculations.