Calculation of the Magnetostatic Energy in Spin Density Functional Theory

In density functional theory calculations of materials and molecules, it is conventional to neglect the relativistic magnetostatic contribution of unpaired electron spins to the total energy and potential. For small systems, the magnetostatic contribution to the total energy is negligible, yet it is not obvious that it remains negligible in extended systems with high spin magnetic moment. We make use of a mathematical shortcut, using a fictitious magnetic charge density, to calculate the magnetic field and to determine the degree to which this relativistic effect can be ignored in electronic structure calculations. Using this, we compare the strength of the magnetostatic energy to the electrostatic energy. This ratio is consistently on the order of 10⁻⁵, which is on the order of 1/c² in atomic units, as is expected from its formula.