Methods for Computing Accurate Atomic Spin Moments for Collinear and Noncollinear Magnetism in Periodic and Nonperiodic Materials

The partitioning of electron spin density among atoms in a material gives atomic spin moments (ASMs), which are important for understanding magnetic properties. We compare ASMs computed using different population analysis methods and introduce a method for computing density derived electrostatic and chemical (DDEC) ASMs. Bader and DDEC ASMs can be computed for periodic and nonperiodic materials with either collinear or noncollinear magnetism, while natural population analysis (NPA) ASMs can be computed for nonperiodic materials with collinear magnetism. Our results show Bader, DDEC, and (where applicable) NPA methods give similar ASMs, but different net atomic charges. Because they are optimized to reproduce both the magnetic field and the chemical states of atoms in a material, DDEC ASMs are especially suitable for constructing interaction potentials for atomistic simulations. We describe the computation of accurate ASMs for (a) a variety of systems using collinear and noncollinear spin DFT, (b) highly correlated materials (e.g., magnetite) using DFT+U, and (c) various spin states of ozone using coupled cluster expansions. The computed ASMs are in good agreement with available experimental results for a variety of periodic and nonperiodic materials. Examples considered include the antiferromagnetic metal organic framework Cu-3(BTC)(2), several ozone spin states, mono- and binuclear transition metal complexes, ferri- and ferro-magnetic solids (e.g., Fe3O4, Fe3Si), and simple molecular systems. We briefly discuss the theory of exchange-correlation functionals for studying noncollinear magnetism. A method for finding the ground state of systems with highly noncollinear magnetism is introduced. We use these methods to study the spin-orbit coupling potential energy surface of the single molecule magnet Fe4C40H52N4O12, which has highly noncollinear magnetism, and find that it contains unusual features that give a new interpretation to experimental data.