Generalization of Bleaney's Theory

We generalize and unify Bleaney’s theory and related inverse-temperature expansions of magnetic properties of paramagnetic species. Our approach is valid for different properties, including NMR chemical shifts beyond the point-dipole approximation, and for both transition-metal and lanthanide complexes. We derive an analytical equation for the 1/T³ term. Furthermore, we implement higher-order terms numerically to investigate the convergence behavior of 1/T expansions. For transition-metal complexes, the second-order and third-order expansions provide quantitatively accurate results for most commonly encountered zero-field splittings. For an isostructural series of lanthanide complexes, the newly derived third-order term substantially improves the accuracy of calculated susceptibility anisotropies compared with Bleaney’s second-order theory.