A Statistical Mechanical Framework for Predicting Fermi Contact NMR Shifts

Solid-state nuclear magnetic resonance (NMR) spectroscopy is a powerful probe of local chemical environments in functional materials, many of which incorporate paramagnetic transition-metal or rare-earth ions. Unpaired electrons can induce strong electron-nuclear hyperfine interactions, giving rise to large paramagnetic shifts that encode detailed information about the local atomic and electronic structure. These same interactions, however, often produce severe line broadening, complicating spectral assignment─particularly in materials exhibiting mixed valence, magnetic and charge ordering, defects, or compositional disorder. Although first-principles calculations can aid in interpreting paramagnetic shifts, their computational cost becomes prohibitive for structurally and chemically complex systems. This limitation motivates the development of new approaches that retain first-principles accuracy while enabling tractable simulations across disordered, multicomponent materials. Here, we introduce an ab initio framework that combines cluster expansion techniques with Monte Carlo sampling to predict finite-temperature paramagnetic (Fermi contact) shifts. We demonstrate the approach for 7Li and 17O NMR shifts in the cathode material Li2MnO3. A magnetic cluster expansion reveals that nearest- and next-nearest-neighbor Mn-O-Li interactions dominate the 7Li Fermi contact shift. Extension to 17O further uncovers significant long-range contributions mediated by Mn-O-Mn-O pathways, identified here for the first time. This methodology enables first-principles-level predictions of paramagnetic NMR shifts in complex materials containing open-shell species, providing a route to interpreting spectra in real-world systems, including those relevant to energy storage, catalysis, and solid-state lighting.