Many-Body Benchmark of Electronic Charge and Spin Densities for Li_1-xNiO₂

Accurate benchmarks are particularly important for highly correlated oxides as mean-field approximations often fail to describe the subtle balance of charge transfer and magnetism in these materials with an accuracy comparable to experimental needs. Here we present accurate diffusion Monte Carlo (DMC) results of the electronic charge and spin densities for the tunable highly correlated oxide Li_1-xNiO₂ for x = 0, 1/2, and 1. To enable quantitative comparisons, we introduce a robust density-partitioning scheme, extending Voronoi analysis to assign atomic charges from spatially noisy DMC densities. We then benchmark common approximations used in density functional theory (DFT). Comparison against DMC shows that r²SCAN delivers the most balanced performance across charge, spin, and radial density descriptors, nearly reproducing DMC results for LiNiO₂ and apical Ni sites in Li_0.5NiO₂. Hybrid functionals (PBE0, SCAN0) perform unexpectedly poorly, and PBE + U + V yields inconsistent trends between charge and spin densities. Therefore, the r²SCAN functional minimizes errors relative to DMC while capturing the variable valence of the Ni ion and also retaining the computational efficiency of DFT for large-scale simulations of the tunable structural and electronic phases of Li_1-xNiO₂. Our study highlights the importance of accurate benchmarking of the fundamental quantities involved in DFT to select appropriate DFT approximations in order to advance the predictive modeling of charge-transfer-driven phenomena in correlated electron systems.