Accuracy of ab initio electron correlation and electron densities in vanadium dioxide

Diffusion quantum Monte Carlo results are used as a reference to analyze properties related to phase stability and magnetism in vanadium dioxide computed with various formulations of density functional theory. We introduce metrics related to energetics, electron densities and spin densities that give us insight on both local and global variations in the antiferromagnetic M1 and R phases. Importantly, these metrics can address contributions arising from the challenging description of the 3d orbital physics in this material. We observe that the best description of energetics between the structural phases does not correspond to the best accuracy in the charge density, which is consistent with observations made recently by Medvedev et al. [Science 355, 371 (2017)] in the context of isolated atoms. However, we do find evidence that an accurate spin density connects to correct energetic ordering of different magnetic states in VO2, although local, semilocal, and meta-GGA functionals tend to erroneously favor demagnetization of the vanadium sites. The recently developed SCAN functional stands out as remaining nearly balanced in terms of magnetization across the M1-R transition and correctly predicting the ground state crystal structure. In addition to ranking current density functionals, our reference energies and densities serve as important benchmarks for future functional development. With our reference data, the accuracy of both the energy and the electron density can be monitored simultaneously, which is useful for functional development. So far, this kind of detailed high accuracy reference data for correlated materials has been absent from the literature.