  Quantitative predictions of the Li intercalation voltage and of the
electronic properties of rechargeable battery cathode materials are a
substantial challenge for first-principles theory due to the possibility of (1)
strong correlations associated with localized transition metal $d$ electrons
and (2) significant van der Waals (vdW) interactions in layered systems, both
of which are not accurately captured by standard approximations to density
functional theory (DFT). Here, we perform a systematic benchmark of electronic
structure methods based on the widely-used generalized gradient approximation
of Perdew, Burke, and Ernzerhof (PBE) and the new strongly constrained and
appropriately normed (SCAN) meta-generalized gradient approximation for battery
cathode materials. Studying layered Li$_x$TiS$_2$, Li$_x$NiO$_2$, and
Li$_x$CoO$_2$, olivine Li$_x$FePO$_4$, and spinel Li$_x$Mn$_2$O$_4$, we compute
the voltage, crystal structure, and electronic structure with and without
extensions to incorporate on-site Hubbard interactions and vdW interactions.
Within pure DFT (i.e., without corrections for on-site Hubbard interactions),
SCAN is a significant improvement over PBE for describing cathode materials,
decreasing the mean absolute voltage error by more than 50%. Although explicit
vdW interactions are not critical and in cases even detrimental when applied in
conjunction with SCAN, Hubbard $U$ corrections are still in general necessary
to achieve reasonable agreement with experiment. We show that no single method
considered here can accurately describe the voltage and overall structural,
electronic, and magnetic properties (i.e., errors no more than 5% for voltage,
volume, band gap, and magnetic moments) of battery cathode materials,
motivating a strong need for improved electronic structure approaches for such
systems.
