Compositional phase stability of correlated electron materials within DFT+DMFT

Predicting the compositional phase stability of strongly correlated electron materials is an outstanding challenge in condensed matter physics, requiring precise computations of total energies. In this work, we employ the density functional theory plus dynamical mean-field theory (DFT+DMFT) formalism to address local correlations due to transition metal $d$ electrons on compositional phase stability in the prototype rechargeable battery cathode material Li$_x$CoO$_2$, and detailed comparisons are made with the simpler DFT+$U$ approach (i.e., the Hartree-Fock solution of the DMFT impurity problem). Local interactions are found to strongly impact the energetics of the band insulator LiCoO$_2$, most significantly via the $E_g$ orbitals, which are partially occupied via hybridization with O $p$ states. We find CoO$_2$ and Li$_{1/2}$CoO$_2$ to be moderately correlated Fermi liquids with quasiparticle weights of 0.6--0.8 for the $T_{2g}$ states, which are most impacted by the interactions. As compared to DFT+$U$, DFT+DMFT considerably dampens the increase in total energy as $U$ is increased, which indicates that dynamical correlations are important to describe this class of materials despite the relatively modest quasiparticle weights. Unlike DFT+$U$, which can incorrectly drive Li$_x$CoO$_2$ towards spurious phase separating or charge ordered states, DFT+DMFT correctly captures the system's simultaneous phase stability and lack of charge ordering. Most importantly, the error within DFT+$U$ varies strongly as the composition changes, challenging the common practice of artificially tuning $U$ within DFT+$U$ to compensate the errors of Hartree-Fock. DFT+DMFT predicts the average intercalation voltage decreases relative to DFT, opposite to the result of DFT+$U$, which would yield favorable agreement with experiment in conjunction with the overprediction of the voltage by the SCAN DFT functional.