Compositional phase stability of correlated electron materials within <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>DFT</mml:mi><mml:mtext>+</mml:mtext><mml:mi>DMFT</mml:mi></mml:math>

Abstract

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 ($\mathrm{DFT}\text{+}\mathrm{DMFT}$) formalism to address local correlations due to transition metal $d$ electrons on compositional phase stability in the prototype rechargeable battery cathode material ${\mathrm{Li}}_{x}{\mathrm{CoO}}_{2}$, and detailed comparisons are made with the simpler $\mathrm{DFT}\text{+}U$ 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 ${\mathrm{LiCoO}}_{2}$, most significantly via the ${E}_{g}$ orbitals, which are partially occupied via hybridization with O $p$ states. We find ${\mathrm{CoO}}_{2}$ and ${\mathrm{Li}}_{1/2}{\mathrm{CoO}}_{2}$ 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 $\mathrm{DFT}\text{+}U, \mathrm{DFT}\text{+}\mathrm{DMFT}$ 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 $\mathrm{DFT}\text{+}U$, which can incorrectly drive ${\mathrm{Li}}_{x}{\mathrm{CoO}}_{2}$ toward spurious phase separating or charge-ordered states, $\mathrm{DFT}\text{+}\mathrm{DMFT}$ correctly captures the system's phase stability and does not exhibit a strong charge-ordering tendency. Most importantly, the error within $\mathrm{DFT}\text{+}U$ varies strongly as the composition changes, challenging the common practice of artificially tuning $U$ within $\mathrm{DFT}\text{+}U$ to compensate the errors of Hartree-Fock. $\mathrm{DFT}\text{+}\mathrm{DMFT}$ predicts the average intercalation voltage decreases relative to DFT, opposite to the result of $\mathrm{DFT}\text{+}U$, which would yield favorable agreement with experiment in conjunction with the overprediction of the voltage by the strongly constrained and appropriately normed DFT functional.

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