Quantification of Coulomb interactions in layered lithium and sodium battery cathode materials

Despite the importance of the electron correlation in the first-principles description of the Li-ion cathode materials, the Coulomb interaction parameter $U$ is often treated as an ad hoc value. In practice, one usually relies on empirical ways of parametric treatment of $U$ to optimally match the experimentally observed physical properties such as band gap or reaction energy. Here, using the constrained random phase approximation (cRPA) method, we self-consistently evaluate the Coulomb $U$ and Hund $J$ values for representative layered cathode materials including not only Li compounds but also Na compounds $\mathrm{Li}\mathrm{Co}{\mathrm{O}}_2, \mathrm{Li}\mathrm{Ni}{\mathrm{O}}_2, \mathrm{Li}\mathrm{Mn}{\mathrm{O}}_2, \mathrm{Na}\mathrm{Co}{\mathrm{O}}_2, \mathrm{Na}\mathrm{Ni}{\mathrm{O}}_2$, and $\mathrm{NaMn}{\mathrm{O}}_2$. We found that the Coulomb interaction parameters for Li and Na compounds and their polymorphs with different layer stacking types do not deviate much, which shows the dominant role of the local environment rather than of global structural features. We have analyzed the origin of variable Coulomb parameters, which is mainly due to the competition between the localization and screening. We provided cRPA Coulomb parameters for battery cathode materials and validate the values by observing systematic improvement in describing the experimentally observed average intercalation voltage and lattice parameters. These results can be applied for the first-principles calculations as well as model-based simulations for the theoretical investigation of cathode systems.

Figure 1

Structures of (a) $A\mathrm{Co}{\mathrm{O}}_2$ ($A=\mathrm{Li}$, Na) in the $R\overline{3}m$ space group (O3 structure), (b) $A\mathrm{Ni}{\mathrm{O}}_2$ and $A\mathrm{Mn}{\mathrm{O}}_2$ in the $C2/m$ space group (${\mathrm{O}}^{\prime }3$ structure), (c) $\mathrm{Co}{\mathrm{O}}_2, \mathrm{Ni}{\mathrm{O}}_2$, and $\mathrm{Mn}{\mathrm{O}}_2$ in the $P\overline{3}m1$ space group (O1 structure). The green, blue, and red balls indicate Li/Na, Co/Ni/Mn, and O, respectively.

Figure 2

The cRPA Hubbard parameters; (a) $U^{\mathrm{bare}}$, (b) Wannier spread, (c) $U$, and (d) $U/U^{\mathrm{bare}}$ in Mn, Co, and Ni systems with different alkali ion intercalations.

Figure 3

Partial density of states (DOS) of intercalated $\text{Li/Na}X{\mathrm{O}}_2$ and deintercalated $X{\mathrm{O}}_2$ ($X$: Mn, Co, and Ni).

Figure 4

The average voltage calculated using several combinations of functionals and vdW correction for different $U$ values. (a) $\mathrm{Li}\mathrm{Co}{\mathrm{O}}_2$, (b) $\mathrm{Li}\mathrm{Ni}{\mathrm{O}}_2$, (c) $\mathrm{Li}\mathrm{Mn}{\mathrm{O}}_2$, (d) $\mathrm{Na}\mathrm{Co}{\mathrm{O}}_2$, (e) $\mathrm{Na}\mathrm{Ni}{\mathrm{O}}_2$, (f) $\mathrm{NaMn}{\mathrm{O}}_2$. The gray dotted lines indicate the experimental values for $\mathrm{Li}\mathrm{Co}{\mathrm{O}}_2$ [12, 68], $\mathrm{Li}\mathrm{Ni}{\mathrm{O}}_2$ [12, 69], $\mathrm{Li}\mathrm{Mn}{\mathrm{O}}_2$ [62, 70], $\mathrm{Na}\mathrm{Co}{\mathrm{O}}_2$ [14, 71], $\mathrm{Na}\mathrm{Ni}{\mathrm{O}}_2$ [72], and $\mathrm{NaMn}{\mathrm{O}}_2$ [73, 74].

Figure 5

Relative errors of (a) the relaxed lattice parameter $c$ and (b) volume/f.u. compared to experiment using PBE, PBE+$U$, PBE+$U$+vdW, SCAN, and SCAN+$U$.