# Replacement of Cobalt in Lithium-Rich Layered Oxides by n-Doping: A DFT Study
## 2 Methods  
All calculations have been performed with the Vienna Ab-initio Simulation Package (VASP), which performs periodic ab initio quantum mechanical calculations within the Kohn-Sham density functional theory (DFT) [38; 39] framework, with projector-augmented wave potentials and plane wave basis sets. We applied the generalized-gradient approximation (GGA) [40] in the spin polarized case with the exchange-correlation density functional by Perdew, Burke, and Ernzenhof (PBE) [41]. We used the DFT + U method [42; 43], which has been extensively validated for correcting the large self-interaction error in transition metal oxides [41], caused by the approximate form of standard exchange-correlation density functional when applied to strongly localized unpaired electrons, such as in the d manifold of Co, Ni, and Mn. An effective value of U-J = 4.00 eV has been used for all Co, Ni, and Mn d electrons. This value is an average between the values of Co, Mn, and Ni, reported from ab-initio UHF calculations, and has been recently validated by us for LiMO\({}_{2}\) layered phases (M = Co, Ni, Mn) [44; 45; 46]. We used a kinetic energy cut-off of 520 eV and Brillouin Zone sampled at the Gamma point. We optimized the structural parameters of supercells by iteratively relaxing the ion positions and the cell lattices without any symmetry constraints until the residual force on each atom was <0.01 eV A\({}^{-1}\). Bader charge analysis [47] was performed on the all-electron charge density files (the core density was generated from the pseudo-potential files) [48; 49]. Magnetic moments have been obtained as a direct output of the spin polarized calculations, using the computational routines embed in the VASP code. The structures of four Li-rich layered oxides with the general formula Li\({}_{1.2}\)Ni\({}_{0.2-x}\)/2 Mn\({}_{0.6-x/2}\)Co\({}_{x}\)O\({}_{2}\) and different Co contents (i.e., x = 0.12, 0.08, 0.04, and 0, namely LNMC12, LNMC08, LNMC04, and LNM) have been built starting from the hR12 prototype unit cell, and using a 5 \(\times\) 2 \(\times\) 5/3 supercell. The final supercell contains 200 atoms (Li\({}_{50}\)(Li\({}_{10}\)Ni\({}_{10}\)Mn\({}_{30}\))O\({}_{100}\) for the LNM stoichiometry) stacked in 20 layers, obtained by 5 repetitions along the c-axis of the stacking of a Li/O/TM/O parallel planes motif. Li and O planes are constituted only by oxygen and lithium atoms, respectively, whereas in TM planes there is the simultaneous presence of nickel, manganese, cobalt, and lithium atoms. The four modeled supercells with different Co contents are shown in Figure 1. The tables with atomic positions and the supercell unit axes matrix are reported in the Supplementary Information (SI), Tables S1-S3. To model transition metal disorder in multicomponent TM layers in the LNM supercell, we have adopted the special quasi-random structure (SQS) approach [50; 51]: this method allows for the modeling of a random solid solution in a supercell of the desired size by mimicking random correlation functions up through nearest-neighbor, next-nearest-neighbor interactions, and so on. The SQS method relies on the cluster expansion (CE) formalism proposed by [PERSON] [52]. We used the ATAT suite (alloy-theoretic automated toolkit) that exploits an SQS-based algorithm in search for a fully randomized distribution of Ni, Mn, and Li ions in the TM layers within the LNM supercell [53]. Starting from the fully randomized LNM lattice (Li\({}_{50}\)(Li\({}_{10}\)Ni\({}_{10}\)Mn\({}_{30}\))O\({}_{100}\)), the other supercells with different Co contents have been obtained by point doping: (LNMC4) 2 Co to replace 1 Ni and 1 Mn (Li\({}_{50}\)(Li\({}_{10}\)Ni\({}_{9}\)Mn\({}_{29}\)Co\({}_{2}\))O\({}_{100}\)); (LNMC8) 4 Co to replace 2 Ni and 2 Mn (Li\({}_{50}\)(Li\({}_{10}\)Ni\({}_{8}\)Mn\({}_{28}\)Co\({}_{4}\))O\({}_{100}\)); and (LNMC12) 6 Co to replace 3 Ni and 3 Mn (Li\({}_{50}\)(Li\({}_{10}\)Ni\({}_{7}\)Mn\({}_{27}\)Co\({}_{6}\))O\({}_{100}\)), respectively.