All the density functional theory (DFT) electronic structure calculations were performed using the Quantum Espresso (QE) software package with the Ultrasoft (US) pseudopotentials (PPs). The wavefunction and charge density cutoffs were set to 40 Ry and 200 Ry, respectively. Cell parameters and atomic positions were relaxed with a threshold of 10 -3 Ry/Bohr for the atomic forces and 10 -5 Ry/Bohr for the energies. The Monkhorst-Pack method was used to sample the k-points in the Brillouin zone with a k-mesh sampling density greater than 15,625 points per Å 3 . As the standard DFT lacks the description of the vdW interactions , we benchmarked three approaches to include vdW interactions: PBE-D3, PBE D3-BJ, and rVV10, and we selected the functional by comparing the DFT calculated lattice parameters, thermodynamic stability, and voltage profile of the Li x C 6 compounds with the experimental results. The thermodynamic stability of Li x C 6 compounds at different Li concentrations (x) and stages was evaluated by calculating the formation energies (E f ) with respect to C 6 and LiC 6 :