Quantum Chemical Investigation of the Interaction of Sodium Ions with Hard Carbon-Based Systems

We present a density functional theory investigation into the interaction of single sodium ions with distinct structural motifs of hard carbon (HC), including armchair and zigzag edges, basal planes, intercalation sites, curved graphene surfaces, and selected functional groups. The aim is to explore and identify new motifs to be added to the structural parameters necessary for the reliable experimental characterization of HC structures and their sodiation process. The results reveal that the strength of interaction between the Na cation and HC mainly follows this order: the edge sites present the stronger anchoring points for the cation; this is followed by intercalation regions between two graphene sheets, concave areas of graphene surfaces, and convex regions, while nearly flat graphene areas exhibit the weakest binding points with sodium ions. A notable monotonic dependence was also identified between the surface curvature and both the sodium interaction energy and the corresponding charge transfer. Additionally, the C 1s binding energies were computed and compared with experimental X-ray photoelectron spectroscopy (XPS) measurements for carbon atoms covalently bound to common functional groups in HC. Our quantum chemical calculations support the consensus that the edge sites drive the sloping capacity through strong Na+ interactions, whereas curvature-induced concave regions may serve as nucleation sites for Na clusters. These clusters could evolve into a pseudometallic state, accounting for the plateau capacity. These findings provide a microscopic framework for understanding sodium storage in hard carbon and offer design principles for optimizing the anode materials in sodium-ion batteries.