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Since superconductivity was discovered in K3C60 films, alkali-metal doped fullerenes have been of interest in the variety of physical properties, and are considered as a potential material for ion reservoir and conducting component. Due to the small ionization energy of an alkali-metal atom and the large electron affinity of a C60 molecule, electron transfer from alkali-metal atoms to C60 molecules occurs in an alkali-metal-doped C60 solid, resulting in formation of ionic bonds between alkali-metal atoms and C60 molecules. The ionic-bonding interaction is dominant for an alkali-metal-doped C60 solid, rather than van der Waals interaction being dominant for a pristine C60 solid. Here, ionic-bonding interaction between a C60 molecule and a sodium atom is theoretically investigated based on density-functional first-principles calculations. So far, ionic-bonding potentials as a function of distance between two species have been fitted using a repulsive interaction and a coulomb attractive interaction with introducing Madelung constant. However, the sodium-C60 ionic-bonding potential obtained by our first-principles calculations is not reproduced well even using the two interactions. The reason is that Madelung constant assumes ionic valency constant. Indeed, our calculations reveal that ionic valency varies as changing the sodium-C60 distance. Then, regarding ionic valency in the coulomb attractive term as of a variable, the sodium-C60 ionic-bonding potential can be fitted well. Using the fitted sodium-C60 potential, we simulate intercalation potentials of a sodium atom in a 3D C60 fcc solid and in a 2D C60 hexagonal sheet. Sodium atom is found to be stable at octahedral site of the fcc solid. In contrast, for the hexagonal sheet, three-fold symmetric site in the plane is stable. This difference in stable site between the fcc solid and the hexagonal sheet suggest unique physical properties of C60 hexagonal sheet different from those of C60 fcc solid. |