3.1 Geometric Structure, Energy, and Electronic Structure of M + @C18 in The optimized geometries of complexes M + @C18 in and M + @C18 out are displayed in Figure , and the Cartesian coordinates of them are listed in Tables and, respectively. As seen from the relative free energy (ΔG) and equilibrium constant (K in/out ) at standard ambient condition in Table , the endohedral complexes M + @C18 in are significantly lower in energy compared to their respective exohedral counterparts, and the relative energies of two configurations increase with the atomic number of the alkali-metal, indicating that M + are more inclined to adsorb inside the C18 ring, and the higher the atomic number, the more pronounced this trend becomes. Based on this, our subsequent discussions in this paper will focus on M + endohedral C18, that is, M + @C18 in , only. Table Absolute free energy (G in and G out , in a.u.), relative free energy (ΔG, in kcal mol -1 ), and equilibrium constant (K in/out ) of complexes M + @C18 in and M + @C18 out at standard ambient condition The distances between M + and the geometric center of C18 ring (d0), as well as the distances between M + and the nearest and farthest C atoms of C18 (d1 and d2, respectively) are shown in Table . Combining Figure as well as Tables and, it can be seen that for complexes M + @C18 in with M + = Li + , Na + , K + , and Rb + , the metal ions are located on the plane of the C18 and gradually approach the geometric center of the ring as the atomic number increases, however, Cs + ion, due to the steric hindrance caused by the larger ionic radius, is 0.673 Å vertically offset from geometric center of the C18. No matter which metal ion is complexed with, the deformation of the C18 ring does not appear obvious, showcasing a degree of rigidity in its structure.