Gibbs free energies G(X) of the M + @C18 were evaluated by summing up the fairly accurate single point energies E(X) of B97X-V 51 /def2-QZVPP level in combination with Counterpoise correction and the thermal corrections to free energy obtained via frequency analysis. Natural population analyses (NPA) and Wiberg bond order (calculated based on natural atomic orbitals) of the M + @C18 in were calculated based on B97XD/ma-TZVP wavefunctions. Electron excitations were investigated by means of the time-dependent DFT (TD-DFT) method at B97XD/ma-TZVP level at optimized ground-state geometries. Charge-transfer spectra (CTS) were plotted based on the TD-DFT results. The B97XD functional combining with very large d-aug-cc-pVTZ(-PP) basis sets within the framework of DFT were employed for calculating optical nonlinearity and (hyper)polarizability density of the M + @C18 in .