3.2.2. Na@C20H20 and Mg@C20H20+
The superatomic shell series of Na@C20H20 is identical to the Li@C20H20 (see Table 3). The first excitation energy of Na@C20H20 is approximately 5.5 times smaller than that of Na atom (0.382 vs 2.10 eV).62 Compared to Li@C20H20, the excitation energies of Na@C20H20 are lower by 0.016-0.085 eV at P3+ level. This is consistent with what we have seen for Li(NH3)4 and Na(NH3)4 superatoms where the excitation energies of the former is greater than the latter by 0.06-0.15 eV.42 Similar to the Li@C20H20, the P3+ excitation energies are greater than P3 but lower than D2, except for the 1s → 2s transition. For all the states P3 and P3+ values are nearly identical (see Table 3).
Mg@C20H20+ has higher excitation energies compared to Na@C20H20 because of the greater Coulombic attraction between the charged center (Mg@C20H202+) and the diffuse electron. The shell model of Mg@C20H20+ is slightly different from the one of Li@C20H20 or Na@C20H20. Specifically, up to 1g it is identical to the Li@C20H20 or Na@C20H20. Unlike Li@C20H20 and Na@C20H20, both2Gg and2Hg of 1g of Mg@C20H20+ are bound. For Mg@C20H20+ case the 3s populates after the 1g. Notice that 3s shell does not populate in either Li@C20H20 or Na@C20H20. After that 2f, 2g, 3p, and 3f superatomic orbitals are being populated. Within the considered 0.000-4.782 eV range, only 2Gg of 2g and 2T2u of 3f are bound. Overall, the introduced shell model for Mg@C20H20+ is 1s, 1p, 1d, 2s, 1f, 2p, 2d, 1g, 3s, 2f, 2g, 3p, 3f.
Table 3. The ten lowest vertical excitation energies (eV) for Na@C20H20 at the D2, P3, and P3+ levels of theory with the Na:TZ, C:TZ, H:DATZ basis sets. The states are ordered according to P3+ excitation energies and collected into quasi-degenerate, superatomic shells.