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.