3.2.1. Li@C20H20
In the past we found that M:TZ, N/O:TZ, H:DATZ basis set is capable of
providing accurate excitation energies for SEPs.43,44A similar basis set combination [M:TZ, C:TZ, H:DATZ; basis set (9)]
was adopted to study excited states of
Li@C20H20 under D2, P3, and P3+ levels
of theory. Under this basis set ten excited states reside within its IE1
limit (see the values reported in the Table 2). The first excited state
(2T1u) lies 0.398 eV above the ground
state at P3+ level and the unpaired electron occupies a p-type
superatomic orbital (see Figure 2). The second excited state
(12Hg at 0.956 eV) bear
1d1 superatomic electron configuration. After that
this electron jumps to 2s and 1f superatomic orbitals. Note thatIh symmetry splits 1f or 1g shells into two
non-degenerate components. Specifically, the 1f1electronic configuration caries by the
12T2u (1.417 eV) and
12Gu (1.477 eV) states. The 2p, 2d 1g,
and 2f shaped orbitals are occupied in next five excited states
(1.460-2.247 eV range). The 1g1 configuration belongs
to two non-degenerate 2Gg and2Hg states. The2Gg state of
Li@C20H20 lies at 1.914 eV but the2Hg is not bound. Overall, the
observed superatomic Aufbau principle of
Li@C20H20 at all levels is 1s, 1p, 1d,
2s, 1f, 2p, 2d, 1g, 2f. Shapes of selected 1s, 1p, 1d, 1f, and 1g
superatomic orbitals are given in Figure 2. Interestingly, it is
identical to the Aufbau rule that we introduced for
Be(NH3)4+ SEP (1s, 1p,
1d, 2s, 1f, 2p, 2d).43 In overall, P3+ values are
lower than D2 but bigger than P3 numbers for all the excitations except
for the 1s → 2s transition (see Table 2). The excitation energy
differences between P3+ and P3 are small (0.003-0.008 eV). The
discrepancy between P3+ and D2 energies are within 0.014-0.057 eV.
Several other basis sets were also probed for
Li@C20H20 (see the values under basis
set (1) − (8) of Table 2). Only the P3+ vertical excitation energies are
listed in Table 2 and corresponding D2 and P3 values are listed in the
ESI (Table S4, S6, S8, S10, S12, S14, S16, and S18). In all the cases
the first excitation corresponds to 1s → 1p transition. The smallest
basis set [basis set (1)] underestimates the first excitation energy
by 0.225 eV compared to the basis set (9). Interestingly, at the basis
set (1) only one more excited state is bound. The second excited state
is at 1.285 eV and the shape of the populating orbital does not resemble
a superatomic orbital. The addition of augmented set of basis functions
to H-atoms increased the number of bound excited states up to six (see
the values under basis set (2) in Table 2). The 1s → 1p transition at
basis set (2) is 0.033 eV greater than the corresponding value at basis
set (9). Similar to the basis set (9), the second transition at the
basis set (2) is 1s → 1d but higher in energy (0.956 vs 1.147 eV). At
basis set (2) the orbital that populates the third excited state does
not resemble a superatomic orbital shape (see b2 in
Table 2). After that the electron promotes to 1f
(12T2u and
12Gu) and 2s superatomic orbitals.
Under the basis set (3) 1s → non-superatomic electron transitions are
absent. The observed orbital model at this level is 1s, 1p, 1d, 1f, 2p
which is different from the one predicted by bigger basis set (9).
Similarly, at basis set (4) only five excited states are bound. Basis
set (5) predicts three 1s → non-superatomic excitations that give rise
to 22Ag,
12T2u, and
22T1u states. Under the basis sets (6)
and (7) the electron populates 1s, 1p, 1d, 2s, 2p, 1f superatomic
orbitals in energy order with only one non-superatomic state.
Even though the basis set (8) has more basis functions than basis set
(9) it describes only six bound excited states, and the orbital order is
1s, 1p, 1d, 2s, 2p, 1f. This shows the importance of doubly augmentation
on H-atoms for accurate representation of excited states of these
systems. Based on this conclusion the basis set (9) was applied to study
excited states of Na@C20H20 and
Mg@C20H20+.
Table 2. Calculated vertical excitation energies (eV) of
Li@C20H20 by electron propagator methods
under various basis sets. States are ordered according to P3+ excitation
energies obtained at Li:TZ, C:TZ, H:DATZ set [basis set (9)] and
collected into quasi-degenerate, superatomic shells.