3.1 Ground States Properties
C20H20− is not stable
with respect to C20H20 + e dissociation.
So, is it possible for endohedral
M@C20H20 (M = Li, Na) to have
M•@C20H20(“•” represents the unpaired electron) electronic
structure rather than
M+@C20H20−?
Based on the findings of this study, the unpaired electron of
M@C20H20 (M = Li, Na,
Mg+) is delocalized in the periphery of the
[M@C20H20]+occupying a pseudo spherical atomic s-type molecular orbital (see Figure
1). This diffuse molecular orbital is doubly occupied in the ground
state of Mg@C20H20.
The top and side views of endohedral
Li@C20H20 are illustrated in Figure 1.
Each Li@C20H20 and
Li@C20H20+ were
optimized at B3LYP and MP2 levels. The MP2 optimized M−C, C−C, and C−H
lengths of Li@C20H20 are 2.186, 1.560,
and 1.090 Å, respectively. Corresponding bond distances of
Li@C20H20+ at the same
level are 2.189, 1.562, and 1.086 Å. B3LYP optimized parameters of these
structures are listed in the Table 1. Evidently, the B3LYP parameters of
Li@C20H20 and
Li@C20H20+ are in very
good agreement with their MP2 values (see Table 1). Since MP2 geometry
optimizations for these species are extremely demanding, only B3LYP
optimizations were performed for all other reported species. Going from
neutral to charged species, M−C and C−C lengths stretch by
~0.004 Å and ~0.002 Å, respectively
(Table 1). Compared to bare C20H20 all
the studied encapsulated systems have longer C−C bonds. C−H distances
shorten by ~0.005 Å going from neutral to charged
complexes. Interestingly, we observed a similar pattern for SEPs in the
past, i.e., going from Li(NH3)4,
Be(NH3)4,
Ca(NH3)6,
Mg(H2O)6 SEPs to their corresponding
charged complexes M−Ligand bonds elongate but N−H/O−H bonds
compress.42–45 The longest C−H was observed for the
Mg@C20H20 (1.096 Å) and it is only 0.007
Å longer than that of C20H20. Complexes
that do not possess outer diffuse electrons, i.e.,
Li@C20H20+,
Na@C20H20+, and
Mg@C20H202+, have
shorter C−H bonds compared to the ones of
C20H20.
MP2//B3LYP and P3+ IEs of all the species are given in Table 1. Only for
Li@C20H20 AIE1 obtained by full MP2
geometry optimizations and the values is 2.410 eV. The difference
between aforementioned value and the MP2//B3LYP AIE1 of
Li@C20H20 is only 0.001 eV (see Table
1). This shows that MP2//B3LYP IEs of
M@C20H20 are reliable. Several basis
sets were implemented at P3+ to obtain VIE1 of
Li@C20H20, i.e., (1)
IE1(Li:TZ, C:TZ, H:TZ) = 1.818 eV, (2)
IE1(Li:TZ, C:TZ, H:ATZ) = 2.373 eV, (3)
IE1(Li:TZ, C:ATZ, H:TZ) = 2.337 eV, (4)
IE1(Li:ATZ, C:TZ, H:TZ) = 2.329 eV, (5)
IE1(Li:TZ, C:ATZ, H:ATZ) = 2.366 eV, (6)
IE1(Li:ATZ, C:TZ, H:ATZ) = 2.350 eV, (7)
IE1(Li:ATZ, C:ATZ, H:TZ) = 2.353 eV, (8)
IE1(Li:ATZ, C:ATZ, H:ATZ) = 2.351 eV, (9)
IE1(Li:TZ, C:TZ, H:DATZ) = 2.350 eV. All the basis sets
except (1) have diffuse basis functions and predicted
~2.3 eV IE1.
The IE1s of naked Li (5.392 eV) and Na (5.139 eV) are bigger
(approximately by 3 eV) compared to those of
Li@C20H20 to
Na@C20H20.60 The
reported B3LYP/6-311+G(d,p) VIE1s of
Li@C20H20 (2.77 eV),
Na@C20H20 (2.67 eV), and
Mg@C20H20 (3.43 eV) by Moran et
al.41 are ~0.4 eV bigger compared to
the calculated P3+ values in this study. Since each
Li@C20H20,
Na@C20H20, and
Mg@C20H20 possesses a lower IE1 than
that of cesium atom, i.e., experimental IE1Cs = 3.894
eV60, they can be categorized as
superalkalis.61