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