Figure 3. a) Evolution of NPA charges in singlet state, b) evolution of NPA charges in triplet state, c) evolution of spin density in triplet state, and d) evolution of energy under external electric fields (EEFs). molecular orbitals at the isovalue of 0.004 au.
For triplet C20F20@K@C20F20@K@C20F20, from Figure 3b and Table 2 as well as Figure 3c, it can be found that both spin density and the absolute values of NPA charges of cage1 decrease but that of cage 3 increase with increasing the intensity of OEEF in negative directions of x-axis (fromF x = 0 to -40 × 10-4 au). The NPA charge of cage 1 under F x = 0 au and that of cage 3 under F x = -20 × 10-4 au (-0.1018 V/Å) in triplet C20F20@K@C20F20@K@C20F20are, respectively, -0.816 |e| and -0.842 |e|. The SOMOs show that an excess electron is confined inside the left C20F20 cage (1 ) for C20F20@K@C20F20@K@C20F20under F x = 0 au but that is confined inside the right C20F20 cage (3 ) for C20F20@K@C20F20@K@C20F20under F x = -20 × 10-4 au (-0.1018 V/Å).
Therefore, applying an OEEF of -20 × 10-4 au (-0.1018 V/Å) in the x-axis direction of triplet C20F20@K@C20F20@K@C20F20results in both left-to-right transfers of the two single-excess-electrons. The transfers of the excess electrons are exhibited that a single-excess-electron transfers from middle C20F20 cage (2 ) to right C20F20 cage (3 ) and the other one transfers from right cage (1 ) to middle C20F20 cage (2 ). Theμx value also increases enormously when going from field-free triplet C20F20@K@C20F20@K@C20F2to electrified ones.
Molecular spin switch and stabilities
By comparing the total energies for field-free C20F20@K@C20F20@K@C20F20in different spin states (see Table 3), it is found that the triplet structure is 8.72 kcal/mol in energy lower than the corresponding singlet one. Therefore, owing to different localizations of the excess electrons, the triplet structure with two single-excess-electrons inside two cages (1 and 2 ) is thermodynamically more stable than the singlet one with lone pair of excess electrons inside one cage (2 ) for field-free C20F20@K@C20F20@K@C20F20. So, the triplet structure is the ground state for field-free C20F20@K@C20F20@K@C20F20. In addition, the small energy difference between singlet and triplet structures may be beneficial to the interconversion between them.
It is worth noticing that, results in Figure 3d and Table 3 show that the energies of triplet C20F20@K@C20F20@K@C20F20under both F x < 111 × 10-4 and F x > -120 × 10-4 au are lower than that of singlet one, while the singlet C20F20@K@C20F20@K@C20F20under both F x ≥ 111 × 10-4 andF x ≤ -120 × 10-4 au are lower in energy than the triplet one. That is to say, the triplet C20F20@K@C20F20@K@C20F20with the range of -120 × 10-4 <F x < 111 × 10-4 au but singlet one with the range of F x ≥ 111 × 10-4 or ≤ -120 × 10-4 au are ground state for C20F20@K@C20F20@K@C20F20.
Considering the electronic stabilities of C20F20@K@C20F20@K@C20F20, we focus on the first and second vertical electron detachment energies (VDE (I) and (II)) in ground state. From Table 3, for the triplet C20F20@K@C20F20@K@C20F20, the VDE (I) and VDE(II) values are 6.61 and 9.34 eV, respectively. These VDEs are far larger than that of the reported solvated dielectron e2@C60F60 structures ((VDEs (I) of 1.720 ~ 2.283 eV, and VDEs (II) of 3.959–5.288 eV)),25e2@(LiF)n (n = 3 ~ 5, -0.021 ~ 1.254 eV (VDE(1))),35 and dipole bound dianions of [(PF5)3・・・dropentalene → Ca].36 Obviously, the triplet C20F20@K@C20F20@K@C20F20are stable solvated dielectrons. Changing from triplet to singlet C20F20@K@C20F20@K@C20F20, both VDE (I) and VDE(II) values considerably decrease to 4.42 and 8.33 eV as applying the EEF of -120 × 10-4 au in the x-axis direction but significantly increase to 11.56 and 13.14 eV as applying the EEF of 110 × 10-4 au in the x-axis direction. Still, the VDE (I) and VDE(II) values singlet C20F20@K@C20F20@K@C20F20under F x = -120 × 10-4 au are far larger than the corresponding ones of reported e2@C60F60 and e2@(LiF)n, which indicates that the singlet C20F20@K@C20F20@K@C20F20under F x = 111 × 10-4 or -120 × 10-4 au may be still stable.
Table 3. Total energies (E tot, au), relative energies (E rel, kcal/mol), interaction energies (E int), and vertical detachment energies (VDE(I&II), eV).