Figure 2 gives the frontier molecular orbitals in both states and spin density distribution in triplet state. The highest occupied molecular orbital (HOMO, see Figure 2a) in singlet state indicates that two excess electrons are trapped inside the middle smallest-sized C20F20 cage (2 ) with NPA charge of -1.345 |e| to form a lone pair of excess electrons. From Figure 2b, the two single occupied molecular orbitals (SOMO1 and SOMO2) and spin density distribution suggest one excess electron is confined inside the left C20F20 cage (1 ) with NPA charge of -0.816 |e| and the other one is confined inside the middle C20F20 cage (2 ) with NPA charge of -0.688 |e|. Then, the two excess electrons are two single-excess-electrons individually inside left (1 ) and middle cage 2 . The right largest-sized C20F20 cage (3 ) is empty for triplet C20F20@K@C20F20@K@C20F20. The sizes of the occupied C20F20 cage(s) are slightly smaller than that of the unoccupied one for both states, which shows that the occupation of electrons makes the occupied cage slightly shrink. These are similar to that of the reported e@C20F18(NH)2C20F18and e@C24F22(NH)2C20F18.26,27
Therefore, the lone pair of excess electrons is confined inside the middle smallest-sized C20F20 cage (2 ) for singlet C20F20@K@C20F20@K@C20F20, while two single-excess-electrons are, respectively, confined inside left and middle smaller-sized C20F20cages (1 and 2 ) for triplet C20F20@K@C20F20@K@C20F20.
Of course, different spatial localizations of the excess electrons lead to clearly different physical properties. From Table 2), the dipole moment component μ x values are, respectively, 0.03 and -35.2 D for singlet structure with lone pair of excess electrons inside smallest-sized C20F20cage (2 ) and triplet one with two single-excess electrons inside left and middle small-sized C20F20 cages (1 and2 ). The difference of μx values between singlet and triplet states is much considerable.
It is reported that, for e@C20F18(NH)2C20F18,26there exists a third structure with an excess electron equally confined in both C20F18 cages. Similarly, a triplet structure with D 5d point group of C20F20@K@C20F20@K@C20F20has been found during our searching. This tripletD 5d structure shows that one excess electron is confined inside the middle C20F20 cage (2 ), and the other one is equally confined in both end C20F20 cage (1 and 3) . However, this D 5d structure is a transition state due to five large imaginary frequencies.
Evolution of excess electron localizations
Recently, we have reported that application of OEEF of -10 × 10-4 au (-0.0514 V/Å) results in of an excess electron transfer from left to right cage of e@C20F18(NH)2C20F18.27For singlet and triplet C20F20@K@C20F20@K@C20F20, the conversions of two excess electrons in three C20F20 cages are especially deserved studied. Both Figure 3 and Table 2 give the evolutions of NPA charges of three cages (1 , 2 , and 3 ) under OEEFs.
For singlet C20F20@K@C20F20@K@C20F20, one can see that the absolute value of NPA charge of cage 2decreases with increasing the intensity of OEEF in both positive and negative directions of x-axis (from F x = 0 to 125 or -125 × 10-4 au). Simultaneously, the absolute value of NPA charge of cage 1 increases but that of cage 3decrease as changing the intensity of OEEF in x-axis direction fromF x = -125 × 10-4 to 125 × 10-4 au. The NPA charge of cage 1 underF x = 111 × 10-4 au (0.5705 V/Å) and that of cage 3 under F x = -120 × 10-4 au (0.6168 V/Å) in singlet C20F20@K@C20F20@K@C20F20are, respectively, -1.592 |e| and -1.687 |e|. The HOMOs of singlet C20F20@K@C20F20@K@C20F20with and without F x are also shown in Figure 3a. From the analysis of HOMOs in Figure 3a, the lone pair of excess electrons is confined inside the left C20F20 cage (1 ) for C20F20@K@C20F20@K@C20F20under F x = 111 × 10-4 au (0.5705 V/Å) and that is confined inside the right one (3 ) for C20F20@K@C20F20@K@C20F20under F x = -120 × 10-4 au (-0.6168 V/Å). Therefore, applying the OEEF of 111 × 10-4 au (0.5705 V/Å) and -120 × 10-4au (-0.6168 V/Å) in the x-axis direction of singlet C20F20@K@C20F20@K@C20F20results in the transfer of the lone pair of excess electrons from middle C20F20 cage (2 ) to left C20F20 cage (1 ) and from middle C20F20 cage (2 ) to right C20F20 cage (3 ), respectively. The μx value increases enormously when going from field-free singlet C20F20@K@C20F20@K@C20F2with lone pair of excess electrons inside middle C20F20 cage (2 ) to the electrified ones with that inside end C20F20 cage (1 or 3 ).