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 μ_x 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 μ_x 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 ).