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1 DOI: 1.138/NCHEM.2363 Cage connectivity and frontier π orbitals govern the relative stability of charged fullerene isomers Yang Wang,,, Sergio Díaz-Tendero, Manuel Alcamí,, and Fernando Martín,,, Departamento de Química, Módulo 13, Universidad Autónoma de Madrid, 2849 Madrid, Spain, Instituto Madrileño de Estudios Avanzados en Nanociencia (IMDEA-Nano), Cantoblanco, 2849 Madrid, Spain, and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, 2849 Madrid, Spain To whom correspondence should be addressed Departamento de Química, Módulo 13, Universidad Autónoma de Madrid, 2849 Madrid, Spain Instituto Madrileño de Estudios Avanzados en Nanociencia (IMDEA-Nano), Cantoblanco, 2849 Madrid, Spain Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, 2849 Madrid, Spain NATURE CHEMISTRY Macmillan Publishers Limited. All rights reserved

2 DOI: 1.138/NCHEM.2363 Contents 1 Comparison of the energies obtained from SCC-DFTB and B3LYP/6-31G(d) 3 2 Correlation between the SCC-DFTB and the simple Hückel molecular orbital (HMO) methods 4 3 The role of electron-electron repulsion in the simple HMO method 6 4 The lowest-energy isomers of neutral fullerenes 8 Predictions by CSI q i compared with experimental and DFT data 9 6 Energy penalty per adjacent pentagon pair 2 7 Bond orders in the HMO theory 22 8 Variation of bond orders resulting from charging a fullerene 23 9 Experimentally identified EMFs 26 NATURE CHEMISTRY Macmillan Publishers Limited. All rights reserved

3 DOI: 1.138/NCHEM Comparison of the energies obtained from SCC-DFTB and B3LYP/6-31G(d) The self-consistent charge density functional tight-binding (SCC-DFTB) 1 calculations have been performed by using the DFTB+ (version 1.2) code. 2 The method implemented in this work is based on the second-order expansion of the Kohn-Sham energy in terms of the charge density fluctuation. 3,4 The resulting energy terms are calculated by applying the tight-binding approximation and some approximate treatments similar to semiempirical quantum chemistry methods. A set of Slater-Koster parameters 1 have been utilized for carbon atoms. The DFTB method has been shown to predict geometries and relative energies for neutral fullerene isomers in good agreement with the results of density functional theory (DFT) using the B3LYP functional. It has also been shown to provide energies in good agreement with the B3LYP/6-31G(d) ones in fullerene dimers. 6 To verify the performance of the SCC-DFTB method for charged fullerenes, we have selected 48 isomers of C 8 and calculated the energies (with fully optimized geometry) in various charge states using the DFT method (B3LYP/6-31G(d)). 7,8 The relative energies with respect to the most stable isomer obtained from SCC-DFTB and DFT methods are compared in Figure S1. As can be seen, the correlation between both sets of data is very close to one E B3LYP (kcal/mol) C 2! C 4! C 6! C E DFTB (kcal/mol) E B3LYP (kcal/mol) C C C 6+ 8 IPR 1 APP 2 APPs 3 APPs E DFTB (kcal/mol) E DFTB (kcal/mol) E DFTB (kcal/mol) Figure S1. Energies of 48 isomers of C q 8 (q =,±2,±4,±6) with respect to the energy of the most stable isomer. The results obtained by using the SCC-DFTB method are compared with those calculated at the B3LYP/6-31G(d)//B3LYP/6-31G(d) level. The data correspond to the isomers containing (IPR), 1, 2 and 3 APPs, indicated by magenta circles, orange triangles, green crosses and blue squares, respectively. NATURE CHEMISTRY Macmillan Publishers Limited. All rights reserved

4 DOI: 1.138/NCHEM Correlation between the SCC-DFTB and the simple Hückel molecular orbital (HMO) methods In Figure 3 of the manuscript, we have shown the correlation of charge stabilization energy between the SCC-DFTB and the simple HMO methods for isomers of C q 8 (q = ±2,±4,±6). We have also found similar correlations for other cage sizes. Here we present the results for two more cage sizes, C 74 and C 9, as shown in Figure S2 and Figure S3, respectively. As can be seen, in both cases, a good correlation of the charge stabilization energy between the SCC-DFTB and the HMO methods is also observed CSE q (kcal/mol) 4 2!2 R 2 =.89 q =!2 2!2!4 R 2 =.9 q =!4 2!2!4 R 2 =.9 q =!6!4!1.!1.!..!6!1.!1.!..!6!1.!1.!.. CSE q (kcal/mol) 6 4 2!2!4 R 2 =.8 q = X q 4 2!2!4 R 2 =.9 q = X q 4 2!2!4 R 2 =.91 q = +6! X q Figure S2. Correlation between the charge stabilization energy, CSE q i, calculated by using the SCC-DFTB method, and the sum of the eigenvalues resulting from diagonalization of the connectivity matrix, X q i (in units of β), for isomers of C q± 74 (q = 2,4,6) containing no more than 3 APPs and no triple fused pentagons. See text for the definitions of the two quantities, CSE q i and X q i. The color code is the same as in Figure S1. 4 NATURE CHEMISTRY Macmillan Publishers Limited. All rights reserved

5 DOI: 1.138/NCHEM.2363 CSE q (kcal/mol) 6 4 2!2!4 R 2 =.9 q =!2!1.!.. 4 2!2!4 R 2 =.97 q =!4!1.!1.!.. 4 2!2!4 R 2 =.98 q =!6!6!1.!1.!.. CSE q (kcal/mol) 4 2!2!4 R 2 =.84 q = X q 4 2!2!4 R 2 =.88 q = +4! X q 4 2!2!4!6 R 2 =.9 q = X q Figure S3. Same as Figure S2 for C q± 9 (q = 2,4,6). NATURE CHEMISTRY 21 Macmillan Publishers Limited. All rights reserved

6 DOI: 1.138/NCHEM The role of electron-electron repulsion in the simple HMO method As shown in previous work (see, e.g., Ref. 9 ), the charge distribution in charged fullerenes is not strictly uniform. However, charge inhomogeneities, which are of the order of.e- in the vicinity of the atomic centers according to our DFT/B3LYP calculations, represent a very small fraction of the total number of electrons occupying the π orbitals. Therefore, contribution of charge inhomogeneities to the total electron-electron interaction energy from all the 2n-q electrons lying in the π orbitals is comparatively very small and, therefore, it is not expected to play a significant role. For this reason, it has been proposed that the π electron density can be represented to zero order by a uniform electron density distribution (or a conducting sphere). This has been used in earlier work to study the ionization of fullerenes, 1 the fragmentation dynamics of charged fullerenes, 11 and to reproduce the experimental/dft ionization potentials and electron affinities for various fullerenes, such as C 6, 12 C 76,C 78 and C As we will show below, the CSI model can only work if the electron-electron repulsion energy is very similar for all isomers in the same charge state and containing the same number of carbon atoms, so that it does not play a relevant role in comparing the relative stability of different isomers with the same size. In this section we will use the conducting sphere model to illustrate this point. The Hamiltonian for the π system of a fullerene C 2n with charge q is, Ĥ q = ( 2n q 2 i i 2 2n Z A A r ia n q j i ) 1 where Z A is the nuclear charge on carbon atom A, r ia the electron-nucleus distance, r ij the distance between electrons i and j. For the i-th electron, the electron-electron repulsion term, 1 2 2n q 1 j i r ij, will be calculated classically by assuming that the distribution of π electrons in all fullerene isomers of a given charge is nearly spherical. Therefore, for the i-th electron, the Coulomb potential induced by all the other π electrons (totally 2n q 1 electrons) is spherical and can be calculated, according to Gaussian law, as (2n q 1)/R (R is the effective radius of the conducting sphere). The Hamiltonian can then be simplified as Ĥ q ( 2n q 2 i i 2 2n Z A A r ij ) + 2n q 1 r ia 2R (1) (2) 6 NATURE CHEMISTRY Macmillan Publishers Limited. All rights reserved

7 DOI: 1.138/NCHEM.2363 and can be written as the sum of single-electron Hamiltonians where ĥ q i = 2 i 2 Ĥ q = 2n q ĥ q i (3) i 2n Z A A + 2n q 1 r ia 2R = ĥ i q 2R. () By applying the same procedures as in the simple HMO model, the secular equation for π electrons is 2n A and the corresponding Hückel determinant is where the Coulomb integral is and the resonance integral is [( HAB S AB ε q ) ] i cia = (6) det ( H AB S AB ε q ) i =, (7) α q H AA = φ A ĥ q i φ A = α q 2R, (8) β q H AB = φ A ĥ q i φ B = β β. (9) As can be seen, including the electron-electron repulsion in this way only affects the Coulomb integral, which depends on charge q, and the resonance integral is independent of charge. Solving Eq. (6), we obtain, ε q i = α q βχ i = α βχ i q 2R. (1) This implies that the charge on the cage shifts all the effective energy levels by the same value q/2r. Combining Eq. (1) and Eq. (3), one obtains the single-electron orbital energy (4) ε q i = ψ i ĥ q i ψ i = ε i q R (11) 7 NATURE CHEMISTRY Macmillan Publishers Limited. All rights reserved

8 DOI: 1.138/NCHEM.2363 indicating that the fullerene charge shifts all the single-electron orbital energy by the same amount of q/r. This means that, in the framework of the conducting sphere model, the missing electronelectron repulsion term in the standard HMO method is not important in comparing the relative π energies of fullerene isomers in the same charge state. 4 The lowest-energy isomers of neutral fullerenes In the definition of CSI q i, the knowledge of the lowest-energy isomer of neutral fullerenes is required. There have been computational studies based on DFT in determining the lowest-energy neutral isomers We have also determined the lowest-energy neutral isomers for fullerenes from C 66 to C 14, based on the B3LYP/6-31G(d)//B3LYP/6-31G(d) methods. The results are summarized in Table S1. Fullerene isomers are labeled following the conventional nomenclature 17 indicating the symmetry and the isomer number according to Fowler-Manolopoulos spiral algorithm. 18 Table S1. The lowest-energy isomers of neutral fullerenes C 2n, determined at the B3LYP/6-31G(d)//B3LYP/6-31G(d) level. C 2n Isomer C 2n Isomer C 66 C s (4169) C C 2 (17) C C 2 (629) C 2 88 C s (17) C 21,22 7 D 6d (1) C 23 9 C 2 (4) C C 2v (11188) C a 92 D 3 (28) C D 3h (1) C a 94 C 2 (43) C D 2 (1) C a 96 C 2 (181) C C 2v (3) C a 98 C 2 (248) C 19 8 D 2 (2) C a 1 D 2 (449) C C 2 (3) C a 12 C 1 (63) C D 2d (23) C a 14 C s (234) a Our B3LYP/6-31G(d) results are in good agreement with the PBE1PBE/6-311G*//DFTB results by Zeng et al. 1 NATURE CHEMISTRY Macmillan Publishers Limited. All rights reserved

9 DOI: 1.138/NCHEM.2363 Predictions by CSI q i compared with experimental and DFT data Here we present CSI q i for fullerene isomers in a wide range of sizes (C 66 to C 14 ) and charge states (q=±2 to ±6). The results are compared with experimental (see Table S2 and Table S3) and DFT data. In those cases where there are no experimental data, the lowest-energy isomers are determined at the B3LYP/6-31G(d)//B3LYP/6-31G(d) level. The isomers are considered to be degenerate in energy if the energy differences between them is less than kcal/mol. For fullerene sizes in the range C 28 -C we have only considered negatively charged species, since due to their small size and the rather large number of APPs in this case, most positively charged species are unstable. 9 NATURE CHEMISTRY Macmillan Publishers Limited. All rights reserved

10 DOI: 1.138/NCHEM.2363 DFT: C 2v(4348) ΔCSI (2 β ) isomers C DFT: C s(441) DFT: C 1(4398) C DFT: C 1(4398) DFT: C s(441) DFT: C 2(444) DFT: C 2(4417) Exp: C 2v(49) C ".2 ".4 ".6 ".2 ".4 ".6 DFT: D h(1) ΔCSI (2 β ) isomers DFT: C s(694) 6332 isomers C C isomers DFT: C 2v(11188) DFT: C 2(1612) C Exp: D h(1) Exp: C 2v(673) C C DFT: C 2v(11188) Exp: C 2(1612) DFT: C s(128) C DFT: D h(1) DFT: C 2(797) Exp: C 2(7892) DFT: C 1(781) DFT: C 2(7887) C 6 68 DFT: C 2v(673) Exp: D 3(614) DFT: C 1(782) C Exp: C s(128) Exp: D 2(1611) Exp: C s(1616) C Exp: C 2v(784) C Exp: D 2(1611) C Figure S4. CSI q i values for the charged fullerenes isomers C q 2n (2n = 66 72,q = 2, 3, 4, 6). Only negative values of CSI q i are shown. For a better visualization, the different isomers are classified in columns according to the s. The experimentally identified cage isomers in the form of EMFs and, in the absence of experimental data, the lowest energy isomers determined by DFT (at B3LYP/6-31G(d) level) are highlighted by a black contour, and labeled as Exp and DFT, respectively. The numbers in the bottom part of the left panel for each fullerene size gives the total number of possible isomers. 1 NATURE CHEMISTRY Macmillan Publishers Limited. All rights reserved

11 DOI: 1.138/NCHEM.2363 DFT: D 3h (1) DFT: D 3h (1) DFT: D 3h (1) ".2 " isomers C C C " Exp: D 3h (1) Exp: D 3h (1) DFT: D 3h (1) DFT: C 2 (13333) DFT: C 2 (1329) ".2 ".4 C 2 74 C 3 74 C 4 74 C 6 74 " DFT: C 2v (19138) DFT: C 1 (1749) ".2 DFT: T d (2) DFT: C 2v (19138) " isomers C 2 76 DFT: T d (2) C 4 76 Exp: T d (2) Exp: C s (1749) C 6 76 " DFT: C 2v (3) DFT: D 3h () DFT: D 3h () ".2 ".4 Exp: D 3h () Exp: C 2 (221) 2419 isomers C 2 78 C 4 78 C 6 78 " Figure S. Same as Figure S4 for C q 2n (2n = 74 78,q = ±2, 3,±4,±6). 11 NATURE CHEMISTRY Macmillan Publishers Limited. All rights reserved

12 DOI: 1.138/NCHEM.2363 DFT: D 3 (4) DFT: C 2v (3) DFT: D d (1) ".2 DFT: C 2v () DFT: C 2v () DFT: D h (6) DFT: D h (6) ".4 ".6 ".2 ".4 ".6 ".8 "1. DFT: C 2v () DFT: D h (6) Exp: C 2v (3) isomers C Exp: C 2v (3) DFT: C 2v () DFT: D h (6) C Exp: C 2v () DFT: D h (6) DFT: I h (7) C ".8 "1. C C C Exp: D h (6) Exp: I h (7) C DFT: C s (4) DFT: C 2 (3) DFT: C 2 (3) DFT: C 2 (1) DFT: C 2 () ".2 " isomers C C C " ".2 ".4 Exp: C 2 () Exp: C s (6) Exp: C 3v (7) Exp: C 2v (9) Exp: C 3v (7) Exp: C s (6) Exp: C 2v (9) DFT: C 3v (8) Exp: C s (6) Exp: C 2v (9) Exp: C 3v (8) Exp: C s (6) Exp: C s (39663) C 2 82 C 3 82 Exp: C 3v (8) C 4 82 Exp: C 2v (9) C 6 82 " Figure S6. Same as Figure S4 for C q 2n (2n = 8 82,q = ±2, 3,±4,±6). 12 NATURE CHEMISTRY Macmillan Publishers Limited. All rights reserved

13 DOI: 1.138/NCHEM.2363 ".2 ".4 DFT: C 2v (7) DFT: D 2d (23) DFT: C s (1) DFT: C s (8) DFT: D 2 (21) DFT: D 2d (23) DFT: D 2 (21) DFT: C 2v (7) DFT: C s (3) DFT: D 2 (22) DFT: D 2d (23) DFT: D 3d (19) DFT: C s (1) DFT: C 2v (6) DFT: C 2 (8) 192 isomers C C C " ".2 ".4 Exp: C 2 (11) Exp: C 1 (12) Exp: D 3d (19) DFT: C s (8) DFT: C 2 (9) Exp: C 2 (13) DFT: C s (1) DFT: D 2 (22) Exp: D 2d (23) DFT: C 1 (12) DFT: D 2 (21) Exp: C 1 (1383) DFT: D 2 (21) Exp: C s (136) C 2 84 C 4 84 C 6 84 " DFT: C 2 (17) DFT: C 1 (11) DFT: C 1 (12) DFT: C 1 (7) ".2 " isomers Exp: D 3 (19) C 2 86 DFT: C 2v (9) C 4 86 C 6 86 " ".2 ".4 DFT: C s (17) DFT: C 1 (1) DFT: C 1 (3) DFT: C 2 (2) DFT: C 2 (27) DFT: C 1 (18) DFT: C s (32) isomers C 2 88 Exp: D 2 (3) C 4 88 Exp: D 2 (3) C 6 88 " Figure S7. Same as Figure S4 for C q 2n (2n = 84 88,q = ±2,±4,±6). 13 NATURE CHEMISTRY Macmillan Publishers Limited. All rights reserved

14 DOI: 1.138/NCHEM.2363 ".2 ".4 DFT: C 2 (23) DFT: C 2 (18) DFT: C 2 (28) DFT: C 1 (2) DFT: C 2 (18) DFT: C 1 (2) DFT: C 2 (28) DFT: C 2 (18) DFT: C 1 (2) DFT: C 2 (28) isomers C 6+ 9 C 4+ 9 C 2+ 9 " Exp: C 2v (46) Exp: C 2 (4) Exp: C 2 (42) ".2 ".4 Exp: C 2 (4) DFT: C 2 (41) Exp: C 1 (21) DFT: C 2 (41) DFT: C 2 (43) DFT: C 2 (44) DFT: C 2 (43) C 2 9 C 4 9 C 6 9 " ".2 ".4 ".6 DFT: T(86) DFT: D 3 (28) DFT: D 2 (81) DFT: D 3 (71) DFT: C 2 (9) DFT: D 3 (83) DFT: C 1 (72) DFT: C 2 (7) DFT: C 2 (7) DFT: D 2 (82) DFT: C 1 (72) DFT: D 2 (81) DFT: D 2 (82) DFT: C 2 (9) DFT: C 1 (12) DFT: C 2 (79) DFT: C 2 (46) DFT: D 3 (83) DFT: D 3 (78) " isomers C C C " DFT: D 3 (78) ".2 ".4 ".6 Exp: C s (24) Exp: C 1 (42) DFT: C 2 (79) DFT: C 2 (8) DFT: C 2 (69) DFT: C s (1) Exp: T(86) ".8 C 2 92 Exp: D 3 (8) C 4 92 DFT: D 3 (8) C 6 92 " Figure S8. Same as Figure S4 for C q 2n (2n = 9 92,q = ±2,±4,±6). 14 NATURE CHEMISTRY Macmillan Publishers Limited. All rights reserved

15 DOI: 1.138/NCHEM.2363 ΔCSI (2 β ).2.4 DFT: C 1 (132) DFT: C 2 (124) Exp: C 3v (134) isomers C 2 94 DFT: C s (12) C 4 94 DFT: C 2 (121) DFT: C 2 (117) C DFT: C 2 (181) DFT: C 1 (114) ".2 ".4 DFT: C 2 (124) isomers DFT: D 2 (183) DFT: C 1 (164) DFT: C 1 (7) DFT: C 1 (91) DFT: C s (161) DFT: C 2 (16) DFT: C 1 (1) DFT: C 1 (11) DFT: C 1 (9) DFT: C 1 (7) C 2 96 DFT: C 2 (18) DFT: C 1 (16) DFT: D 2d (163) DFT: D 2 (186) DFT: C 2 (17) C 4 96 Exp: D 2 (186) C 6 96 " ".2 ".4 ".6 DFT: C 1 (247) DFT: C 1 (161) DFT: C 1 (226) DFT: C 2 (22) DFT: C 2 (182) DFT: C 2 (22) isomers DFT: C 1 (143) DFT: C 3 (23) DFT: C 1 (227) DFT: C 2 (166) DFT: C 1 (137) DFT: C 2 (21) DFT: C 1 (184) DFT: C 1 (14) DFT: C 2 (231) C DFT: C 2 (221) DFT: C 1 (169) DFT: C 2 (183) DFT: C 2 (166) DFT: C 1 (81) DFT: C 1 (173) DFT: C 1 (18) DFT: C 1 (168) DFT: C 2v (167) DFT: C 1 (17) C DFT: C 1 (247) DFT: C 2 (166) C DFT: C 1 (427) DFT: C 1 (441) ".2 ".4 DFT: C 2 (43) DFT: C 2 (439) DFT: C 2 (42) DFT: C 2 (33) DFT: D (4) DFT: C 2 (41) isomers C 2 1 C 4 1 Exp: D (4) C 6 1 " Figure S9. Same as Figure S4 for C q 2n (2n = 94 1,q = 2, 4, 6). 1 NATURE CHEMISTRY Macmillan Publishers Limited. All rights reserved

16 DOI: 1.138/NCHEM.2363 ".2 ".4 DFT: C 2v (43) isomers C 2 12 DFT: C 2 (12) DFT: C 1 (4) DFT: C 2 (42) DFT: C 1 (437) DFT: C 1 (47) DFT: C 1 (424) DFT: C 2 (1) DFT: C s (127) DFT: C 1 (434) C 4 12 DFT: C 2 (1) C 6 12 " DFT: C 2 (766) DFT: C 2 (674) ".2 ".4 DFT: D 3 (81) isomers C 2 14 Exp: D 3d (822) C 4 14 DFT: D 3d (822) DFT: D 2 (821) C 6 14 " Figure S1. Same as Figure S4 for C q 2n (2n = 12 and 14,q = 2, 4, 6). 16 NATURE CHEMISTRY Macmillan Publishers Limited. All rights reserved

17 DOI: 1.138/NCHEM CSI ( 2β) DFTB: T d (2) DFT: T d (2) DFTB: T d (2) 2 isomers 2 C C C CSI ( 2β) CSI ( 2β) DFTB: C 2v (3) 3 isomers 2 C DFTB: D 3 (6) 6 isomers 2 C DFT: C 2v (3) DFTB: C 2v (3) 4 C DFT: C 2 (4) DFT: D 3 (6) 4 C C DFTB: C 2 (4) DFTB: D 3 (6) 6 C CSI ( 2β) DFTB: C 2v () 6 isomers 2 C DFT: C 2v () DFT: C s (2) 4 C DFTB: C 2v () DFTB: C 2 (4) DFTB: C s (2) 6 C Figure S11. CSI q i values for the charged fullerenes isomers C q 2n (2n = 28, 3, 32, 34 and q = 2, 4, 6). For a better visualization, the different isomers are classified in columns according to the. The lowest energy isomers determined by DFT 24 or SCC-DFTB (present work) are highlighted by a black contour, and labeled as DFT or DFTB. The number in the bottom part of the left panel for each fullerene size gives the total number of all possible isomers. 17 NATURE CHEMISTRY Macmillan Publishers Limited. All rights reserved

18 DOI: 1.138/NCHEM DFTB: C 2v (9) CSI ( 2β) CSI ( 2β) CSI ( 2β) DFTB: D 6h (1) DFT: D 6h (1) DFTB: D 6h (1) 1 isomers 2 C DFTB: C 2 (17) 17 isomers 2 C DFTB: D 2 (38) 4 isomers DFTB: C 3v (16) DFTB: C 2 (13) DFTB: C 2 (1) DFTB: C s (31) DFTB: C s (29) 2 C DFT: D 2d (14) 4 C DFT: C 2 (17) DFT: C 2 (1) 4 C DFT: C s (31) DFT: D 2 (38) DFT: C 2 (13) DFT: C s (24) DFT: T d (4) 4 C DFTB: D 2d (14) 6 C DFTB: C 2 (17) 6 C DFTB: D 2 (38) DFTB: C s (31) 6 C CSI ( 2β) DFTB: D 3 (4) 4 isomers 2 C DFT: D 3 (4) DFT: C 1 (33) DFT: C 1 (32) 4 C DFTB: D 3 (4) 6 C Figure S12. Same as Figure S11 for C q 2n (2n = 36,38,4,42 and q = 2, 4, 6). 18 NATURE CHEMISTRY Macmillan Publishers Limited. All rights reserved

19 DOI: 1.138/NCHEM CSI ( 2β) DFTB: D 2 (7) DFTB: D 3h (72) DFTB: D 2 (89) DFTB: D 2 (7) 89 isomers 2 C DFT: D 2 (89) 4 C C CSI ( 2β) DFTB: C 2 (116) DFTB: C 1 (114) DFTB: C s (18) DFTB: C 2 (19) 116 isomers 2 C DFT: C 1 (114) DFT: C 2 (116) 4 C DFTB: C 2 (116) DFTB: C 2 (19) DFTB: C 1 (114) 6 C CSI ( 2β) CSI ( 2β) DFTB: C 2 (199) 199 isomers 2 C isomers DFTB: D h (271) 2 C DFT: C 1 (196) DFT: C s (197) 4 C DFT: C 2 (26) DFT: D h (271) DFT: C 2 (199) DFT: C s (266) 4 C DFTB: C 2 (199) 6 C DFTB: D h (271) DFTB: D 3 (27) 6 C Figure S13. Same as Figure S11 for C q 2n (2n = 44,46,48, and q = 2, 4, 6). 19 NATURE CHEMISTRY Macmillan Publishers Limited. All rights reserved

20 DOI: 1.138/NCHEM Energy penalty per adjacent pentagon pair To keep the CSI model as simple as possible, in the manuscript we have chosen a characteristic value of the energy penalty per APP, namely.2 (in units of -2β) for all fullerene isomers, irrespective of the cage size. However, the actual value of this energy penalty varies with the fullerene size (see, e.g., Ref. 2 ). We have computed the actual energy penalty per APP, ε P, as explained by Albertazzi et al 26 using our calculated SCC-DFTB energies for the neutral fullerene isomers. For the smaller cage sizes (C 28 to C 64 ), all possible isomers have been taken into account. For cage sizes from C 66 to C 8, we have included all isomers with 3 and without triple fused pentagons, and for cage sizes from C 82 to C 9, all isomers with 2, since those with 3 never lead to the most stable structure for any charge state. Likewise, for cage sizes from C 9 to C 14, only isomers with 1 have been considered. The calculated energy penalties per APP are shown in Figure S14 below. When possible, our results are compared with those obtained from the QCFF/PI (quantum mechanical consistent force field/π) 2 and the DFTB2 26 methods. The agreement with the existing results is reasonably good. Energy penalty per APP (kcal/mol) Present work (DFTB) Campbell et al (QCFF/PI) Albertazzi et al (DFTB) Cage size 2n Energy penalty per APP (kcal/mol) Present work (DFTB) Cage size 2n Figure S14. Energy penalty per APP obtained from SCC-DFTB calculations for small (left panel) and large (right panel) fullerene cages. Our DFTB results are compared with those obtained from the QCFF/PI (quantum mechanical consistent force field/π 2 ) and the DFTB2 26 methods. To express the above results in units of -2β, we have calculated β, for each size and charge state, from the correlation between the SCC-DFTB charge stabilization energy (CSE q ) and the sum of the eigenvalues of the connectivity matrix, X q, (see Eq. 2 and Fig. 1 of the manuscript, and Figs. S2 and S3 of this SI for specific examples). Figure S1 shows the calculated values of β. As can be seen, the resonance integral β depends both on cage size and on charge state. Figure S16 shows the energy penalty per APP in units of -2β as a function of cage size and charge state. As can be seen, with very few exceptions, the value of the energy penalty per APP lies in the interval In the manuscript we have used.2 (indicated by a dashed line in NATURE CHEMISTRY Macmillan Publishers Limited. All rights reserved

21 DOI: 1.138/NCHEM Resonance integral β (ev) q = 2 q = 3 q = 4 q = 6 q = +2 q = +4 q = Cage size 2n Figure S1. Resonance integral β as a function of cage size and charge state, obtained from the SCC-DFTB and HMO calculations. the figure), which is a lower bound for the calculated values. We have checked that, by using the average value.23 or the actual values given in Figure S16, the predictions of the relative ordering of the different isomers are nearly identical to those reported in Fig. 4 of the manuscript and in Figs. S4-S13 of this SI. Therefore, the use of a constant value for this energy penalty, which is what makes this model so simple and useful, is fully justified. Nevertheless, the model can be trivially refined by just replacing the value.2 in Eq. 3 of the manuscript by the numbers given in Figure S16. Energy penalty per APP ( 2β) q = 2 q = 3 q = 4 q = 6 q = +2 q = +4 q = Cage size 2n Figure S16. Energy penalty per APP in units of -2β, as a function of cage size and charge state. The value.2 used in the definition of CSI in the manuscript is indicated by a dashed line. NATURE CHEMISTRY Macmillan Publishers Limited. All rights reserved

22 DOI: 1.138/NCHEM Bond orders in the HMO theory In the HMO theory, the energy of the k-th π molecular orbital (MO) is ε k = α + βχ k (12) where α is the Coulomb integral, β is resonance integral, and χ k is the k-th eigenvalue of the adjacency matrix in descending order. On the other hand, ε k =< Ψ k Ĥ Ψ k > (13) where Ψ k is the wave function of the k-th MO, which is written as a linear combination of p z atomic orbitals φ A centered in every atom A: Substituting Eq. (14) in Eq. (13), one obtains ε k = A Ψ k = c k, A φ A (14) A c k, A c k, B < φ A Ĥ φ B > (1) B c 2 k, A < φ A Ĥ φ A > + c k, A c k, B < φ A Ĥ φ B > + c k, A c k, B < φ A Ĥ φ B > (16) A A B A B where A B represents the sum over all bonded atom pairs, and A B the sum over all nonbonded atom pairs. According to the HMO theory, < φ A Ĥ φ A >= α, and < φ A Ĥ φ B > equals β if atoms A and B are bonded, and zero if A and B are not bonded. Since A c 2 k, A = 1 as a result of the normalization of Ψ k, Eq. (16) thus becomes Comparing Eq. (17) and Eq. (12), one obtains The bond order, BO, for a given A B bond is defined as ε k = α + β c k, A c k, B (17) A B χ k = c k, A c k, B (18) A B BO A B = c k, A c k, B (19) k where the sum runs over all π molecular orbitals. Thus Eq. (18) implies that the adjacent matrix 22 NATURE CHEMISTRY Macmillan Publishers Limited. All rights reserved

23 DOI: 1.138/NCHEM.2363 eigenvalue χ k is the sum over all bond order contributions BO k,a B = c k, A c k, B resulting from the k-th MO. The variation of the bond order in a given A B bond as a result of charging a fullerene of size 2n is given by BO q A B = n k=n q/2+1 c k, A c k, B : q > n q/2 c k, A c k, B : q < k=n+1 where q is the charge of the system. Thus, the π contribution to CSI q i for the i-th isomer with charge q can be related with the variations of bond order according to the equation: (2) X q i = BO q A B (21) A B 8 Variation of bond orders resulting from charging a fullerene Using Eq. (19), we have evaluated the bond orders for all carbon-carbon bonds in the following neutral and charged species: C 82,C 84 and C 9. Figure S17 and Figure S18 show the variation of bond orders when particular neutral isomers get negative and positive charge, respectively. The charged isomers that have been considered are those leading to the most stable structures in the charged state (left panels) and in the neutral state (right panels). To simplify the analysis, the different bonds have been grouped in the six categories shown in the central part of the figure. These are the only types of bonds that can be found in fullerene cages containing no more than 3 APPs and no triple fused pentagons. The bar diagrams show the changes in bond order with respect to the corresponding neutral isomer in each category. NATURE CHEMISTRY Macmillan Publishers Limited. All rights reserved

24 DOI: 1.138/NCHEM.2363 Most stable isomer in charge state q = ±6 Most stable isomer in charge state q = C 6 82: C 2v (9) Counts of bonds 1 pp hh ph ph 1 ph hh hh pp 1 hh ph x 2 hh hh Bond order variation ( 2β) 1 pp hh ph ph 1 ph hh hh pp 1 hh ph hh hh Bond order variation ( 2β) C 6 82: C 2 (3) C 6 84: C s (136) Counts of bonds 1 pp hh ph ph 1 ph hh x 2 hh pp 1 hh ph x 2 hh hh Bond order variation ( 2β) 1 pp hh ph ph 1 ph hh x 2 hh pp 1 hh ph x 2 hh hh Bond order variation ( 2β) C 6 84: D 2d (23) C 6 9: C 2 (43) Counts of bonds 1 pp hh ph ph 1 ph hh hh pp 1 hh ph hh hh Bond order variation ( 2β) 1 pp hh ph ph 1 ph hh x 2 hh pp 1 hh ph x 2 hh hh Bond order variation ( 2β) C 6 9: C 2 (4) Figure S17. Changes in bond orders (in units of 2β) resulting from negatively charging the C 82, C 84 and C 9 fullerenes. The shown charged isomers are those leading to the most stable structures in the corresponding charged state (left panels) and in the neutral state (right panels). Each isomer is identified by its group symmetry and index according to the spiral algorithm. The different bonds have been grouped in the six categories shown in the central part of the figure. These categories are denoted inside the bar diagrams as pp-hh, ph-ph, ph-hh, hh-pp, hh-ph, and hh-hh, where the h and p labels refer to hexagonal and pentagonal rings, respectively, and the first two labels indicate the two rings sharing the bond and the last two labels the other two rings surrounding that bond. The bar diagrams show the changes in bond order with respect to the corresponding neutral isomer in each category. The values of these changes in bond order are also indicated in the three-dimensional (3D) representations by using the color scales shown on top of the bar diagrams. 24 NATURE CHEMISTRY Macmillan Publishers Limited. All rights reserved

25 DOI: 1.138/NCHEM.2363 Most stable isomer in charge state q = ±6 Most stable isomer in charge state q = C 6+ 82: C s (4) Counts of bonds 1 pp hh ph ph 1 ph hh hh pp 1 hh ph hh hh Bond order variation ( 2β) 1 pp hh ph ph 1 ph hh hh pp 1 hh ph hh hh Bond order variation ( 2β) C 6+ 82: C 2 (3) C 6+ 84: D 2 (21) Counts of bonds 1 pp hh ph ph 1 ph hh hh pp 1 hh ph hh hh Bond order variation ( 2β) 1 pp hh ph ph 1 ph hh hh pp 1 hh ph hh hh Bond order variation ( 2β) C 6+ 84: D 2d (23) C 6+ 9: C 2 (23) Counts of bonds 1 pp hh ph ph 1 ph hh hh pp 1 hh ph hh hh Bond order variation ( 2β) pp hh ph ph ph hh 1 hh pp hh ph 1 hh hh Bond order variation ( 2β) C 6+ 9: C 2 (4) Figure S18. Same as Figure S17 for positively charging the C 82,C 84 and C 9 fullerenes. 2 NATURE CHEMISTRY Macmillan Publishers Limited. All rights reserved

26 DOI: 1.138/NCHEM Experimentally identified EMFs The experimentally identified EMFs are summarized in Table S2 and Table S3. NATURE CHEMISTRY Macmillan Publishers Limited. All rights reserved

27 DOI: 1.138/NCHEM.2363 Table S2. Experimentally isolated and identified EMFs with carbon cages from C 66 to C 82 and formal charge transfer q = 2, 4, 6 to the cage. C 2n Isomer q = 2 q = 4 q = 6 C 66 C 2v (4348) Sc C 68 C 2v (673) Sc 2 C 2 3 D 3 (614) Sc 3 N, DySc 2, 34 LuSc 2, 34 Lu 2 Sc 34 C 7 D h (1) C 2 (7892) Sc 2 S 24 C 2v (784) Sc 3 N 3 C 72 C s (1612) C s (128) Sc 2 S 36 D 2 (1611) La 2, Ce 2, 41,42 Pr 2 43,44 C 74 D 3h (1) Ca, 4 Sr, 46 Ba, 47,48 Sm, 49 Eu,,1 Yb 2,3 C 76 T d (2) Lu 2 4 C s (1749) La 2, DySc 2 N 6 C 78 Sc 3 N D 3h () La 2, 41,7,8 Ce 2, 41,9 Ti 2 C 2, 6 63 C 2 (221) Y 3 N, 7,71 Gd 3 N, 72 Dy 3 N, 73 C 2v (3) Sm, 77,78 Yb 79,8 C 2v () Sc 2 C 2 68,81 83 Tm 3 N, 73 CeSc 2 N, 74 GdSc 2 N, 7 Sc 3 NC 76 D h (6) Ce 2, 84,8 Sc 3 N, 68,86 9 Y 3 N, 74,91 Tb 3 N, 92 Tm 3 N 93,94 Gd x Sc 3 x N, 9 Dy x Sc 3 x N, 96 Ho x Sc 3 x N 97 C 8 I h (7) Lu x Sc 3 x N 96 La 2, 41,98 18 C 2 () Ca, 14 Sm, 1 17 Tm, 18 Eu, 19 Yb 79,16,161 Ce 2, 41,8,13,18 11 Pr 2, 111 Sc 3 N, 9,1,18, Y 3 N, 74,18,124, Gd 3 N, 13 Tb 3 N, 129 Dy 3 N, 131,132 Ho 3 N, 129 Er 3 N, 69 Tm 3 N, 93,94,133 Lu 3 N, 18,113 TiSc 2 N, 134 LaSc 2 N, 13 CeSc 2 N, 136 Nd x Sc 3 x N, 96 Gd x Sc 3 x N, 137,138 TbSc 2 N, 138 Dy x Sc 3 x N, 96 Ho x Sc 3 x N, 97 Er x Sc 3 x N, 129,139 Lu x Sc 3 x N, 14 Ce x Y 3 x N, 74 Lu x Y 3 x N, 14 CeSc 2 N, 141 CeY 2 N, 141 CeLu 2 N, 141,142 Sc 3 NC, 18,143 Sc 4 O 2, 69,18,144,14 Sc 4 O 3, 146 Sc 3 C 2, 69,18, Sc 4 C 2, 1 Sc 3 CH 11 Sc 4 C 2 H, 12 Sc 4 (µ 3 -C 2 )(µ 3 -CN) 13 C s (6) Ca, 14 Sm, 1,17 Tm, 18 Sc 2 C 2, 162,163 Y 2 C 2, 164,16 Er 2, 69,166,167 Tm Eu,, 19,169 Yb 79,16,161 Tb 2 C 2, 17 Dy 2 C 2, 171 Er 2 C 2, 167 ErYC 2, 172 Sc 2 O, 68,173 Sc 2 S 174,17 C 3v (7) Ca, 14 Sm 17 C 82 C 3v (8) Sc 2, 68,176 Y Tm 2, 168,177 Er 2, 69,167,178 HoTm 168 Sc 2 C 2, 83,148, Y 2 C 2, 164,16,18,186 Dy 2 C 2, 171 Er 2 C 2, 167 Tm 2 C 2, 177 ErYC 2, 172 Y 2 S, 187 Dy 2 S,, 187 Lu 2 S 187 C 2v (9) Ca, 14 Sm, 1 Eu, 19,169 Sc 2 C 2, 163,188 Y 2 C 2, 164 Er 2, 167 Tm 2, 168 HoTm 168 Tm, 18 Yb 79,16,161 Dy 2 C 2, 171 Er 2 C C s (39663) Y 3 N, 91 Gd 3 N 189,19 NATURE CHEMISTRY Macmillan Publishers Limited. All rights reserved

28 DOI: 1.138/NCHEM.2363 Table S3. Experimentally isolated and identified EMFs with carbon cages from C 84 to C 14 and formal charge transfer q = 2, 4, 6 to the cage. C 2n Isomer q = 2 q = 4 q = 6 C 2 (11) Sm, 191 Yb 79 C 1 (12) Yb 79 C 2 (13) Sm, 191 Yb 3,79,192 C 84 D 3d (19) Sm 191 D 2d (23) Sc 2 C 2 83,148,193,194 C 1 (1383) Y 2 C 2 16,19 C s (136) Y 3 N, 91 Gd 3 N, 189,196 Tb 3 N, 197 Tm 3 N 196 Ce x Sc 3 x N, 74 Ce x Y 3 x N, 74 CeLu 2 N 74 C 86 D 3 (19) Y 3 N, 91 Gd 3 N, 189,198 Tb 3 N 92 Ce x Sc 3 x N, 74 Ce x Y 3 x N 74 C 88 D 2 (3) Sm 2, 199 Gd 2 C 199,2 2 Y 3 N, 189,21 Gd 3 N, 189 Tb 3 N, 92 Tm 3 N, 22 Lu 3 N, 23 C 2 (4) Sm 24 C 2 (42) Sm 24 Ce x Sc 3 x N, 74 Ce x Y 3 x N, 74 Lu 3 C 2 23 C 9 C 2 (4) Sm 24 C 2v (46) Sm 24 C 1 (21) Sm 2, 199 Gd 2 C 199,2 2 C s (24) Sm 2 C 92 C 1 (42) Sm 2 D 3 (8) Sm 2, 199 Y 2 C 2, 16,26 Gd 2 C 2 2 T (86) La 3 N 27 C 94 C 3v (134) Ca, 28 Sm, 2 Tm 28 C 96 D 2 (186) La 3 N 27 C 1 D (4) La 29 2 C 14 D 3d (822) Sm 21 2 References (1) Elstner, M.; Porezag, D.; Jungnickel, G.; Elsner, J.; Haugk, M.; Frauenheim, T.; Suhai, S.; Seifert, G. Phys. Rev. B 1998, 8, (2) Aradi, B.; Hourahine, B.; Frauenheim, T. J. Phys. Chem. A 27, 111, 678. (3) Koskinen, P.; Mäkinen, V. Comput. Mater. Sci. 29, 47, (4) Seifert, G.; Joswig, J.-O. Wiley Interdisciplinary Reviews: Computational Molecular Science 212, 2, NATURE CHEMISTRY Macmillan Publishers Limited. All rights reserved

29 DOI: 1.138/NCHEM.2363 () Zheng, G.; Irle, S.; Morokuma, K. Chem. Phys. Lett. 2, 412, (6) Wang, Y.; Zettergren, H.; Rousseau, P.; Chen, T.; Gatchell, M.; Stockett, M. H.; Domaracka, A.; Adoui, L.; Huber, B. A.; Cederquist, H.; Alcamí, M.; Martín, F. Phys. Rev. A 214, 89, (7) Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B 1988, 37, 78. (8) Becke, A. D. J. Chem. Phys. 1993, 98, 648. (9) Rodríguez-Fortea, A.; Alegret, N.; Balch, A. L.; Poblet, J. M. Nat Chem 21, 2, (1) Thumm, U. J. Phys. B 1994, 27, 31. (11) Stace, A. J.; Bichoutskaia, E. Phys. Chem. Chem. Phys 211, 13, (12) Zettergren, H.; Forsberg, B. O.; Cederquist, H. Phys. Chem. Chem. Phys. 212, 14, (13) Ehrler, O. T.; Furche, F.; Mathias Weber, J.; Kappes, M. M. The Journal of Chemical Physics 2, 122, (14) Díaz-Tendero, S.; Sánchez, G.; Alcamí, M.; Martín, F. International Journal of Mass Spectrometry 26, 22, (1) Shao, N.; Gao, Y.; Yoo, S.; An, W.; Zeng, X. C. The Journal of Physical Chemistry A 26, 11, , PMID: (16) Popov, A. In Handbook of Computational Chemistry; Leszczynski, J., Ed.; Springer Netherlands, 212; pp (17) Popov, A. A.; Yang, S.; Dunsch, L. Chemical Reviews 213, 113, (18) Fowler, P.; Manolopoulos, D. E. An Atlas of Fullerenes; Clarendon Press: Oxford, U.K., 199. (19) Chen, Z.; Cioslowski, J.; Rao, N.; Moncrieff, D.; Bühl, M.; Hirsch, A.; Thiel, W. Theoretical Chemistry Accounts 21, 16, (2) Sun, G. Chemical Physics Letters 23, 367, (21) Zettergren, H.; Sánchez, G.; Díaz-Tendero, S.; Alcamí, M.; Martín, F. The Journal of Chemical Physics 27, 127, NATURE CHEMISTRY Macmillan Publishers Limited. All rights reserved

30 DOI: 1.138/NCHEM.2363 (22) Zettergren, H.; Alcam ı, M.; Mart ın, F. Phys. Rev. A 27, 76, 432. (23) Sun, G. Chemical Physics 23, 289, (24) Chen, N.; Mulet-Gas, M.; Li, Y.-Y.; Stene, R. E.; Atherton, C. W.; Rodriguez-Fortea, A.; Poblet, J. M.; Echegoyen, L. Chem. Sci. 213, 4, (2) Campbell, E.; Fowler, P.; Mitchell, D.; Zerbetto, F. Chemical Physics Letters 1996, 2, (26) Albertazzi, E.; Domene, C.; W. Fowler, P.; Heine, T.; Seifert, G.; Van Alsenoy, C.; Zerbetto, F. Phys. Chem. Chem. Phys. 1999, 1, (27) Wang, C.-R.; Kai, T.; Tomiyama, T.; Yoshida, T.; Kobayashi, Y.; Nishibori, E.; Takata, M.; Sakata, M.; Shinohara, H. Nature 2, 48, (28) Takata, M.; Nishibori, E.; Sakata, M.; R-Wang, C.; Shinohara, H. Chemical Physics Letters 23, 372, (29) Yamada, M.; Kurihara, H.; Suzuki, M.; Guo, J. D.; Waelchli, M.; Olmstead, M. M.; Balch, A. L.; Nagase, S.; Maeda, Y.; Hasegawa, T.; Lu, X.; Akasaka, T. J. Am. Chem. Soc. 214, 136, (3) Shi, Z.-Q.; Wu, X.; Wang, C.-R.; Lu, X.; Shinohara, H. Angewandte Chemie International Edition 26, 4, (31) Stevenson, S.; Fowler, P. W.; Heine, T.; Duchamp, J. C.; Rice, G.; Glass, T.; Harich, K.; Hajdu, E.; Bible, R.; Dorn, H. C. Nature 2, 48, (32) Olmstead, M. M.; Lee, H. M.; Duchamp, J. C.; Stevenson, S.; Marciu, D.; Dorn, H. C.; Balch, A. L. Angewandte Chemie International Edition 23, 42, (33) Yang, S.; Kalbac, M.; Popov, A.; Dunsch, L. Chemistry A European Journal 26, 12, (34) Yang, S.; Popov, A. A.; Dunsch, L. Chem. Commun. 28, (3) Yang, S.; Popov, A. A.; Dunsch, L. Angewandte Chemie International Edition 27, 46, (36) Chen, N.; Beavers, C. M.; Mulet-Gas, M.; Rodríguez-Fortea, A.; Munoz, E. J.; Li, Y.-Y.; Olmstead, M. M.; Balch, A. L.; Poblet, J. M.; Echegoyen, L. Journal of the American Chemical Society 212, 134, NATURE CHEMISTRY Macmillan Publishers Limited. All rights reserved

31 DOI: 1.138/NCHEM.2363 (37) Kato, H.; Taninaka, A.; Sugai, T.; Shinohara, H. Journal of the American Chemical Society 23, 12, , PMID: (38) Lu, X.; Nikawa, H.; Nakahodo, T.; Tsuchiya, T.; Ishitsuka, M. O.; Maeda, Y.; Akasaka, T.; Toki, M.; Sawa, H.; Slanina, Z.; Mizorogi, N.; Nagase, S. Journal of the American Chemical Society 28, 13, (39) Lu, X.; Nikawa, H.; Tsuchiya, T.; Maeda, Y.; Ishitsuka, M.; Akasaka, T.; Toki, M.; Sawa, H.; Slanina, Z.; Mizorogi, N.; Nagase, S. Angewandte Chemie International Edition 28, 47, (4) Dunsch, L.; Bartl, A.; Georgi, P.; Kuran, P. Synthetic Metals 21, 121, , Proceedings of the International Conference on the Science and Technology of Synthetic Metals. (41) Popov, A. A.; Kästner, C.; Krause, M.; Dunsch, L. Fullerenes, Nanotubes and Carbon Nanostructures 214, 22, (42) Yamada, M.; Wakahara, T.; Tsuchiya, T.; Maeda, Y.; Akasaka, T.; Mizorogi, N.; Nagase, S. The Journal of Physical Chemistry A 28, 112, (43) Plant, S. R.; Ng, T. C.; Warner, J. H.; Dantelle, G.; Ardavan, A.; Briggs, G. A. D.; Porfyrakis, K. Chem. Commun. 29, (44) Nicholls, R. J.; Sader, K.; Warner, J. H.; Plant, S. R.; Porfyrakis, K.; Nellist, P. D.; Briggs, G. A. D.; Cockayne, D. J. H. ACS Nano 21, 4, (4) Kodama, T.; Fujii, R.; Miyake, Y.; Suzuki, S.; Nishikawa, H.; Ikemoto, I.; Kikuchi, K.; Achiba, Y. Chemical Physics Letters 24, 399, (46) Haufe, O.; Hecht, M.; Grupp, A.; Mehring, M.; Jansen, M. Zeitschrift für anorganische und allgemeine Chemie 2, 631, (47) Friese, K.; Panthöfer, M.; Wu, G.; Jansen, M. Acta Crystallographica Section B 24, 6, (48) Reich, A.; Panthöfer, M.; Modrow, H.; Wedig, U.; Jansen, M. Journal of the American Chemical Society 24, 126, , PMID: (49) Xu, W.; Hao, Y.; Uhlik, F.; Shi, Z.; Slanina, Z.; Feng, L. Nanoscale 213,, () Kuran, P.; Krause, M.; Bartl, A.; Dunsch, L. Chemical Physics Letters 1998, 292, NATURE CHEMISTRY Macmillan Publishers Limited. All rights reserved

32 DOI: 1.138/NCHEM.2363 (1) Rappoport, D.; Furche, F. Phys. Chem. Chem. Phys. 29, 11, (2) Xu, J.; Tsuchiya, T.; Hao, C.; Shi, Z.; Wakahara, T.; Mi, W.; Gu, Z.; Akasaka, T. Chemical Physics Letters 26, 419, (3) Ruan, J.; Xie, Y.; Cai, W.; Slanina, Z.; Mizorogi, N.; Nagase, S.; Akasaka, T.; Lu, X. Fullerenes, Nanotubes and Carbon Nanostructures 214, 22, (4) Umemoto, H.; Ohashi, K.; Inoue, T.; Fukui, N.; Sugai, T.; Shinohara, H. Chem. Commun. 21, 46, () Suzuki, M.; Mizorogi, N.; Yang, T.; Uhlik, F.; Slanina, Z.; Zhao, X.; Yamada, M.; Maeda, Y.; Hasegawa, T.; Nagase, S.; Lu, X.; Akasaka, T. Chemistry A European Journal 213, 19, (6) Yang, S.; Popov, A. A.; Dunsch, L. The Journal of Physical Chemistry B 27, 111, , PMID: (7) Cao, B.; Wakahara, T.; Tsuchiya, T.; Kondo, M.; Maeda, Y.; Aminur Rahman, G. M.; Akasaka, T.; Kobayashi, K.; Nagase, S.; Yamamoto, K. Journal of the American Chemical Society 24, 126, (8) Cao, B.; Nikawa, H.; Nakahodo, T.; Tsuchiya, T.; Maeda, Y.; Akasaka, T.; Sawa, H.; Slanina, Z.; Mizorogi, N.; Nagase, S. Journal of the American Chemical Society 28, 13, (9) Yamada, M.; Wakahara, T.; Tsuchiya, T.; Maeda, Y.; Kako, M.; Akasaka, T.; Yoza, K.; Horn, E.; Mizorogi, N.; Nagase, S. Chem. Commun. 28, 8 6. (6) Cao, B.; Hasegawa, M.; Okada, K.; Tomiyama, T.; Okazaki, T.; Suenaga, K.; Shinohara, H. Journal of the American Chemical Society 21, 123, (61) Tan, K.; Lu, X. Chem. Commun. 2, (62) Yumura, T.; Sato, Y.; Suenaga, K.; Iijima, S. The Journal of Physical Chemistry B 2, 19, , PMID: (63) Sato, Y.; Yumura, T.; Suenaga, K.; Moribe, H.; Nishide, D.; Ishida, M.; Shinohara, H.; Iijima, S. Phys. Rev. B 26, 73, (64) Olmstead, M. M.; de Bettencourt-Dias, A.; Duchamp, J. C.; Stevenson, S.; Marciu, D.; Dorn, H. C.; Balch, A. L. Angewandte Chemie International Edition 21, 4, NATURE CHEMISTRY Macmillan Publishers Limited. All rights reserved

33 DOI: 1.138/NCHEM.2363 (6) Campanera, J. M.; Bo, C.; Olmstead, M. M.; Balch, A. L.; Poblet, J. M. The Journal of Physical Chemistry A 22, 16, (66) Cai, T.; Xu, L.; Gibson, H. W.; Dorn, H. C.; Chancellor, C. J.; Olmstead, M. M.; Balch, A. L. Journal of the American Chemical Society 27, 129, , PMID: (67) Krause, M.; Popov, A.; Dunsch, L. ChemPhysChem 26, 7, (68) Chen, C.-H.; Lin, D.-Y.; Yeh, W.-Y. Chemistry A European Journal 214, n/a n/a. (69) Stevenson, S.; Rottinger, K. A. Inorganic Chemistry 213, 2, (7) Ma, Y.; Wang, T.; Wu, J.; Feng, Y.; Xu, W.; Jiang, L.; Zheng, J.; Shu, C.; Wang, C. Nanoscale 211, 3, (71) Zhang, J.; Bearden, D. W.; Fuhrer, T.; Xu, L.; Fu, W.; Zuo, T.; Dorn, H. C. Journal of the American Chemical Society 213, 13, (72) Beavers, C. M.; Chaur, M. N.; Olmstead, M. M.; Echegoyen, L.; Balch, A. L. Journal of the American Chemical Society 29, 131, , PMID: (73) Popov, A. A.; Krause, M.; Yang, S.; Wong, J.; Dunsch, L. The Journal of Physical Chemistry B 27, 111, , PMID: (74) Zhang, Y.; Popov, A. A.; Dunsch, L. Nanoscale 214, 6, (7) Svitova, A. L.; Popov, A. A.; Dunsch, L. Inorganic Chemistry 213, 2, (76) Wu, J.; Wang, T.; Ma, Y.; Jiang, L.; Shu, C.; Wang, C. The Journal of Physical Chemistry C 211, 11, (77) Xu, W.; Niu, B.; Shi, Z.; Lian, Y.; Feng, L. Nanoscale 212, 4, (78) Yang, H.; Wang, Z.; Jin, H.; Hong, B.; Liu, Z.; Beavers, C. M.; Olmstead, M. M.; Balch, A. L. Inorganic Chemistry 213, 2, (79) Lu, X.; Slanina, Z.; Akasaka, T.; Tsuchiya, T.; Mizorogi, N.; Nagase, S. Journal of the American Chemical Society 21, 132, 896 9, PMID: (8) Lu, X.; Lian, Y.; Beavers, C. M.; Mizorogi, N.; Slanina, Z.; Nagase, S.; Akasaka, T. Journal of the American Chemical Society 211, 133, (81) Kurihara, H.; Lu, X.; Iiduka, Y.; Mizorogi, N.; Slanina, Z.; Tsuchiya, T.; Akasaka, T.; Nagase, S. Journal of the American Chemical Society 211, 133, NATURE CHEMISTRY Macmillan Publishers Limited. All rights reserved

34 DOI: 1.138/NCHEM.2363 (82) Kurihara, H.; Lu, X.; Iiduka, Y.; Nikawa, H.; Mizorogi, N.; Slanina, Z.; Tsuchiya, T.; Nagase, S.; Akasaka, T. Journal of the American Chemical Society 212, 134, (83) Kurihara, H.; Lu, X.; Iiduka, Y.; Nikawa, H.; Hachiya, M.; Mizorogi, N.; Slanina, Z.; Tsuchiya, T.; Nagase, S.; Akasaka, T. Inorganic Chemistry 212, 1, (84) Yamada, M.; Mizorogi, N.; Tsuchiya, T.; Akasaka, T.; Nagase, S. Chemistry A European Journal 29, 1, (8) Feng, L.; Suzuki, M.; Mizorogi, N.; Lu, X.; Yamada, M.; Akasaka, T.; Nagase, S. Chemistry A European Journal 213, 19, (86) Duchamp, J. C.; Demortier, A.; Fletcher, K. R.; Dorn, D.; Iezzi, E. B.; Glass, T.; Dorn, H. C. Chemical Physics Letters 23, 37, (87) Cai, T.; Xu, L.; Anderson, M. R.; Ge, Z.; Zuo, T.; Wang, X.; Olmstead, M. M.; Balch, A. L.; Gibson, H. W.; Dorn, H. C. Journal of the American Chemical Society 26, 128, , PMID: (88) Yang, S.; Chen, C.; Jiao, M.; Tamm, N. B.; Lanskikh, M. A.; Kemnitz, E.; Troyanov, S. I. Inorganic Chemistry 211,, (89) Krause, M.; Dunsch, L. ChemPhysChem 24,, (9) Cerón, M. R.; Li, F.-F.; Echegoyen, L. Chemistry A European Journal 213, 19, (91) Fu, W.; Xu, L.; Azurmendi, H.; Ge, J.; Fuhrer, T.; Zuo, T.; Reid, J.; Shu, C.; Harich, K.; Dorn, H. C. Journal of the American Chemical Society 29, 131, , PMID: (92) Zuo, T.; Beavers, C. M.; Duchamp, J. C.; Campbell, A.; Dorn, H. C.; Olmstead, M. M.; Balch, A. L. Journal of the American Chemical Society 27, 129, (93) Zuo, T.; Olmstead, M. M.; Beavers, C. M.; Balch, A. L.; Wang, G.; Yee, G. T.; Shu, C.; Xu, L.; Elliott, B.; Echegoyen, L.; Duchamp, J. C.; Dorn, H. C. Inorganic Chemistry 28, 47, (94) Krause, M.; Wong, J.; Dunsch, L. Chemistry A European Journal 2, 11, (9) Yang, S.; Popov, A.; Kalbac, M.; Dunsch, L. Chemistry A European Journal 28, 14, NATURE CHEMISTRY Macmillan Publishers Limited. All rights reserved

35 DOI: 1.138/NCHEM.2363 (96) Yang, S.; Popov, A. A.; Chen, C.; Dunsch, L. The Journal of Physical Chemistry C 29, 113, (97) Zhang, Y.; Popov, A. A.; Schiemenz, S.; Dunsch, L. Chemistry A European Journal 212, 18, (98) Akasaka, T.; Nagase, S.; Kobayashi, K.; Wälchli, M.; Yamamoto, K.; Funasaka, H.; Kako, M.; Hoshino, T.; Erata, T. Angewandte Chemie International Edition in English 1997, 36, (99) Nishibori, E.; Takata, M.; Sakata, M.; Taninaka, A.; Shinohara, H. Angewandte Chemie International Edition 21, 4, (1) Yamada, M.; Wakahara, T.; Nakahodo, T.; Tsuchiya, T.; Maeda, Y.; Akasaka, T.; Yoza, K.; Horn, E.; Mizorogi, N.; Nagase, S. Journal of the American Chemical Society 26, 128, , PMID: (11) Yamada, M.; Minowa, M.; Sato, S.; Kako, M.; Slanina, Z.; Mizorogi, N.; Tsuchiya, T.; Maeda, Y.; Nagase, S.; Akasaka, T. Journal of the American Chemical Society 21, 132, (12) Yamada, M.; Someya, C.; Wakahara, T.; Tsuchiya, T.; Maeda, Y.; Akasaka, T.; Yoza, K.; Horn, E.; Liu, M. T. H.; Mizorogi, N.; Nagase, S. Journal of the American Chemical Society 28, 13, (13) Yamada, M.; Okamura, M.; Sato, S.; Someya, C.; Mizorogi, N.; Tsuchiya, T.; Akasaka, T.; Kato, T.; Nagase, S. Chemistry A European Journal 29, 1, (14) Ishitsuka, M. O.; Sano, S.; Enoki, H.; Sato, S.; Nikawa, H.; Tsuchiya, T.; Slanina, Z.; Mizorogi, N.; Liu, M. T. H.; Akasaka, T.; Nagase, S. Journal of the American Chemical Society 211, 133, (1) Feng, L.; Gayathri Radhakrishnan, S.; Mizorogi, N.; Slanina, Z.; Nikawa, H.; Tsuchiya, T.; Akasaka, T.; Nagase, S.; Martín, N.; Guldi, D. M. Journal of the American Chemical Society 211, 133, (16) Yamada, M.; Minowa, M.; Sato, S.; Slanina, Z.; Tsuchiya, T.; Maeda, Y.; Nagase, S.; Akasaka, T. Journal of the American Chemical Society 211, 133, (17) Wakahara, T.; Yamada, M.; Takahashi, S.; Nakahodo, T.; Tsuchiya, T.; Maeda, Y.; Akasaka, T.; Kako, M.; Yoza, K.; Horn, E.; Mizorogi, N.; Nagase, S. Chem. Commun. 27, NATURE CHEMISTRY Macmillan Publishers Limited. All rights reserved