Ythrene: From the Real Radical Fullerene Substructure to Hypothetical

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C: Physical Processes in Nanomaterials and Nanostructures

Ythrene: From the Real Radical Fullerene Substructure to Hypothetical (Yet?) Radical Molecules Ayrat R. Khamatgalimov, Manuel Melle-Franco, Alsu Akhmetovna Gaynullina, and Valeri I. Kovalenko J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b10526 • Publication Date (Web): 31 Dec 2018 Downloaded from http://pubs.acs.org on January 9, 2019

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The Journal of Physical Chemistry

Ythrene: From the Real Radical Fullerene Substructure to Hypothetical (Yet?) Radical Molecules Ayrat R. Khamatgalimov,1,2 Manuel Melle-Franco,3 Alsu A. Gaynullina2 and Valeri I. Kovalenko1,2* 1A.

E. Arbuzov Institute of Organic and Physical Chemistry, FRC Kazan Scientific Center, Russian Academy of Sciences, 8 Arbuzov str., Kazan, 420088, Russian Federation

2Kazan

National Research Technological University, 68 Karl Marx str., Kazan, 420015, Russian Federation

3CICECO-Aveiro

Institute of Materials, Department of Chemistry, University of Aveiro, 3810-

193, Aveiro, Portugal

ACS Paragon Plus Environment

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ABSTRACT Among higher fullerenes that obey the isolated pentagon rule (IPR) there are appreciable share of fullerenes with open electron shells. For the long time this rule was used as a criterion for fullerene stability. Notwithstanding the IPR, fullerene radicals are unstable as pristine fullerenes but may be stabilized as their derivatives. Mainly, the molecules of such fullerenes contain phenalenyl radical substructures. Here for the first time we found and theoretically investigated a new radical substructure of fullerene molecules of IPR isomer 7 (C3v) of C82 that bears two unpaired electrons and of IPR isomer 822 (D3d) of C104 with two equivalent substructures (four unpaired electrons). The fullerenes were obtained and their molecular structures were reliable characterized experimentally as endohedral derivatives. According to our computations, two hypothetical polyaromatic radical molecules C34H18 and C34H12, which are the models of the fullerene substructure, have the same open-shell triplet ground states. Peculiarities of distribution of spin densities of radical substructures are disclosed.


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I. INTRODUCTION The remarkable feature of fullerenes Cn is their strict geometrical forms as closed convex polyhedra; the structural topology of any isomer of any fullerene Cn is a priori known, i.e., the relative positions of 12 pentagons and (n-20)/2 hexagons in the molecule are completely defined.1 Next important distinctive feature of fullerenes is the absence of a priori information about their stability, i.e., it is unknown whether it would be possible to synthesize and isolate a given fullerene and to characterize the stability of its molecule. In general, up to now, fullerenes are obtained sporadically. An empirical rule of isolated pentagons (IPR) appeared after the discovery of the molecular structures of first most stable fullerenes C60, C70, etc. IPR suggested that fullerene molecule in which all 12 pentagons are separated by hexagons have to be stable and conversely the molecule with some abutting pentagons is unstable.2,3 In fact, all fullerenes that were obtained, isolated and characterized during the first period after their discovery in 1985, were obeying IPR. Later, many of non-IPR fullerenes were obtained as derivatives, see e.g.4,5 Moreover, we showed that some IPR fullerenes are unstable due to their geometry or electronic features and cannot be extracted as pristine fullerenes.6,7 The first one is a topological problem when there are fragments of a molecule containing too many condensed hexagons. They tend to be flat against curved fullerene cage. This is the reason for high local overstrains, that prevent the formation of fullerene molecules. The number of such fullerenes is limited, most prominent examples are C84 IPR isomers 1 (D2), 2 (C2), and 20 (Td), none of them has been obtained experimentally as pristine fullerenes or as their derivative.8 The hexagon overcrowding of such fullerenes is easy to catch by analyzing only its Schlegel diagram. On the contrary, the electronic problem requires more detailed analysis; first of all, it concerns the radical origin of a fullerene molecule. The number of such unstable fullerenes is very high; for example, starting


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with C72 up to C86 the whole number of IPR isomers is equal to 68; between them, there are only 6 overstrained molecules but 30 radical ones (Table 1). Table 1. IPR isomers of unstable pristine fullerenes Cn (n = 72-86)7 unstable IPR isomers*

total number of IPR isomers

overstrained

radicals

(closed electronic shell)

(open electronic shell)

72

1

1(D5h)

-

74

1

-

1(D3h)

76

2

-

2(Td)

78

5

4(D3h)

-

80

7

-

3(C2v); 4(D3); 5(C2v); 6(D5h); 7(Ih)

82

9

-

7(C3v); 8(C3v); 9(C2v)

84

24

1(D2); 2(C2); 20(Td)

3(Cs); 8(C2); 9(C2); 10(Cs)

86

19

2(C2)

1(C1); 3(C2); 4(C2); 5(C1); 6(C2); 7(C1); 8(Cs); 9(C2v); 10(C2v); 11(C1); 12(C1); 13(C1); 14(C2); 15(Cs); 18(C3); 19(D3)

Cn

*IPR isomer numbering according to1. Earlier Diener and Alford proposed that fullerenes should be divided into two classes, first one would include fullerenes that have a large energy gap between the highest occupied and lowest unoccupied molecular orbitals (HOMO-LUMO), in particular, fullerenes C60 and C70, and the other class was suggested to consist of fullerenes that have either small HOMO-LUMO gap or a radical structure with unpaired electrons.9 Stabilization of radical-fullerene arises by filling-up an open electron shell with "lacking" electron(-s), i.e. by closing its electron shell. It occurs in reactions of radical addition: a) of the fullerene molecules themselves, e.g. polymerization of C74 (D3h) and C76 (Td);10,11 b) of some organic molecules to fullerene, e.g. perfluoroalkylation of C74 (D3h), C76 (Td), and C80 (C2v), etc.12-14 The list of endohedral derivatives of radical fullerenes is


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much wider.4 In the electric arc such fullerene appears to get deficient electrons from plasma forming an ionic pair of the fullerene cage as an anion with closed electron shell and metal cation(-s) inside. In the semiempirical approach developed by us (for details see Supporting Information), a fullerene molecule is considered as containing a number of different substructures which form the fullerene cage and are resembling their aromatic analogues such as corannulene, s-indacene, coronene, pyrene, perylene, phenalenyl-radical, etc. (Figures S1-S3).6,7 Most of studied IPR fullerenes include phenalenyl-radical substructures in their cages;7 all of them are unstable as pristine fullerenes. Here we found for the first time and theoretically investigated a new radical substructure, which has two unpaired electrons: one is in the molecule of the IPR isomer 7 (C3v) of C82 and two equivalent substructures are in IPR isomer 822 (D3d) of C104; both fullerenes were obtained and characterized experimentally as endohedral derivatives. The molecular structures of both endohedral IPR fullerene Sm@C82 (C3v) and Sm2@C104 (D3h) were strictly defined by singlecrystal X-ray analysis and by

13C

NMR method.15-17 The molecule of isomer 822 of the

Sm2@C104 (D3h) looks like a closed short nanotube with the pair of equivalent cups at the poles;17 each of both Sm2+ cations inside the cage is located close to the substructure. According to our computations of hypothetical polyaromatic radical molecules C34H18 and C34H12 - the models of the fullerene substructure - have the same open-shell triplet ground states as the fullerene substructure. II. METHODOLOGY AND COMPUTATIONAL DETAILS All calculations were accomplished using the GAUSSIAN`03 and GAUSSIAN`09 program packages.18,19 The molecular structures of all researched structures were fully optimized using


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DFT B3LYP functional20,21 with the 6-31G* basis. In addition, CAM-B3LYP with the 6-31G** basis set, which was found to reproduce better higher-level calculations in a related system, were performed in selected cases. The geometry optimization was performed without the symmetry constraints. The default cutoffs on forces and step size at structural optimizations were used: our calculated molecular geometries were relaxed until forces were below 0.000450 Hartree/Bohr and 0.001800 Hartree/Radians. The standard keywords in the GAUSSIAN were used in optimization processes. Because the researched structures were suggested as radicals, the quantum-chemical calculations were carried out also in triplet and singlet biradical configurations using unrestricted Kohn-Sham methodology. For singlet open-shell configuration we used a quadratically convergent SCF procedure since regular SCF with DIIS extrapolation did not lead to SCF convergence. To ensure the calculated structures were indeed minima, vibrational analyses were performed using the same methods. III. RESULTS AND DISCUSSION As we mentioned earlier, the presence of phenalenyl-radical substructure(-s) (PRS) with unpaired electron leads to instability of the whole fullerene molecule. Many IPR fullerene molecules have more than one PRS, which are spatially separated in the molecule, e.g. two PRS of fullerene C74 (D3h)22 as well as four PRS of fullerene C76 (Td) (see Figure S2 in Supporting Information).23 Moreover, there are complicated molecular structures of IPR fullerenes which appear to contain radical substructures comprising stuck together PRS "constructions".7 When studying new IPR fullerene molecule of isomer 822 (D3d) of C104 we found out that both cups of it contain the same substructure that was found earlier in isomer 7 (C3v) of IPR fullerene C82, which has been shown to be a radical one (Figure 1).24


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Figure 1. 3D (two views) and Schlegel diagrams of the IPR fullerene molecules: C104, isomer 822 (D3d) (top), and C82, isomer 7 (C3v) (bottom). Radical substructures are shown by dashed lines, central atoms of their phenalenyl fragments marked by bold points. To the best of our knowledge, there is no data concerning the molecular and electronic structure of polyaromatic molecules, which may serve as models for this substructure similarly as phenalenyl molecule is a suitable model for PRS. That is why we study here two molecules C34H18 and C34H12 as analogues of the substructure in question. The molecule C34H18 (Figure 2a) has a structure resembling three-blade propeller and we named it, as well as all structures in the paper as Ythrene, by analogy with Zethrene and Uthrene. These molecules are both isomers of C24H14, which consist of two fused phenalenyl fragments, and resemble the alphabet letters Z and U; yet they present very different electronic properties, Uthrene is a diradical while Zethrene has a closed-shell ground state.25 Ythrene-p molecule C34H12 is more similar to the Ythrene substructure of the fullerenes, as it contains three pentagons (Figure 2b) forming a bowl shaped fragment that perfectly meets the fullerene curvature. Being comprised of three phenalenyls, the


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Ythrenes are fused in such a way that an additional, fourth, central phenalenyl moiety appears (atoms a-b-c-d in Figure 2).

A

B

C

Figure 2. (A) Ythrene C34H18, (B) Ythrene-p C34H12 and (C) Ythrene substructure in fullerene. Upper row: schemes of molecular structures with bonds distribution; middle and bottom rows: the calculated 3D molecular structures (two projections). Recently we showed that isomer 7 (C3v) of C82 fullerene (Figure 1, bottom), including Ythrene substructure, has a radical character, i.e. its molecule contains two unpaired electrons and, accordingly, it may be unstable.24 Quantum-chemical calculations show that the lowest energy wave function of this open-shell isomer is a triplet (Table 2). The structure of IPR isomer 822 (D3d) of C104 fullerene contains just two Ythrene substructures (Figure 1, top). Quantum-chemical calculations also proved the assumption of the open nature of


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the electron shell of isomer 822 (D3d) of C104 fullerene (Table 2): both the calculated relative energies and the size of the HOMO-LUMO gap for the singlet biradical configuration seem to be more energetically favorable than for the quintet one. There is an apparent contradiction of experimental data and calculations (see below): the sharp drop of molecular symmetry from D3d to C1 for the best energetic parameter of singlet biradical and only two unpaired electrons instead of two pairs of them according to the molecular structure of the isomer 822 (D3d); the symmetry "returns" for quintet but fail in energy. Both Ythrene molecules C34H18 and p-C34H12 have a triplet ground state (Table 2). Table 2. Relative energies (ΔE, kcal/mol) and HOMO-LUMO gaps (eV) of IPR isomers 7 (C3v) of C82 and isomer 822(D3d) of C104 fullerenes, Ythrene C34H18 and Ythrene-p C34H12 configuration

ΔE

HOMO-LUMO

isomer 7 (C3v) of C82 fullerene singlet (Cs)

4

0.85

singlet biradical (Cs)

3

0.97

triplet (C3v)

0

1.16

quintet (C3v)

30

0.48

isomer 822 (D3d) of C104 fullerene singlet (D3d)

1

0.91

singlet biradical (C1)

0

1.00

triplet (C1)

4

0.58

quintet (D3d)

5

0.72

Ythrene C34H18 singlet

0 (0)*

1.08

singlet biradical

-3 (-5)

1.19

triplet

-6 (-10)

1.46


9


quintet

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51

1.32

Ythrene-p C34H12 singlet

*

0 (0)*

0.33

singlet biradical

-10 (-9)

1.26

triplet

-16 (-26)

1.61

quintet

53

1.56

In parentheses – results by CAM-B3LYP/6-31g(*) level of theory. The spin densities of triplet ground state for Ythrenes are presented in Table 3: the maximal

spin densities are symmetrically localized on three adjacent atoms b of central phenalenyl as well on periphery atoms f and g as also found for uthrene.25 The distribution of spin densities of C34H18 and C34H12 are very similar (Figure 3). It should be noted that spin densities are mainly concentrated on Ythrene substructures in triplet configuration of isomer 7 (C3v) of C82 fullerene and isomer 822 (D3d) of C104 fullerene (see Tables S1 in Supporting Information). Table 3. Mulliken spin densities of Ythrene molecule C34H12 (C3v) and fullerene substructures atoms* a (1)

b (3)

c (6)

d (3)

e (3)

f (6)

g (6)

h (6)

C34H12 (C3v)

-0.173

0.329

-0.111

0.075

-0.052

0.185

0.179

-0.060

C82 #7 (C3v)

-0.187

0.315

-0.105

0.062

-0.045

0.151

0.152

-0.047

C104 #122 (D3d)

-0.138

0.254

-0.083

0.051

-0.024

0.175

0.131

-0.046

*numbering

is according to Figure 2c; the numbers of equivalent atoms are given in the

brackets.


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Figure 3. Distribution of spin densities in the molecules C34H12 (left) and C34H18 (right). Hydrogen atoms are not shown. So, molecules of IPR isomer 7 (C3v) of C82 fullerene and IPR isomer 822 (D3d) of C104 fullerene have an open-shell structure as they include radical substructures (like phenalenylradical substructure). It means that they are chemically unstable and cannot be obtained as empty molecules. However, they may become stable as exohedral or endohedral derivatives due to well known “donating” electrons to the electron-deficient radical substructures of fullerene cage or in polymeric forms. Our results are in excellent agreement with published experimental and theoretical data that altogether shed light on the steps of structural transformations of radical-fullerenes. The biradical origin of the Ythrene substructure of IPR isomer 7 (С3v) of fullerene C82 led to obtaining of [email protected],16 Thus, this fullerene molecule has the charge of -2 and closed electron shell that makes it more stable resulting in a neutral molecule with Sm2+ cation inside. The endohedral molecule of IPR isomer 822 (D3d) of Sm2@C104 goes through the same transformations keeping in mind four unpaired electrons in two equivalent Ythrene substructures on the cups of fullerene cage.17 The stability of a closed electron shell has convincing corroboration with data published by A. Fortea-Rodriguez et al.;26 their calculations showed that IPR isomer 822 (D3d) of C104 conceded in stability to nearly all IPR isomers of C104, but conversely it became the most stable isomer in the row of tetraionic IPR isomers of C104. The next convincing evidence of the Ythrene


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substructure in IPR isomer 7 (С3v) of fullerene C82 is the durable experimental study of the synthesis and molecular structure of stable La@C82(C6H3Cl2), which was unambiguously revealed by single-crystal X-ray analysis.27 Lanthanum has valence of 3, but, according to our data, the IPR isomer 7 of fullerene C82 has two unpaired electrons. In this case, the fullerene cage needs one extra electron to form a neutral ionic pair of endohedral species. It means that such a construction becomes unstable ion-radical, but after addition of aromatic radical C6H3Cl2● it transforms into a stable substance, consisting of anion C82(C6H3Cl2)3-, with closed electronic shell, keeping La3+ cation inside. Now we have some important information concerning a distribution of spin densities in molecules of radical fullerenes. The spin density is mainly concentrated on atoms of radical substructure and so added electrons locate namely at that substructure, but not on the whole molecule. In turn, it predetermines a position of cation(-s) inside its endohedral derivative or the order of radical addition in reactions of synthesis of exohedral derivatives. The problem of the interplay of retention of symmetry, matching of multiplicity, and total energy calculations are outside of the scope of this report and will be discussed elsewhere. IV. CONCLUSIONS Thus, for the first time we disclosed and theoretically studied the new radical substructure of IPR fullerene molecules, namely, isomer 7 (C3v) of C82 that includes two unpaired electrons and isomer 822 (D3d) of C104 that contains two equivalent substructures (four unpaired electrons); both fullerenes were obtained as endohedral derivatives Sm@C82 and Sm2@C104 and characterized experimentally by single-crystal X-ray analysis. Such substructure(-s) leads to the open-shell electron structure of the whole fullerene molecule and respectively to its chemical instability. However, radical fullerenes can be stabilized as various derivatives (exohedral or


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endohedral) or in polymeric forms. We proposed two new polyaromatic radical Ythrene molecules C34H18 and C34H12, they are the models of the fullerene substructure and also have the open-shell triplet ground states.

ASSOCIATED CONTENT Supporting Information. Modeling procedure. Schlegel diagrams of IPR fullerene molecules: C60 (Ih) which consists only of corannulene substructures, and C70 (D5h) which contains two corannulene substructures and five s-indacene substructures. Schlegel diagrams of fullerene C74 (D3h), phenalenyl-radical substructure and fullerene C76 (Td). Most common substructures of fullerene molecules, named after their organic analogues: corannulene, its components sumanene, naphthalene; s-indacene; coronene; and phenalenyl-radical. Mulliken atomic spin densities. Atoms numbering in IPR fullerene molecules of C104 (isomer 822 (D3d)), C82 (isomer 7 (C3v)) and Ythrene-p C34H12. Calculated frequencies, IR intensities and IR spectra for IPR isomer 7 (C3v) of fullerene C82, IPR isomer 822 (D3d) of fullerene C104, and hypothetical structures Ythrene C34H18 and Ythrene-p C34H12. This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author * E-mail: [email protected] Author Contributions


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The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. ACKNOWLEDGMENT This work was partially funded by Russian Foundation for Basic Research, research project No. 18-29-19110mk. M. Melle-Franco would like to acknowledge support from the Portuguese “Fundação para a Ciência e a Tecnologia” (IF/00894/2015) and from CICECO – Aveiro Institute of Materials, POCI-01-0145-FEDER007679 (UID/CTM/50011/2013). Authors thank Mrs. Yekaterina Kovalenko (University of Florida) for her assistance in preparing the manuscript. REFERENCES (1) Fowler, P. W.; Manolopoulos, D. E. An Atlas of Fullerenes; Dover Publications, Inc.: Mineola, NY, USA, 2006. (2) Kroto, H. W. The Stability of the Fullerenes Cn, with n = 24, 28, 32, 36, 50, 60 and 70. Nature 1987, 329, 529-531. (3) Schmalz, T. G.; Seitz, W. A.; Klein D. J.; Hite G. E. Elemental Carbon Cages. J. Am. Chem. Soc. 1998, 110, 1113-1127. (4) Yang, S.; Wang, C. R. Endohedral Fullerenes. From Fundamentals to Applications; World Scientific Publ. New Jersey, London, Singapore, Beijing, Shanghai, Hong Kong, Taipei, Chennai, 2014. (5) Tan, Y. Z.; Xie, S. Y.; Huang, R. B.; Zheng, L. S. The Stabilization of Fused-Pentagon Fullerene Molecules. Nature Chem. 2009, 1, 450-460.


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(6) Kovalenko, V. I.; Khamatgalimov, A. R. Regularities in the Molecular Structure of Stable Fullerenes. Russ. Chem. Rev. 2006, 75, 981-988. (7) Khamatgalimov, A. R.; Kovalenko, V. I. Structures of Unstable Isolated-Pentagon-Rule Fullerenes C72-C86 Molecules. Russ. Chem. Rev. 2016, 85, 836-853. (8) Khamatgalimov, A. R.; Luzhetskii, A. V.; Kovalenko. V. I. Unusual Pentagon and Hexagon Geometry of Three Isomers (No 1, 20, and 23) of Fullerene C84. Int. J. Quant. Chem. 2008, 108, 1334–1339. (9) Diener, M. D.; Alford, J. M. Isolation and Properties of Small-Bandgap Fullerenes. Nature 1998, 393, 668-671. (10) Yeretzian, C.; Wiley, J. B.; Holczer, K.; Su, T.; Nguyen, S.; Kaner, R. B.; Whetten, R. L. Partial Separation of Fullerenes by Gradient Sublimation. J. Phys. Chem. 1993, 97, 1009710101. (11) Khamatgalimov, A. R.; Kovalenko, V. I. Radical IPR Fullerenes C74 (D3h) and C76 (Td): Dimer, Trimer, etc. Experiments and Theory. J. Phys. Chem. C 2018, 122, 3146-3151. (12) Shustova, N. B.; Kuvychko, I. V.; Bolskar, R. D.; Seppelt, K.; Strauss, S. H.; Popov, A. A.; Boltalina, O. V. Trifluoromethyl Derivatives of Insoluble Small-HOMO LUMO-Gap Hollow Higher Fullerenes. NMR and DFT Structure Elucidation of C2-(C74-D3h)(CF3)12, Cs-(C76Td(2))(CF3)12, C2-(C78-D3h(5))(CF3)12, Cs-(C80-C2v(5))(CF3)12, and C2-(C82-C2(5))(CF3)12. J. Am. Chem. Soc. 2006, 128, 15793-15798. (13) Boltalina, O. V.; Popov, A. A.; Kuvychko, I. V.; Shustova, N. B.; Strauss, S. H. Perfluoroalkylfullerenes. Chem. Rev. 2015, 115, 1051−1105.


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(21) Lee, C.; Yang, W.; Parr, R.G. Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density. Phys. Rev. B 1988, 37, 785-789. (22) Kovalenko, V. I.; Khamatgalimov, A. R. Open-Shell Fullerene С74: Phenalenyl-Radical Substructures. Chem. Phys. Lett. 2003, 377, 263-268. (23) Khamatgalimov, A. R.; Kovalenko, V. I. Stability of Isolated-Pentagon-Rule Isomers of Fullerene C76. Fuller. Nanotub. Car. Nanostruct. 2015, 23, 148-152. (24) Khamatgalimov, A. R.; Kovalenko, V. I. Electronic Structure and Stability of Fullerene C82 IPR Isomers J. Phys. Chem. A 2011, 115, 12315-12320. (25) Melle-Franco, M. Uthrene, a Radically New Molecule? Chem. Commun. 2015, 51, 53875390. (26) Rodriguez-Fortea, A.; Alegret, N.; Balch, A. L.; Poblet, J. M. The Maximum Pentagon Separation Rule Provides a Guideline for the Structures of Endohedral Metallofullerenes. Nature Chem. 2010, 2, 955-961. (27) Akasaka, T.; Lu, X.; Kuga, H.; Nikawa, H.; Mizorogi, N.; Slanina, Z.; Tsuchiya, T.; Yoza, K.; Nagase, S. Dichlorophenyl Derivatives of La@C3v(7)-C82: Endohedral Metal Induced Localization of Pyramidalization and Spin on a Triple-Hexagon Junction. Angew. Chem. Int. Ed. 2010, 49, 9715 –9719. TOC Graphic


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Figure 1. 3D (two views) and Schlegel diagrams of the IPR fullerene molecules: C104, isomer 822 (D3d) (top), and C82, isomer 7 (C3v) (bottom). Radical substructures are shown by dashed lines, central atoms of their phenalenyl fragments marked by bold points. 121x73mm (300 x 300 DPI)



Figure 2. (A) Ythrene C34H18, (B) Ythrene-p C34H12 and (C) Ythrene substructure in fullerene. Upper row: schemes of molecular structures with bonds distribution; middle and bottom rows: the calculated 3D molecular structures (two projections). 122x99mm (300 x 300 DPI)


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82x38mm (300 x 300 DPI)


Ythrene: From the Real Radical Fullerene Substructure to Hypothetical

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