From Fulleranes to Icosahedral Diamondoids - American Chemical

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J. Phys. Chem. C 2007, 111, 18118-18126

Structural Characteristics of Hydrocarbon Cages: From Fulleranes to Icosahedral Diamondoids Mikko Linnolahti,* Antti J. Karttunen, and Tapani A. Pakkanen UniVersity of Joensuu, Department of Chemistry, P.O. Box 111, FI-80101 Joensuu, Finland ReceiVed: August 6, 2007; In Final Form: September 18, 2007

We describe the structural principles of two novel families of cage hydrocarbons: icosahedral fulleranes and diamondoids. Quantum chemical calculations are performed for the fulleranes and the diamondoids up to C980H980 and C1100H300 in size. The fulleranes are significantly stabilized by partial endo-hydrogenation, resulting in remarkably stable hollow (CH)n cages. The structural principles of the icosahedral diamondoids can be derived from multilayered fulleranes. Thermodynamic stabilities of the icosahedral diamondoids are verified by comparisons to crystalline forms of hydrocarbons together with the conventional octahedral diamondoids up to C969H324. Spectral features of the fulleranes and diamondoids are analyzed from the perspectives of their possible existence in space and structural characterization. The described structural motifs of the fulleranes and diamondoids are expected to aid in identification and characterization of the experimentally known hydrocarbon and diamond nanostructures.

Introduction The structural chemistry of hydrocarbons is exceptionally rich. In addition to the infinite combinations of chains and rings, the hydrocarbons are capable of forming both hollow and filled cages. Among the hollow hydrocarbon cages, the polyhedral cubane1 and dodecahedrane,2 synthesized in 1964 and 1982, respectively, are illustrative examples. An example of a filled cage is the decamantane, one of the higher diamondoids, which can be isolated from petroleum.3 The Ih-symmetric dodecahedrane, C20H20, is the smallest fullerane, i.e., perhydrogenated fullerene. Several attempts have been made to prepare higher fulleranes, C60H60 in particular.4 The buckminsterfullerene5 has been partially hydrogenated up to C60H36.6 Perhydrogenation of C60 would introduce significant structural strain due to the bond angles being unfavorable for sp3 hybridization. However, the fulleranes can be stabilized by partial endo-hydrogenation.7 To fully exploit this “in-out” isomerism, one needs to shift to fulleranes larger than C60H60. The smallest Ih-symmetric fulleranes significantly stabilized by partial endo-hydrogenation are C80H80 and C180H180. They were recently shown to be thermodynamically favored over previously reported (CH)n cages,8 including the dodecahedrane.9 Adamantane,10 the smallest hydrocarbon cage in the series of diamondoids, was first isolated from petroleum in 1933.11 Its facile synthesis followed in 1957.12 To date, diamondoids up to tetramantane13 have been synthesized; preparation of higher diamondoids having been prevented by kinetic aspects.14 However, the higher diamonds can be isolated from petroleum.15 Dahl and co-workers3,16 have recently reported the isolation and structures of diamondoids up to undecamantane consisting of 11 fused adamantane cages. Structurally, the diamondoids can be considered as finite hydrogen-terminated clusters cut from the diamond lattice. The line drawn between what is a diamondoid and what is a diamond is undefined.17 * To whom correspondence should be addressed. E-mail: Mikko. [email protected].

In the theoretical study reported herein, we derive the structural principles of the icosahedral fulleranes and introduce a new family of icosahedral diamondoids. The thermodynamic stabilities of the hydrocarbon cages are determined by comparisons with octahedral diamondoids cut from diamond lattice together with crystalline forms of hydrocarbons. Computational Details The fulleranes and the diamondoids were studied by hybrid density functional B3LYP and ab initio MP2 methods. The structures of the molecules were fully optimized within their respective point group symmetries using TURBOMOLE versions 5.8 and 5.9.18,19 Periodic geometry optimizations and frequency calculations of cubic diamond, hydrogenated diamond (111) slab, and polyethene chain were carried out by the CRYSTAL06 program.20 To enable comparisons between molecular and periodic B3LYP calculations, a modified 6-21G* basis set for carbon21 and the standard 6-31G** basis set for hydrogen were employed. In the MP2 calculations, the resolution-of-the-identity (RI) technique22 was utilized. A triple-ζ valence basis set23 in combination with a matching RI auxiliary basis set24 was applied with MP2. B3LYP vibrational frequency calculations25 were performed for systems up to 286 carbon atoms, verifying them as true minima. A harmonic frequency scaling factor of 0.9614 was adopted for B3LYP frequencies.26 The Gaussian 03 program27 was used for calculation of the Raman spectra. The NMR spectra were calculated by TURBOMOLE.28 The NMR chemical shifts are reported with respect to TMS. In the case of the TMS reference, the SVP29 basis set was used for silicon in B3LYP calculations and TZVP in MP2 calculations. Results and Discussion Icosahedral Fulleranes. Dodecahedrane,2 C20H20, is the first member in the series of icosahedral fulleranes, the next being C60H60, i.e., the perhydrogenated buckminsterfullerene (Figure 1).30 Most efforts to synthesize fulleranes have been focused

10.1021/jp076284s CCC: $37.00 © 2007 American Chemical Society Published on Web 11/16/2007

Structural Characteristics of Hydrocarbon Cages

Figure 1. The four smallest Ih-symmetric fullerenes and their perhydrogenated fullerane counterparts together with the hydrogenated diamond (111) sheet (C∞H∞). Equivalent atoms are marked by colors: gray ) C in the pentagon; white ) H connected to the pentagon; yellow ) C of the six-membered ring pointing inward toward the cage center; red ) H pointing inward; green ) C of the six-membered ring pointing outward from the cage; blue ) H pointing outward from the sixmembered ring.

on C60H60,4 but it has remained unattainable. There is an apparent reason for the dodecahedral C20H20 being stable, but the truncated icosahedral C60H60 not. The bond angles of 108° in dodecahedron, composed of 12 pentagons, are nearly optimal for sp3 hybridization. In addition to the 12 pentagons, C60 contains 20 hexagons. The bond angles in hexagons are 120°, which is optimal for sp2 hybridization but unfavorable for sp3 hybridization. The structural strain of perhydrogenated fulleranes can be decreased by partial hydrogenation inside the cage. This “inout” isomerism results in puckering of the hexagons, allowing them to adopt angles more favorable for sp3 hybridization. In the case of C60H60,7 the puckering of the hexagons breaks the optimal planar arrangement of the pentagons, providing only marginal gains in energy. The in-out isomerism becomes relevant from C80H80 on (Figure 1).9 Each set of three pentagons of the Ih-symmetric C80 is connected via a carbon atom. Endo-

J. Phys. Chem. C, Vol. 111, No. 49, 2007 18119 hydrogenation of the interconnecting atoms combined with exohydrogenation of the pentagons results in optimal puckering of the hexagons, while allowing the pentagons to retain their planarity. The in-out isomeric structural motif of the C80H80 applies also for larger fulleranes, as has been demonstrated for C180H180, the next Ih-symmetric fullerane in size. Both C80H80 and C180H180 are thermodynamically favored over the C20H20 dodecahedron, previously considered as the least strained (CH)n cage.8 Here we apply the in-out isomerism to larger fulleranes, allowing us to deduce the general structural principles of the icosahedral fulleranes. On the basis of the ring topologies, the fulleranes can be divided into two structural families of (CH)n cages: (1) n ) 20, 80, 180, 320, 500, ..., 20m2 and (2) n ) 60, 240, 540, 960, 1500, ..., 60m2. The members of the first and the second series have ring topologies corresponding to the Ihsymmetric (h, 0) and (h, k), h ) k fullerenes, respectively.31 The first member of series 60m2 is the perhydrogenated C60 fullerene with 20 fully exo-hydrogenated hexagons, which are present in each member of the series. The first three members of the series 20m2 are those reported previously,9 namely, C20H20 dodecahedrane, C80H80, and C180H180. The next members of the series, C320H320, C500H500, C720H720, and C980H980 are shown in Figure 2. The faceted icosahedral shape is clearly seen in the larger fulleranes. The cages can be considered as being sewed up from 20 hydrogenated diamond (111) slabs (Figure 1). As a consequence, the structures of the icosahedral fulleranes approach the hydrogenated diamond (111) slab as a function of their size. The same applies for the 60m2 series, but the number of facets is 60 due to the additional 20 exo-hydrogenated hexagons. The structural principles described here apply likewise to the heavier group 14 hydrides32 and to phosphorus.33 The hydrogenated diamond (111) slab is a representative of a strain-free system, which we hence applied as a reference for determination of the strain energies of the fulleranes. The strain energies calculated at the B3LYP level of theory are listed in Table 1. The strain energies of the fulleranes systematically decrease as a function of the size of the cage within each series, approaching the hydrogenated diamond (111) slab. The series 20m2 is favored over the 60m2 series, which is due to the 20 fully exo-hydrogenated hexagons in the latter. This destabilizing structural feature affects most the long sought C60H60, making it clearly the most strained icosahedral fullerane. The experimentally known dodecahedrane, C20H20, has the largest calculated strain energy, 14.7 kJ/mol per CH unit, among the 20m2 series. For comparison, experimental strain energy of the dodecahedrane is 12.8 kJ/mol per CH unit.34 In the series 60m2, C540H540 is the first fullerane, which is less strained than the dodecahedrane. We repeated the calculations up to C320H320 by the MP2 method (Table 2). Because periodic MP2 calculations are generally unavailable, we used the dodecahedrane as a reference structure. Increasing the level of theory from B3LYP to MP2 further increases the stabilities of the larger fulleranes with respect to the dodecahedrane. On the other hand, the C60H60 becomes even more unfavorable. The icosahedral fulleranes can form multilayered structures, where smaller cages are inside the larger ones. Within the favored 20m2 series, the first feasible bilayered fullerene is C20H20@C180H180. We optimized its structure at the B3LYP level of theory, for which we also calculated the MP2 energy. The carbon-carbon interlayer distance is 3.8 Å. The dispersive interactions, present in multilayered fulleranes, are not adequately described by the B3LYP density functional method.35

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Linnolahti et al. TABLE 1: Strain Energies, HOMO-LUMO Gaps, and Diameters of the Icosahedral Fulleranes Calculated at the B3LYP Level ∆Ea C20H20 C80H80 C180H180 C320H320 C500H500 C720H720 C980H980

14.7 13.6 9.8 7.7 6.2 5.3 4.5

C60H60 C240H240 C540H540 C∞H∞

43.6 20.8 14.2 0.0

gap (eV)

diameter (nm)

Series 20m2 8.49 7.75 7.66 7.45 7.32 7.24 7.18

0.66 1.09 1.55 2.01 2.49 2.96 3.44

Series 60m2

a The strain energies in kJ/mol per CH unit are given relative to the hydrogenated diamond (111) slab (C∞H∞).

TABLE 2: Relative Total Energies of the Icosahedral Fullerenes Calculated at the MP2 Level ∆Ea Series

20m2

C20H20 C80H80 C180H180 C320H320

0.0 -4.9 -8.4 -10.1b Series 60m2

C60H60 C240H240 b

Figure 2. B3LYP-optimized structures of icosahedral fulleranes belonging to the series n ) 20m2, with m ) 4-7.

The B3LYP method finds C20H20@C180H180 1.8 kJ/mol per CH less stable than C180H180, whereas at the MP2 level, accounting for the dispersion, the bilayered fullerane is favored by 1.0 kJ/ mol per CH. Generally, the mth member of the series 20m2 fits

32.0 4.3b

a The energies in kJ/mol per CH unit are given relative to C20H20. Single-point energy calculation for B3LYP-optimized structure.

inside the (m + 2)th member, giving rise to two multilayered series, C20H20@C180H180@C500H500@... and C80H80@C320H320 @C720H720... The described multilayered hydrocarbon nanostructures could help to understand the structural characteristics of the experimentally known hydrocarbon nanoonions.36 Icosahedral Diamondoids. The C80H80 fullerane has 60 exo- and 20 endo-hydrogens. Replacement of the 20 endohydrogens with carbon atoms generates a dodecahedral C20 into the interior of the cage (Figure 3). C20 fits almost perfectly inside the C80H60 outer shell, the layers being covalently bound by C-C bonds with nearly optimal sp3 hybridization. At the B3LYP level of theory, the bond lengths between the layers of C20@C80H60 are 1.53 Å compared to 1.54 Å in bulk diamond. Correspondingly, the C180H180 fullerane having 60 endohydrogens matches with the C20@C80H60 with 60 exohydrogens. Removal of the matching hydrogens results in C20@C80@C180H120, a three-layer icosahedral diamondoid (Figure 3). The structural principles can be generalized, producing a series of icosahedral diamondoids based on the 20m2 series of fulleranes: mth member with its exo-hydrogens removed fits inside the (m + 1)th member with its endo-hydrogens removed. We studied the series up to C20@C80@C180@C320@C500H300, i.e., C1100H300 (Figure 3). Because of the variable C/H ratio, determination of the strain energies for the diamondoids is less straightforward than for the fulleranes. The icosahedral diamondoids consist of two types of sp3-hybridized carbon atoms: Core atoms bound to four other carbons and surface atoms bound to three carbons and to one hydrogen. The bonding of the core carbon atoms is analogous to bulk diamond, whereas the bonding of the surface carbon atoms is analogous to the hydrogenated diamond (111) slab. Bulk diamond and the hydrogenated diamond (111) slab represent strain-free systems with stoichiometries of C and CH,


J. Phys. Chem. C, Vol. 111, No. 49, 2007 18121

Figure 3. B3LYP-optimized structures of the icosahedral diamondoids. The figures on the right are cross sections, illustrating the interior of the diamondoids. The layers are marked by colors: yellow ) C20; green ) C80; blue ) C180; red ) C320; gray ) C500.

respectively. Hence, the strain energy per carbon atom (∆E) of an icosahedral diamondoid (CxHy) can be determined according to eq 1

∆E ) [E(CxHy) - yE(CH) - (x - y)E(C)]x-1

(1)

where E(CH) is the energy of the infinite hydrogenated diamond (111) slab per CH unit and E(C) is the energy of the bulk diamond per C atom. From the computational point of view, the described equation has the further advantage of being homodesmotic,37 i.e., the number of bonds of each type and the states of hybridization are conserved. The strain energies of the icosahedral diamondoids (Table 3) systematically decrease as a function of the size, at least up

TABLE 3: Strain Energies, HOMO-LUMO Gaps, and Diameters of the Icosahedral Diamondoids Calculated at the B3LYP Level C20H20 C100H60 C280H120 C600H200 C1100H300 a

∆Ea

gap (eV)

diameter (nm)

14.7 8.3 6.3 5.2 4.6

8.49 7.39 7.01 6.72 6.46

0.66 1.09 1.56 2.03 2.51

Strain energies in kJ/mol per C atom are calculated from eq 1.

to C1100H300 with diameter of 2.5 nm. Extrapolation to infinity, i.e., to icosahedral diamond, produces a strain energy of 2.9 kJ/mol per C. There is an apparent relationship between the


Linnolahti et al.

Figure 4. B3LYP-optimized structures of the first eight octahedral Td-symmetric diamondoids.

icosahedral diamondoids and the envisaged icosahedral nanodiamonds and silicon quantum dots,38 the diamondoids being nanodiamonds with hydrogenated surfaces. Although there is experimental evidence of diamonds with icosahedral morphology,39 it is not clear if the diamondoids could lead to icosahedral quasicrystals;40 it might require the layers (see Figure 3) to match each other perfectly. This appears not to be the case, however. Although the match is nearly perfect, the inner layers of the larger diamondoids become slightly compressed. This is best seen in the largest of the studied diamondoids, C20@C80@C180@C320@C500H300, where the C-C bond distances between the layers are 1.48, 1.51, 1.53, and 1.55 Å, respectively. Notwithstanding the slight compression, C1100H300 has the lowest strain energy among the studied diamondoids. The situation may change, however, in the case of even larger cages, where the compression becomes substantial. This being the case, the extrapolation of strain energy to 2.9 kJ/mol per C, reported above, does not hold true. Instead, there should be an optimal size for the icosahedral diamondoids. Unfortunately, the study of the next member of the series, C1820H420, was not

practical at the B3LYP level of theory. The inner-core compression of the larger diamondoids might be avoidable by formation of hollow multilayered cages. To examine this possibility, we removed the C20 core of the largest studied diamondoid by replacing the carbon atoms with hydrogens, resulting in a hollow C80H20@C180@C320@C500H300. This species has a strain energy of 4.8 kJ/mol per C, which is somewhat higher than the 4.6 kJ/mol per C for its filled counterpart. Hence, the icosahedral diamondoids, at least up to 2.5 nm in size, favor filled structures. Octahedral Diamondoids. Conventional diamondoids, i.e., cage hydrocarbons with carbon-carbon framework of the diamond lattice,41 have been studied extensively by both experimental42 and theoretical methods.43 The simplest diamondoid, adamantane (C10H16), is an octahedral molecule with Td symmetry. Larger diamondoids can be considered as fused adamantanes. The number of isomers rapidly increases as a function of the size of the diamondoids.44 Here we focus on the octahedral Td-symmetric series, the first eight members of which are illustrated in Figure 4. The next octahedral diamondoid is the decamantane (C35H36), which has been isolated from


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TABLE 4: Strain Energies, HOMO-LUMO Gaps, and Diameters of the Octahedral Diamondoids Calculated at the B3LYP Level C10H16 C35H36 C84H64 C165H100 C286H144 C455H196 C680H256 C969H324 a

∆Ea

gap (eV)

diameter (nm)

3.8 2.4 1.5 0.98 0.66 0.44 0.29 0.18

9.65 8.20 7.55 7.19 6.96 6.79 6.66 6.56

0.50 0.86 1.21 1.57 1.93 2.28 2.64 3.00

Strain energies in kJ/mol per C atom are calculated from eq 2.

petroleum.3 Early theoretical studies suggest it to be energetically favored over adamantane.43b C84H64 was first studied already in 1987 by Almlo¨f et al.43a Spectral features of the diamondoids up to C84H64 have been recently investigated by ab initio methods and, beyond that, by molecular mechanics.43j Little is known about the stabilities of the larger octahedral diamondoids, however.43d We determined the strain energies for the octahedral diamondoids up to C969H324 using the approach described above for the icosahedral diamondoids. In this particular case, there are three types of carbon atoms in the system: (1) core carbon atoms analogous to bulk diamond, (2) surface carbon atoms (CH) analogous to the hydrogenated diamond (111) slab, and (3) one CH2 unit at each vertex of the octahedron, giving a total of six CH2 units for each cage independent of their size. For the stoichiometry of CH2 the strain-free reference is an infinite chain of polyethene. Hence, the strain energy per carbon atom (∆E) of an octahedral diamondoid (CxHy) can be determined from eq 2

∆E ) [E(CxHy) - 6E(CH2) - (y - 6)E(CH) (x - y - 6)E(C)]x-1 (2) where E(CH2) is the energy of the infinite polyethene chain per CH2 unit, E(CH) is the energy of the infinite hydrogenated diamond (111) slab per CH unit, and E(C) is the energy of the bulk diamond per C atom. Note that, likewise to the eq 1, this approach is homodesmotic.37 The strain energies of the octahedral diamondoids are given in Table 4. At the B3LYP level, the strain energy of adamantane is 3.8 kJ/mol per C. For comparison, the early estimation of the strain of adamantane, using acyclic alkanes as references, gives a strain energy of 2.7 kJ/mol per C.45 Prior to that, admantane was generally considered strain-free.10 As expected on the basis of previous calculations,43b the decamantane (C35H36) is less strained than the adamantane. Being cut from the diamond lattice, the diamondoids converge toward the bulk diamond as a function of the size. The strain energies of the larger diamondoids are thus very small, dropping down to only about 0.2 kJ/mol per C for C969H324, the largest of the studied cages. Comparisons between the Diamondoids. The variations in the strain energies of the icosahedral and conventional octahedral diamondoids as a function of their size are illustrated in Figure 5. Expectedly, the strain energies are lower for the octahedral diamondoids, the structures of which approach bulk diamond. The icosahedral diamondoids approach icosahedral diamond quasicrystal, extrapolation to which gives a strain energy of 2.9 kJ/mol per C. However, as noted above, the generation of icosahedral quasicrystals from the diamondoids may require an exact match between the layers, which does not quite seem to

Figure 5. Strain energies and Gibbs corrected strain energies of icosahedral and octahedral diamondoids at the B3LYP level.

be the case. The first member of the icosahedral diamondoids is the experimentally known dodecahedrane, with a strain energy of 14.7 kJ/mol per C. Larger icosahedral diamondoids studied here have strain energies between that of the dodecahedrane and the adamantane. For diamondoids of about the same size, the icosahedral series is approximately 5 kJ/mol per C above the octahedral series in terms of strain energies. Next, we determined the effect of thermodynamics by calculating Gibbs corrections to the strain energies at T ) 298.15 K. Equations 1 and 2, with all energy quantities replaced by the corresponding Gibbs free energies, were employed for icosahedral and octahedral diamondoids, respectively. It is notable that entropy effects make small cycloalkanes favored over the infinite polyethene chain, giving the lowest Gibbs free energies for cyclohexane. Therefore, the reference value for the CH2 unit is taken from the Gibbs free energy of cyclohexane instead of the polyethene chain, previously applied in the case of strain energies. The strain energies together with the Gibbs corrected strain energies are shown in Figure 5. The Gibbs corrections stabilize the smaller diamondoids with respect to the larger ones. The effect is best seen in the case of adamantane, the most strained octahedral diamondoid in terms of strain energies. Gibbs corrections make it more stable than any of the studied diamondoids up to 300 carbon atoms. Beyond C286H144, the Gibbs corrected strain energies are likely to become lower, converging toward bulk diamond. The effects of Gibbs corrections are evident also in the icosahedral series, while not affecting the trends of the stabilities. Notwithstanding the very high thermodynamic stabilities of the conventional diamondoids, the synthesis of diamondoids beyond tetramantane has proven extremely difficult. The routes for their synthesis appear to be blocked by kinetic aspects.14 Larger diamondoids, up to undecamantane, have been isolated from petroleum,3 but their formation apparently requires millions of years.15 The icosahedral diamondoids, possessing high thermodynamic stabilities as well, might be producible by very different approaches, in particular by the methods familiar from fullerene chemistry. There may be a structural relation between the icosahedral diamondoids and carbon buckyonions,46 detailed molecular structures of which have remained elusive. Indeed, the cores of buckyonions have been observed to transform to diamond.47 Besides terrestrial diamonds, diamond nanoparticles are existent in interstellar dust, as proposed already in 1969 by Saslaw and Gaustad.48 The interstellar diamonds,49 are the most abundant form of presolar grains in meteorites.50 The nanodia-


Linnolahti et al.

TABLE 5: Infrared C-H Stretching Vibrations of the Icosahedral Fulleranes, the Icosahedral Diamondoids, and the Octahedral Diamondoids Calculated at the B3LYP Level wavenumber (cm-1)

assignment

Fulleranesa C20H20 C80H80 C180H180

C100H60 C280H120

C10H16 C35H36 C84H64 C165H100 C286H144 a

2920 2870-2890 2960 2820 2860-2890 2920

CH (pentagons) CH (pentagons) CH (hexagons, in) CH (hexagons, out) CH (pentagons) CH (hexagons, in)

Icosahedral Diamondoids 2870-2900 CH (pentagons) 2830-2860 CH (hexagons) 2870-2900 CH (pentagons) Octahedral Diamondoids 2850-2880 CH 2880-2910 CH2 2830-2850 CH 2870-2900 CH2 2810-2850 CH 2870-2900 CH2 2810-2850 CH 2870-2900 CH2 2810-2850 CH 2870-2900 CH2

Ref 9.

monds with euhedral morphologies vary in size, typical diameters being 2-3 nm.50 Furthermore, there is evidence of radial growth of the interstellar and chemically vapor-deposited (CVD) nanodiamonds from central cores with pentagonal or icosahedral symmetries.50 Fullerenes, such as C60 and C70, have been studied as potential nucleation centers for the CVD nanodiamonds.51 It is notable, however, that having C2052 as the nucleation center could lead to the icosahedral diamondoids reported here. Spectral Features. Spectroscopy serves as a useful tool for characterization of molecular structures. The B3LYP-calculated infrared C-H stretching vibrations of the studied fulleranes and diamondoids are listed in Table 5. We start by shortly summarizing the previously reported spectral features of the fulleranes.9 The calculated spectrum of the dodecahedrane shows a C-H stretching vibration at 2920 cm-1, the experimental value being 2945 cm-1.2 The next icosahedral fullerane, C80H80, has three C-H stretching vibrations: two resulting from exohydrogens (2870 and 2890 cm-1) and one from endo-hydrogens (2960 cm-1). The corresponding vibrations, slightly shifted to lower wavenumbers (2860, 2890, 2920 cm-1) are present in the spectrum of C180H180, as well. In addition, the exo-hydrogens connected to hexagons give rise to a vibration at 2820 cm-1. These four main vibrations of C180H180 are in a striking resemblance with the unidentified astronomical infrared emissions at 2800, 2850, 2890, and 2940 cm-1. These spectral features are seen in various interstellar objects,53 their source being interpreted as hydrocarbon compounds such as polycyclic aromatics54 and the fulleranes.55 Hydrogenated diamond (111) surfaces show a single sharp C-H stretching vibration at about 2830 cm-1.56 This particular absorption is clearly visible in the calculated spectra of the studied diamondoids (Table 5). In the case of icosahedral diamondoids, it is due to hydrogens bound to six-membered carbon rings, and in the case of octahedral diamondoids, it is due to the tertiary CH groups. The absorption at 2830 cm-1 has also been observed in diamond nanocrystals, in which it is accompanied with another group of absorptions at about 2930 cm-1.57 These have been attributed to C-H stretching on (100)

Figure 6. 13C NMR spectra of the octahedral C84H64 and the icosahedral C100H60 calculated at the B3LYP level.

surface,57 and are absent in the studied diamondoids, in which another range of absorptions is visible at 2870-2900 cm-1. These absorptions are characteristic for both the icosahedral and the octahedral diamondoids. In the icosahedral ones, they are due to C-H stretching in pentagons, and in the octahedral ones, they are due to the CH2 groups at each vertex. Their relative intensities decrease as a function of the size of the diamondoid, because the number of pentagons and CH2 groups remains constant, 12 and 6, respectively. However, at least for diamondoids up to 2 nm in diameter, the absorptions at 2870-2900 cm-1 are clearly visible. Interestingly, these absorptions match with the 2880 cm-1 absorption features of dense interstellar molecular clouds, the feature having been considered as evidence of molecular diamonds in space.58 Beyond dodecahedrane and adamantane, the IR spectra of the icosahedral and octahedral diamondoids are practically identical, which makes their discrimination very difficult. In addition to the IR spectra, we calculated the Raman spectra for two diamondoids of about equal size, the octahedral C84H64 and the icosahedral C100H60, at the B3LYP level. The Raman spectrum of the C84H64 shows the features characteristic for conventional diamondoids:43j (a) low-frequency modes below 500 cm-1, (b) several modes between 1000-1400 cm-1, and (c) modes at about 1500 cm-1. The icosahedral C100H60 shows the a and b modes but lacks the c modes at about 1500 cm-1. This due to the assignment of the 1500 cm-1 feature for CH2 scissor modes, CH2 groups being absent in the icosahedral series. Next we considered 13C NMR spectroscopy, which turned out even more useful in discrimination between the two classes of diamondoids. We first focused on the NMR spectrum of adamantane. The experimental chemical shifts relative to TMS are δ ) 28.2 and δ ) 37.6 ppm,59 corresponding to CH and CH2, respectively. The chemical shifts calculated by the B3LYP method are δ ) 30.0 and δ ) 34.9 ppm, which are in accordance with the experimental values. For comparison, the MP2 chemical shifts are δ ) 32.0 and δ ) 41.2 ppm, respectively. The NMR spectra of the larger diamondoids were studied by the B3LYP method. The NMR spectrum of the dodecahedral C20H20 is distinctly different from that of adamantane. The experimental spectrum of dodecahedrane shows only one chemical shift at δ ) 66.9 ppm,2 the B3LYP-calculated value being δ ) 58.3 ppm. Similar to the case of Raman spectroscopy, we compared the NMR spectra of the octahedral C84H64 and the icosahedral C100H60 (Figure 6). The spectrum of C84H64 shows nine chemical shifts in the range of δ ) 33-45 ppm. The spectrum of C100H60 is

Structural Characteristics of Hydrocarbon Cages distinctly different with only three chemical shifts at δ ) 32.2, 41.8, and 59.6 ppm. The δ ) 59.6 ppm is due to the inner C20 core (see Figure 3), being close to the value of δ ) 58.3 ppm obtained for dodecahedrane. As a conclusion, we find Raman spectroscopy and, in particular, 13C NMR spectroscopy useful for characterization of the diamondoids. Conclusions We have described the structural principles of icosahedral fulleranes and diamondoids. The novel cage hydrocarbons are thermodynamically stable, which has been demonstrated by quantum chemical calculations. Structural characterization of the cage hydrocarbons, alongside with their possible existence in space, have been analyzed from the calculated spectral features. The first member of the stable family of icosahedral fulleranes is the experimentally known C20H20 dodecahedrane. The larger fulleranes are thermodynamically favored over the dodecahedrane, being significantly stabilized by partial endo-hydrogenation. Two series of fulleranes are described, the energetically favored series possessing molecular formula of (CH)n, where n ) 20, 80, 180, 320, 500, ..., 20m2. The stabilities of the fulleranes increase as a function of the size, the structures and stabilities converging toward hydrogenated diamond (111) sheet. The icosahedral diamondoids are structurally related to the fulleranes. The covalently bound layers of the diamondoids are constructed of the carbon framework of the energetically favored series of fulleranes, with the outer layer saturated by hydrogens. Hence, the first member in the series of the icosahedral diamondoids is the C20H20 dodecahedrane, followed by C20@C80H60, C20@C80@C180H120, and larger structures. The diamondoids were studied up to C20@C80@C180@C320@C500H300, i.e., C1100H300, until which, at least, the thermodynamic stabilities continue to increase. The match between the layers appears to be nearly perfect. In the case of the match being perfect, the diamondoids would approach an icosahedral diamond quasicrystal as a function of the size. The structural strain of the icosahedral diamondoids is shown to be low by comparisons to crystalline forms of hydrocarbons together with the conventional octahedral diamondoids. Raman and NMR spectroscopy appear promising for discrimination between the conventional and the icosahedral diamondoids. Overall, the novel icosahedral fulleranes and diamondoids introduced here provide new insight into the structural variety of hydrocarbons. The described structural motifs and spectral features are expected to aid in identification and characterization of the experimentally known hydrocarbon and diamond nanostructures. Furthermore, they can be utilized as guidelines by experimentalists, potentially leading to a new branch of hydrocarbon chemistry. Acknowledgment. We thank Dr. Uwe Huniar from COSMOlogic GmbH&Co.KG for providing us with a modified version of TURBOMOLE 5.9. References and Notes (1) Eaton, P. E.; Cole, T. W., Jr. J. Am. Chem. Soc. 1964, 86, 31573158. (2) Ternansky, R. J.; Balogh, D. W.; Paquette, L. A. J. Am. Chem. Soc. 1982, 104, 4503-4504. (3) Dahl, J. E.; Liu, S. G.; Carlson, R. M. K. Science 2003, 299, 9699. (4) Nossal, J.; Saini, R. K.; Alemany, L. B.; Meier, M.; Billups, W. E. Eur. J. Org. Chem. 2001, 4167-4180. (5) Kroto, H. W.; Heath, J. R.; O’Brien, S. C.; Curl, R. F.; Smalley, R. E. Nature 1985, 318, 162-163.

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