Structural, Cohesive, Electronic, and Aromatic Properties of Selected

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Structural, Cohesive, Electronic, and Aromatic Properties of Selected Fully and Partially Hydrogenated Carbon Fullerenes Aristides D. Zdetsis Department of Physics, University of Patras, GR-26500 Patras, Greece ABSTRACT: The structural, cohesive, electronic, and aromatic properties of some representative fully (CnHn, n = 8180) and partially (C60H2,3640, C70H3640) hydrogenated carbon fullerenes are studied by accurate density functional theory, in an attempt to establish stability trends and correlate these properties with “stability”, and with respect to each other, seeking ways for improving stability and pinpointing best candidates for future design. To this end, comparisons are made with other isoelectronic and isovalent structures including open structures, such as fullerane fragments and prismatic ladderanes, as well as homologous silicon fulleranes. The main difficulty, among many, is to establish reliable general “stability indices” in analogy to aromaticity indices, although both concepts are rather nebulous. This becomes even more difficult if one has to compare structures of different size, bonding, and/or composition. Nevertheless, by restricting the detailed search to a judicially chosen representative set of structures, it is hoped that useful and apparently reliable trends could emerge. For both fully and partially hydrogenated fullerenes, it appears that aromaticity, as expressed by standard aromaticity indices, does not correlate well with “stability”, as expressed by standard cohesive and other criteria. This is largely due to kinetic reasons, as well as subtleties in the stability and aromaticity concepts and criteria. Neither different “stability criteria”, such as cohesive (cohesive and/or binding energies per C atom) and kinetic (HOMOLUMO gaps), can correlate well with each other. On the basis of the table with the calculated (1) cohesive/binding energies (cohesive stability), (2) HOMOLUMO gaps (“kinetic stability”), and (3) aromaticity-NICS(0) values (electron delocalization), the top four list for each of these criteria has been constructed. The three top four lists (in decreasing order) are [C20H20, C180H180, C80H80, C50H50], [C8H8, C20H20, C60H60, C50H50], and [C60H2, C50H50, C70H40, C70H36], respectively. All three of them include at least one hydrogenated cage which has been already synthesized. The rather unknown C50H50 fullerane is the only one common in all three lists. This is highly suggestive that it could be synthesized in the very near future. A rather obvious general trend is that stability decreases dramatically from fulleranes to fullerane fragments all the way to prismatic ladderanes. It is also shown here that one of the most efficient ways to improve “stability”, on the basis of cohesive criteria is puckering of the HCCH bonds, induced by partial endohydrogenation, which facilitates optimization of the sp3 bonding. Selective doping by “appropriate” atoms, such as phosphorus, can also improve cohesion and/or functionalization of the cages. Contrary to partially hydrogenated C60 and C70 cages which have been synthesized, puckered CnHn fulleranes have not as yet synthesized despite their energetic advantages in binding and cohesive energy. This is attributed to existing barriers for penetration of hydrogen into the cage. Overall, dodecahedrane appears to be the most stable of all fully and partially hydrogenated fullerenes. This is not true for the “analogous” hydrogenated silicon cage (Si20H20). Among the partially hydrogenated cages examined here, C70H36 and C70H40 appear to be the most stable due to the five linked equatorial benzene-like rings that form a highly conjugated, graphite-like region.

1. INTRODUCTION The discovery of buckminsterfullerene (C60) and other related substances simulated a lot of interest in their use (among others) as substrates for addition reactions, among which is hydrogenation. Attempts to synthesize the fully hydrogenated C60H60 hydride or “fullerane” have failed so far, although its existence in stellar atmospheres was postulated since 19911 through comparison of the observed spectral lines with semiempirical calculated infrared (IR) spectra. Instead, partially hydrogenated cages of the form C60Hn and C70Hn, with n up to 36 have been synthesized.2,3 The only fully hydrogenated fullerene which has been synthesized up to now is dodecahedrane,4 C20H20, while r 2011 American Chemical Society

cubane C8H8, the smallest fully hydrogenated cage with octahedral symmetry, was synthesized as early as 1964,5,6 much earlier than the discovery of fullerenes, although its stability due to nonfavored 90° bond angle arrangement and the induced strains was unexpected. Two of the well-known lower energy structures are ethenylbenzene and cyclooctatetraene.6 At the B3LYP/def2TZVP level of theory, the energy difference found here between ethenylbenzene and cubane is 5.5 eV, which is equivalent to a Received: March 10, 2011 Revised: May 12, 2011 Published: June 30, 2011 14507

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The Journal of Physical Chemistry C binding energy difference of about 0.69 eV per C atom (or CH unit). Clearly cubane is not the lowest energy isomer of C8H8 by far, but is obviously “stable”, in the most commonly used sense of this term (i.e., it has been synthesized for a long time and is stable up to about 230 °C, see ref 6). It should be emphasized at this point (for reasons which will become clear below) that the HOMOLUMO gap of cubane is 8.2 eV, almost 3.2 eV larger compared to the HOMOLUMO gaps of both planar structures, ethenylbenzene and cyclooctatetraene (at around 5 eV at the B3LYP/TZVP level of theory). Furthermore, the structure and properties of the rest of the fullerene hydrides, and in particular of the fully hydrogenated cages, CnHn, are largely unknown. Even for the “known” hydrides such as C60H60, there seem to be several conflicts in the literature. The structure of fullerane, C60H60, which gives the name “fulleranes” to the entire family of CnHn hydrides, has been controversial.7,8 After the initial work of Weber,1 which was based on icosahedral symmetry similar to C60, subsequent work7 has suggested a C1 symmetric (nonsymmetrical) structure as the lowest energy isomer of C60H60. More recent reexamination of the lowest energy structure of C60H60 by the present author8 has shown that the lowest energy isomer should be neither the C1 nonsymmetric structure nor the very high symmetry icosahedral structure. Instead a structure of D5d symmetry, a high subgroup (the highest after I) of the icosahedral Ih group, qualifies best for the lowest energy C60H60 structure, since it has lower energy than either one of the two. The D5d structure is very appealing (aesthetically and scientifically) due to its close similarity to the icosahedral structure (in symmetry, vibrational and optical properties8) and its high stability (binding energy). Moreover, the D5d structure shares with the C1 symmetric structure a very important and powerful feature, which is behind their higher stability compared to the Ih structure. They both have 10 out of the 60 hydrogen atoms bonded endohedrally (inside the cage) rather than exohedrally.8 The idea of endo-hydrogenation first surfaced in the literature in the early 1990s.9,10 This allows each HCCH fragment, corresponding to a CC shared edge, to adopt a chairlike structure with one hydrogen atom pointing inside the cage and one pointing outward which facilitates the optimization of the sp3 bonding. This puckering is responsible for the stabilization of the larger icosahedral fulleranes.8,11,12 It is shown here that smaller fulleranes, such as C50H50 can profit from such puckering, as well, and in fact much more so. However, contrary to the large icosahedral fulleranes,11 which can preserve the Ih symmetry, the symmetry of the puckered structures is in general lower (usually a high subgroup of the initial symmetry). The strong influence of puckering on the stability of isovalent (and isostructural) silicon fulleranes has been also demonstrated by Karttunen et al.,12 and by the present author.13 Furthermore it has been recently shown that puckering is also important for other than silicon and carbon fulleranes, such as group 15 fullerenes.14 As it becomes apparent from this discussion, the attempt to compare trends in stabilities or “stabilities” (for whatever the real meaning of the word is) for a very large and complex category of hydrogenated (fully or partially) carbon fullerenes, including also ladderanes and fullerene fragments, is very ambitious but very challenging as well. To finalize this ultimate target of the present work, one needs to find ways to select various representative species and treat them theoretically on an (as much as possible) equal footing, as far as “stability” (on its various “forms”) and aromaticity are concerned, considering “representative” stability

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and aromaticity indices (criteria). To this end, relative and not absolute comparisons of possible “stability indices” (in full analogy to “aromaticity indices”) have been made (with the same theoretical methods and computational techniques) for a very large and diverse category of materials (known and “unknown”). Having in mind all possible complications connected with what “stability” could really mean (or what really “stability” means to an experimentalist), the ultimate “criterion of stability” used here is the relative comparisons with structures already synthesized. This way, one could possibly assert what is the most promising structure for future synthesis from the (representative) ones examined here. Unavoidably, comparisons should be made with partially hydrogenated cages which have been synthesized, involving structures with different numbers of carbon atoms but also structures with the same number of carbon atoms but different numbers of hydrogen atoms. Whereas the first problem (different number of CH pairs) is easily solved for the cohesive stability, by dividing the total binding energy by the number of CH units, the second case (same number of C atoms different number of H atoms) is not trivial. For this particular case it has been illustrated8 that the concept of the “cohesive energy” of the carbon skeleton, involving the chemical potential of hydrogen, is very useful and efficient replacement of the total binding energy per atom used for the fully hydrogenated fullerenes. Obviously, one cannot exhaust all possibilities and cases, but one has to select representative cases from “well-known” cages (to test the criteria, “indices”, used) to less known or largely unknown fulleranes (to be able to make useful “predictions”). In what follows, the results of the calculations for the energetic, electronic, and “stability” properties of n = 8, 20, 40, 50, 60, 70, 76, 80, and 180 fully hydrogenated, as well as of the C60H2, C60H36, C70H36, and C70H40 partially hydrogenated cages will be presented and discussed with special emphasis on “stability” and aromaticity “indices”.

2. BRIEF DESCRIPTION OF THE CALCULATIONS The general theoretical and computational method followed here is based on all-electron density functional theory (DFT) with the hybrid, nonlocal exchange, and correlation functional of Becke-Lee, Parr, and Yang (B3LYP)15 and the TZVP basis set.16 The accuracy and adequacy of this method for producing reliable results have been tested before.8,18 The starting geometries were obtained by hydrogenation of the corresponding “bare” Cn cages. For the puckered isomers as well as for the partially hydrogenated structures, puckering was “induced” by suitable partial endohydrogenation (or exo-hydrogenation) in several possible ways, guided by symmetry, coordination, and sp3 bond angle optimization. The geometry optimizations were initially run without symmetry constrains (C1) using the PBE functional and the resolution of the identity (RI) approximation, as they are implemented in the TURBOMOLE program package,16 which was used for these calculations. The lower energy structures were afterward symmetrized (wherever possible) and reoptimized using the B3LYP functional under the assumed symmetry constrains. For all these calculations, medium (initially) and fine (finally) grids were used for the DFT integrations16 and tight convergence criteria were enforced on the SCF energy (107 au), the one electron density (root mean square of the density matrix up to 107), and the norm of the Cartesian gradient (104 au). 14508

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The Journal of Physical Chemistry C

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Table 1. Binding Energy per C Atom (or CH unit), Eb (in eV/atom), and HOMOLUMO Gap, H-L (in eV), for Each Structure, Characterized by Symmetry (Sym) and Figure Number (Fig)

Figure 1. Representative lowest and/or lower energy (high symmetry) structures of CnHn, n = 8, 20, 40, 50, 60, 70, 76, 80, and 180 fulleranes. The individual structures are not drawn to scale.

*

Puckered structures.

3. RESULTS AND DISCUSSION All results related to “stability” for the fully hydrogenated structures, including more and less known carbon (and a few Si) “fulleranes”, prismatic ladderanes, and fullerene fragments, are summarized in Table 1, using light and heavy highlighting for the last two categories (ladderanes and fullerene fragments, respectively). The binding energy, Eb, per C atom (or CH unit), is defined as usual by Eb(CNHN) = [N E(C) + N E(H) Etot(CNHN)]/N (in eV/atom), where E(C) and E(H) are the atomic energies of carbon and hydrogen, respectively. Both fullerane fragments and ladderanes are open structures in contrast to closed spherical fulleranes. In addition ladderanes are singly bonded, contrary to fulleranes and fullerane fragments which include both double (or near double) and single bonds. The table also includes puckered structures (both fulleranes and ladderanes) indicated by an asterisk (*). The puckered C50H50 isomers, for reasons that will become apparent later, are grouped together at the end of the table. The geometrical structures of all fulleranes (puckered or nonpuckered), except the puckered C50H50 cages, are shown in Figure 1.

From an overall inspection of this table we can see that the most “stable” cage, according to the binding energy per carbon atom (or per CH unit) is the dodecahedrane, C20H20, with second the puckered icosahedral C180H180 fullerane. However, according to the largest HOMOLUMO gap criterion which is a measure of “kinetic stability”, dodecahedrane,4 C20H20, is second to cubane.5 Both dodecahedrane and cubane have been synthesized.4,5 Cubane (C8H8) is a special case between closed fulleranes and prismatic ladderanes (this is why it is listed twice in Table 1 with fulleranes and ladderanes), but it can clearly be considered as closer to prismatic ladderanes, for which should be also considered as the reference structure. The same role could be played by prismane (C6H6) as well, which has been also synthesized,19 although much less “stable” (by about 3 eV/atom, as was found here at the B3LYP/TZVP level of theory) from the isoelectronic benzene. Obviously, we are talking about different types (and levels) of stability for these two structures. Yet with reference to whether or not these structures could be synthesized, they might be considered as “equally probable” in the sense that they both can be (have been) synthesized. Remarkably enough, they are both characterized by similarly large HOMOLUMO gaps (6.63 eV in prismane, 6.67 eV in benzene), which are considered measures of “kinetic stability”. Clearly benzene is of much higher binding energy and of much more different bonding than prismane, irrespective of the almost equal HOMOLUMO gaps, which however are not as large as cubane and dodecahedrane. Dodecahedrane is unambiguously the reference structure and turning point for fulleranes, in terms both of “stability” and of size. One way to remove the ambiguities mentioned above for cages of the same and of different sizes is to compare between structures of the same type of bonding, before we compare between different groups of structures. Thus, smaller (than n = 20) CnHn cages should be considered as very stable “ladderanes” (not as fulleranes), and according to the above-mentioned convention, their stability (and other properties) should be compared to cubane. This is also true for larger prismatic ladderanes, which are obviously much less stable. In other words, the reference structure for the stability of prismatic ladderanes is cubane, whereas the reference structure for judging the stability of fulleranes is dodecahedrane. Hence, it is possible and perfectly “legitimate” that some fullerane of lower stability could be more stable than a ladderane of assumed higher stability (for a given 14509



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Figure 2. The frontier orbitals of C20H20 dodecahedrane.

stability criterion), and vice versa. Obviously, it could also happen that two fulleranes (or two ladderanes, or in general two structures of the same structural and bonding category) could have different relative stabilities for different stability criteria. From an overall inspection of Table 1, we can form top four “stability lists” based both in binding energy per CH unit and in size of HOMOLUMO gaps. According to the binding energy per carbon atom (or per CH unit) the top four list includes C20H20, C180H180, C80H80, and C50H50. According to the largest HOMOLUMO gap, the first tetrad consists of the following: C8H8, C20H20, C60H60, and C50H50. As we can see, besides C20H20, which has been already synthesized, C50H50, which is one of the lesser known (or rather unknown) fulleranes, is the only one common in the two stability tetrads. This is why this fullerane is discussed more extensively below. 3.a. Small Cages: C8H8, C20H20. The smallest hydrogenated fullerenes considered here are cubane5 (C8H8) and dodecahedrane4 (C20H20), shown in Figure 1 (8, 20.1, respectively), which have been both synthesized at very different times.4,5 These cages are used as reference structures for prismatic ladderanes and fullerane cages, respectively. Cubane has the largest HOMOLUMO gap and dodecahedrane has the largest binding energy per CH unit. As mentioned above, HOMOLUMO gaps are considered as measures of “kinetic stability” for a molecule (or as zeroth order estimates of “chemical hardness”). Thus, no matter how strange it sounds, it could be argued that cubane has higher kinetic stability than dodecahedrane, which is also characterized by a large HOMOLUMO gap compared to the rest of the fulleranes. Clearly, in addition to HOMOLUMO gaps, the symmetry and structure of both HOMO and LUMO, and in general of the frontier orbitals, is very important for “kinetic stability” and for the electronic structure in general. Conceptually, this information is the finite analogue of the valence and conduction band structures in infinite crystals. Yet, this information although quite transparent, as can be seen in Figure 2 which shows the frontier orbitals of dodecahedrane C20H20, cannot always convey additional quantitative information, except perhaps for visualizing the regions of electron “localization” (as in the LUMO+1 orbital) and possible functionalization, as well as for expected possible chemical similarities. In addition, several

Figure 3. Open structures of 8, 20, and 40 CH units. Structures F20.1, F20.2, and F40 are fullerane fragments. The rest of the structures are prismatic ladderanes of 8 (L8) and 20 (L20.3, L20.4) CH pairs. The L20.3 and L20.4 ladderanes are shown in both top (a) and side (b) views.

times, from the structure of the frontier orbitals, one could draw some feeling about the possible aromatic character of the cage (see discussion about aromaticity of C20H20 in Section 3.e. below). Cubane, with the highest HOMOLUMO gap, but much lower “cohesive stability” (binding energy per CH unit) is much more stable (cohesively) from all larger prismatic ladderanes. These laderanes which are very “unstable” (very low binding energy per CH unit), although some of them could be present in living organisms, are included in Table 1 and in Figure 3 mainly for comparison(s). 3.b. ) C20H20 and C40H40 Prismatic Ladderanes and Fullerane Fragments. After the discussion in section 3.a, and in particular the discussion and comparisons about cubane, it becomes clear that stability comparisons between fulleranes and ladderanes are rather meaningless. It is interesting, however, to compare ladderanes to each other and to other open structures of the same size, and also to examine the effect of puckering in their (in)stability. To this end, we have considered in Figure 3 some representative ladderanes (L8, L20.3, L20.4) and fullerane fragments (3.F20.1, 14510


The Journal of Physical Chemistry C 3F20.2, F40). The 3.F20.1 and 3.F20.2 fragments have been obtained by a particular endo-hydrogenation (and resulting puckering) of specific carbon sites in the C60H60 icosahedral fullerene, as described in ref 7. After geometry optimization, the resulting D5d isomer disintegrates into three disjointed C20H20 fragments (two similar, top and bottom, bowl-shaped pieces and one (middle) ring fragment (see Figure 2b in ref 8). Fragments F20.1 and F20.2 in Figure 3 are the optimized versions of these bowl and ring fragments, respectively. The F40 fragment has been obtained by an analogous way from the C50H50 fullerane. As we can see in Table 1, these two fragments have the highest binding energy of all ladderanes in this table, while the two F3.20.1 and F3.20.2 fragments have larger binding energies than cubane itself. Between the two F3.20.1 and F3.20.2 fragments, the ring in Figure 3, F20.2, in which each carbon atom is bonded to one hydrogen and to two neighboring carbon atoms alternatively by single and double bonds, has lower stability (lower binding energy) compared to the bowl structure. A similar bowl structure is a very low-lying isomer of the bare C20 cluster. In L20.3 and L20.4 in Figure 3 we can see the two C20H20 ladderanes of D10h and D5d symmetry, respectively. L20.3 in Figure 3 consists of two parallel decagons and is totally exohydrogenated and nonpuckered. The ladderane in Figure 3, L20.4, is obtained from the one in Figure 3, L20.3, by partial endohydrogenation and bond-puckering. The 3.L20.3 ladderane, although energetically the worst (by far) compared to the fullerene fragments (and certainly much more in comparison to dodecahedrane), is much more stable (with respect to both, the binding energy and the HOMOLUMO gap criteria) than the puckered 3.L20.4 ladderane. This illustrates that contrary to the expectations that puckering could be beneficial for prismatic ladderanes as well, due to the highly strained bonds, this is not the case. All attempts to improve stability through puckering (induced by partial endohydrogenation) for the C20H20 ladderanes have dramatically failed, leading to structures of much higher energies. The L20.4 ladderane in Figure 3 is the best possible case of such attempts. Even in this case, as our present calculations showed the binding energy per atom was reduced by more than 1 eV/ atom (see Table 1). This is mainly due to the fact that, although puckering by alternating (both “horizontally” and “vertically”, see L20.4b, Figure 3) endo- and exo-hydrogenation slightly improves the horizontal bond angles (as is shown in the Figure 3, L20.4a and L20.4b), it worsens as the bond lengthens. At the B3LYP/TZVP level of the present calculations the bond lengths in the puckered ladderane become much larger (1.66 Å from 1.56 Å in the nonpuckered isomer). It could be also argued on the basis of L204a in Figure 3 that in addition the mutual repulsion of the endohedrally bonded hydrogens could also play a significant role for the horizontal bond elongation and, therefore, to the lower binding energy of the puckered ladderane. However, comparisons of detailed calculations (with only 20 hydrogens or 20 bare carbon atoms at the equilibrium positions of ladderanes, 3.L20.3 and 3.L20.4) reveal that hydrogen repulsion is substantially higher in the nonpuckered compared to the puckered isomer. Thus, the picture in Figure 3, L20.4a, is simply misleading, since the 10 endohydral hydrogens are not in the same horizontal plane (see Figure 3, L20.4b). Moreover, generally, ladderanes are unstable and highly strained. However, for the very small cages such as the cubane, C8H8, where there is not a very clear distinction between ladderanes and fulleranes (cages), this is not as important as for the larger ones. The competition between fulleranes (or fullerene fragments) and ladderanes

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Figure 4. Low energy structures of C50H50 in top and side (bottom) views.

(wherever they could coexist) is dramatically in favor of fulleranes, as could be expected. Cubane is clearly a closed form of prismatic ladderane and so is the C6H6 hexaprismane, the stability of which (on the basis of binding energy) is only second to benzene.15 These comparisons are also true for silicon fulleranes or “fullerenes”,18,20 SinHn, which are fully analogous and isolobal21 to CnHn. The Si12H12 and C12H12 hexagonal prisms are classical examples of closed ladderanes which are clearly more stable (energetically) than the corresponding isoelectronic icosahedral “fulleranes”.18,21 This is due to overcoordination of the carbon or silicon atoms in these highly symmetric fulleranes.18,21 From all fulleranes and ladderanes examined here, n = 12 is the only case where a (closed form) ladderane is more stable than the corresponding isoelectronic fullerene. 3.c. Medium Cages: C50H50. The stability study of the lesserknown C50H50 fullerane signifies the very efficient operation of puckering, which is a relatively new and very efficient approach to the stabilization of mediumlarge fulleranes, although the idea of endo-hydrogenation, which is not in general equivalent to puckering, has surfaced many times in the literature since the early 1990s until today. As was explained above, puckering was very successful8,9 for the very large icosahedral fulleranes9 (without altering their symmetry) and for C60H60 by reducing its symmetry8 to D5d. In this last case the gain in binding energy was more than 10%. Puckering in C50H50 fullerane, induced by partial endo-hydrogenation of 5, 10, and 20 carbon atoms, has a very profound effect, as we can see in Figure 4 and Table 1. The lowest energy C50H50 isomer is the puckered structure in Figure 4a with ten endo-hydrogenated carbon atoms. This isomer is much more stable (in terms of binding energy per CH unit) than the lowest energy C60H60 fullerane but less stable than dodecahedrane. The symmetry of this isomer was originally C5v, but after (unconstrained) optimization and resymmetrization of the final geometry, it turned to higher D5h symmetry. This structure, surprisingly enough, has not only higher cohesive stability compared to the energetically best C60H60 and C70H70 isomers but also higher or equal “kinetic stability”(HOMO LUMO gap). The corresponding Si50H50 “fullerane” is more stable even from Si20H20, as is shown in Table 1. The next best in stability is the C5v symmetric structure with five endohedral hydrogens. However, when doping with the P atom (for example) is considered, the energetical gain ΔE, or equivalently, the embedding energy Eemb, where Eemb = [E(C50H50) + E(P)] E(P@C50H50), is higher for this structure compared to the structure in Figure 4a. As a result the lowest energy P@C50H50 isomer corresponds to the C5v structure with a difference of 0.77 eV from the D5h best puckered P@C50H50 14511



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Figure 5. The frontier orbitals [HOMO, (a), (d); LUMO, (b), (e); and spin density, (c), (f)] of the C5v (top two rows) and the D5h (bottom tow rows) P@C50H50 structures, respectively. Primed labels in rows 2 and 4 denote side views.

isomer. This is due to the fact that the embedding energy Eemb for the C5v isomer is 2.28 eV, whereas Eemb for the D5h is negative, equal to 6.75, meaning that the P atom at the center of the cage is repelled by the cage and it is in fact under pressure in this case. These are mainly the two principal cage structures for which phosphorus embedding has been studied in considerable detail. For these two cages, C50H50 and P@C50H50 in both C5v and D5h symmetries, additional DFT calculations were run with the B97D functional, which accounts for dispersive interactions,22 to avoid misconceptions about the necessity of such interactions here. With this functional, the embedding energy of the of the C5v symmetric P@C50H50 isomer (at the B97D/def2-TZVP level) was found to be 2.05 eV, compared to the B3LYP value of 2.28 eV, whereas for the D5h symmetric isomer Eemb was calculated at 6.13 eV (6.75 eV at the B3LYP/def2-TZVP level). This illustrates that, contrary to sp2 bonded carbon cages in which hydrogen is doped endohedrally, dispersive interactions are not that crucial for the sp3 bonded P@C50H50 systems, which are fully saturated by hydrogen (endohedrally and exohedrally). The large energy gain of the C5v isomer is due to the fact that the P atom, as a result of the lack of center of symmetry, can move closer to the bottom of the “ink pot” shaped C5v structure, thus improving its bonding. This is also reflected in the structure of the frontier orbitals shown in Figure 5. In both cases, as we can see from the corresponding spin densities, the spin is localized at the doping atom (for the D5h isomer) or around the doping atom (for the C5v isomer). Spins (and in particular localized spins) in

semiconductor nanostructures are promising qubit candidates for solid state quantum computing.23 It should be noted that the original nonpuckered structure in Figure 4c is only third in stability among the C50H50 isomers, while the elongated structure in Figure 4d, with 20 endohedrally bonded hydrogen atoms, is energetically much higher than all of them. It has been already demonstrated7 that puckering is very efficient for the fullerene C60H60 for which two puckered structures of D5d symmetry have been found with binding energy gain of about 0.20 eV/atom (structure 60 shown in Figure 1) and 0.05 eV/atom, respectively. Structure 60 in Figure 1, with the large energy gain (0.20 eV/atom, a total of about 12 eV), is characterized by D5d symmetry, with ten endohedral hydrogen atoms, similar to the one with the smaller binding energy (0.05 eV/ atom) which shares the same symmetry and 10 (different) endohydrally bonded carbon atoms. The difference between the two structures is that the endohedral hydrogens are bonded to different sets of carbon atoms belonging to different types of carbon rings. In the higher binding energy structure the “puckering” of hexagonal (and pentagonal) rings is energetically more favorable compared to the lower binding energy structure, in which more pentagons and fewer hexagons are puckered. As has been explained elsewhere7,10 puckering is favorable for hexagons, where the bond angles of 120° are far away from the ideal sp3 bond angles (although very close to the sp2 bond angles), but not for pentagons in which the bond angles are very close to the ideal tetrahedral bond angles. Therefore there is always an energetic 14512


The Journal of Physical Chemistry C compromise involved in puckering. Obviously, for C20H20 (and Si20H20), which consists solely of pentagons, the puckering is totally unfavorable. Puckering is also unfavorable in CnHn cages when the number of endohedral hydrogens, Nend, is larger than a critical value dependent on n. For both C50H50 and C60H60 this critical number seems to be 10 or around 10 (not smaller than 10 and not larger than 15). For C50H50 when Nend = 20 we get either the elongated structure in Figure 4d with lower binding energy compared to the nonpuckered isomer or a totally disjointed nonstable structure part of which is the n = 40 fullerane fragment F40 in Figure 3. 3.d. Larger Cages: C60H60, C70H70. For C60H60 the structure with 20 hydrogen atoms pointing inward becomes very unstable breaking in two disjoint pieces, parts of which are the bowl structure F20.1 and the ring fragment F20.2 in Figure 3. This has been shown in ref 8, where more results and details on the puckered C60H60 isomers can be found. In the same work (ref 8) the relations of the various disjoint pieces with structural units of carbon nanotubes have been examined, together with some partially hydrogenated C60 cages. Here, the results and comparisons for partially hydrogenated C60 and C70 cages will be discussed below. C70H70 is not a particularly stable isomer (its binding energy after optimum puckering, induced by 10 endohedrally bonded hydrogens, is only 9.50 eV/atom, compared to 9.60 ( 0.01 for its n = 60 and n = 76 “neighbors”). However, partially hydrogenated C70 cages have been synthesized and are known to be very stable, similarly to partially hydrogenated C60 cages.8 3.e. Partially Hydrogenated Cages: C60H2, C60H36, C70H36, and C70H40. Partially hydrogenated cages such as C60H2, C60H36, C70H36, and C70H40, and many others3 have been synthesized many years ago.3,24,25 Yet their structure is not unambiguously (well) known even now, and certainly there is a tremendous number of possible isomers2426 which makes the identification of the global minimum (with confidence) practically impossible. Here we examine and compare the structure and stability of C70H36 and C70H40 together with C60H2 and C60H36 partially hydrogenated cages and we investigate the possible correlation between stability and aromaticity of these structures. It is well-known27 that the stability of C60 is not directly related with aromatic stabilization but with strain reduction. This is consistent with the much lower aromaticity of C60 compared to the aromaticity of C70, as it is measured by the magnetic aromaticity index of nucleus independent chemical shifts (NICS) evaluated at the center (0) of the cage, NICS(0). The NICS(0) values, which are calculated by finding the NMR shift of a ghost atom at the center of the cage, are very useful criteria for determining the aromatic character by examining the delocalization of electrons and the resulting diatropic (negative) NICS) values.28 On the other hand antiaromatic cages are identified by their paratropic (positive) NICS values, because the magnetic field induces a ring current which strongly effects the local magnetic environment. The direction of the induced magnetic field depends on the orientation of the orbitals; the fewer the nodes in the molecular orbitals around the ring or cage, the more diatropic the NICS value are expected to be, while antibonding or nonbonding p-orbitals along the ring or perpendicular to the cage are most likely to produce a paratropic shift. This last possibility, seems to fit the picture with the orbitals of C20H20 (in Figure 2), which is indeed characterized by paratropic NICS(0) values (see discussion below). The NICS(0) values of C60 and of C70 obtained here at the B3LYP/TZVP level of theory are 2.8 and 27.2 ppm (parts per million), respectively. It is interesting to examine the relation (if any) of aromaticity (in this case of spherical aromaticity) and

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Table 2. Stability (through “Cohesive Energy”, Ec) and Aromaticity (through NICS(0)) of Selected Hydrogenated Fullerenes

a

structurea

Ec (eV/atom)

NICS(0), ppm

*C20H20

7.16

+1.81

C50H50

7.06

2.86

C60H60

7.01

0.56

*C60H2

6.88

6.81

*C60H36 C70H70

6.87 6.92

0.66 1.11

*C70H36

6.95

1.26

*C70H40

6.97

1.32

Asterisk indicates cages that have been already synthesized.

Figure 6. The structures of the C70H36 (top) and C70H40 (bottom) partially hydrogenated cages in top (a, a0 ), and side (b, b0 ) views.

stability, measured with some reasonable criteria. This is done in Table 2. The lowest energy structures of the partially hydrogenated C60 and C70 cages are based on the structures reported in refs 8, 24, and 26. The lowest energy structures of C70H36 and C70H40, obtained here, are shown in Figure 6. Although C70H36 is the major product of the reduction of C70 by dihydroanthracene, substantial amounts of C70H38, C70H40, C70H42, C70H44, and C70H46 are also formed and could be detected by field desorption.3,25 Similarly, C70H36 and C70H38 are formed when a mixture of C60 and C70 in toluene is hydrogenated catalytically with 5% ruthenium-oncarbon catalyst.3,25 The C2v symmetric C70H36 obtained here as the lowest energy isomer is very similar to the C2v structure obtained by Book and Scuseria24 as one of the low energy isomers. As we can see in Figure 6, both cages have the hydrogens concentrated in the poles of the C70 structure. The stability of these cages is especially high because the equatorial region of the fullerene cage contains five linked, benzene-like rings that form a highly conjugated, graphite-like region. This is clearly shown in Figure 7 which shows 14513



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Figure 7. The frontier orbitals (HOMO-1, HOMO, LUMO), and electron density (e-DENS) of C70H36 (top) and C70H40 (bottom).

the frontier orbitals (HOMO-1, HOMO, LUMO) and electronic charge density of C70H36 and C70H40. To judge and compare the stability of the partially hydrogenated structures on an equivalent basis with the fully hydrogenated fullerenes, we make use of the “cohesive energy of the carbon skeleton”, Ecoh, instead of the binding energy (BE). The cohesive energy, Ecoh, which depends on the structure’s size, can be defined by the relation8 Ecoh ¼ ½BEðCNC HNH Þ þ μH HH =NC where BE(CNCHNH) is the binding (or atomization) energy of the CNCHNH cage. NC, NH are the numbers of C and H atoms, respectively, and μH is the chemical potential of H, which is taken at a constant value, with zero corresponding to the value at which the formation energy of methane (CH4) is zero. In so doing, we have effectively removed the energy contribution of all CH bonds in every system and essentially considered the binding energy of the “carbon skeleton”. Such type of cohesive “stability” evaluation, although very simple, has been illustrated to be very efficient and successful for diverse structures, such silicon nanowires,29 partially hydrogenated carbon fullerenes,8 and silicon nanoparticles and “fullerenes”.13 Although, as we can see in both Tables 1 and 2 that dodecahedrane is by far the indisputable “champion” in stability among hydrogenated carbon fullerenes, based on the “cohesive energy”, on the basis of aromaticity it seems to be last. As will be explained below this is due to its high symmetry. The corresponding isovalent icosahedral Si20H20 cluster13 presents similar behavior, although its cohesive stability is lower compared to the larger Si80H80 and Si180H180 puckered fulleranes. Yet their stability is not related with aromatic delocalization, but rather, as in the case of non-hydrogenated fullerenes, is mainly due to strain reduction. From Table 2 we can see that C20H20 has a positive (paratropic) value of NICS(0) = +1.81 ppm. This is similar to the case of Si62 dianion30 and is due, as was mentioned earlier,30 to the high Ih symmetry and the mixing of the very paratropic 3-fold degenerate t1u orbitals which offsets the diatropicity of the other “nearby” bonding orbitals such as the t2g orbital in Si6. Similarly the low aromaticity of C60, indicated by

the value NICS(0) = 2.8 ppm, compared to 27.2 ppm in C70, is due to diatropic hexagons and paratropic pentagons.27 The present values of NICS(0) for C60 and C70 are in full agreement with the values of Chen and King.31 Interestingly enough, if we form the top tetrad in aromaticity as for cohesive and kinetic stability from Table 1, we would have in order of decreasing aromaticity C60H2, C50H50, C70H40, C70H36, which shows that C50H50 is also (actually second) in the top aromaticity tetrad. C50H50 is the only one that is common in all three top stability lists. 3.f. Much Larger Cages: C76H76, C80H80, and C180H180. Similarly to Si76H76 (see ref 13), there are four distinct types of puckering for C76H76 with Nend = 4, 12, 16, 24, respectively, all of which are compatible with its tetrahedral symmetry and all of which are more stable than the unpuckered structure. However the Nend = 12 structure, shown in Figure 1 (76) is the most stable of all of them. The puckered (with Nend = 12) fully hydrogenated C76H76 cage, with a binding energy difference of about 0.30 eV/atom from its unpuckered isomer, is more stable (as far as binding energy is concerned) from the best puckered C60H60 and C70H70 cages but less stable than either C50H50 or C80H80 lowest energy puckered structures. Endo-hydrogenation of 20 out of the 80 carbon atoms is very efficient for improving the binding of C80H80 by about 0.50 eV/atom, preserving at the same time its high icosahedral symmetry. Although this energy gain is significant, it is not enough (by 0.03 eV/atom, according to the present calculations) to overpass the stability of the dodecahedrane, contrary to opposite reports in the literature (Linnolahti et al.11). This is also contrary to the behavior of the corresponding isovalent silicon “fulleranes”, 13 Si80 H80 and Si20 H20 . C180H180, similarly to C80H80, although very high in stability, is again less stable (in terms of binding energy and HOMO LUMO gaps) in comparison to C20H20 dodecahedrane. There are two types of puckering that preserve the icosahedral symmetry of C180H180 with Nend = 60 and 120. Although both types of puckering lead to very stable structures, much more stable than the normal fully exohedrally hydrogenated isomer, the Nend = 60 isomer is the most stable, but less stable than dodecahedrane. 14514


The Journal of Physical Chemistry C This is in contrast to the corresponding silicon fulleranes13 and reports in the literature,11,12 suggesting exactly the opposite. We have thus seen that puckering is a very efficient mechanism in the full range fulleranes from n = 50 to n = 180 for the stabilization of medium and large size cages. Perhaps, one could be skeptical about the large number of possible combinations of endo- and exo- sites, but here (as in many cases in scientific research) physical (or chemical) intuition based on a spherical knowledge of the subject could be very important. In the present case, scientific intuition based on symmetry and bonding (coordination) provides important guidelines. Since fullerenes and fulleranes are (and expected to be) highly symmetric “spherical” cages, guided by symmetry we are led to consider puckered structures of the same high symmetry group as the original or as high as possible subgroups of it, searching from higher to lower subgroups through trial and error. Through this process we can find the optimum minimum (and maximum) number Nend as well as the optimum combination of possible sites in such a way as to preserve the (high) symmetry of the selected symmetry group or subgroup. Although there is no absolute guarantee about the uniqueness of the results, this symmetry constraint has been already successfully tested through its application7 in C60H60. The resulting D5d symmetric structure with the same Nend = 10 as in the C1 structure in the literature (see ref 8 and references therein) was more stable (higher binding energy and larger HOMOLUMO gap). In addition, the arbitrary Nend = 10 in the C1 structure came out naturally in the D5d symmetric isomer from the D5d symmetry of the point group.

4. SUMMARY AND CONCLUSIONS In an attempt to find ways to rationalize and correlate the various aspects of “stability” in order to be able to predict or pinpoint “best candidates for future synthesis”, we have examined in a consistent way the structural, cohesive, electronic, and aromatic characteristics of representative “known” and “unknown” hydrogenated carbon fullerenes. In view of a lack of clear correlation between various stability criteria (“stability indices”) based on cohesion (cohesive and binding energies per C atom), or HOMOLUMO gaps (“kinetic stability”), or aromaticityelectron delocalization (NICS values), we have considered as a general and uniform “ultimate test” of “stability” the comparison with structures already synthesized. This kind of chemical stability is a more complex concept and depends on several parameters and conditions, which are not easy to quantify in a single number (binding energy or HOMOLUMO gap), representing a “stability index” in analogy to aromaticity indices. For instance, it is not sufficient that a “stable” structure would be a low-lying minimum on the potential energy surface, but there must be sufficiently high barriers between that minimum and all other lower energy minima. Furthermore, it must not dimerize or polymerize, and this could not be enough. For example, C60H60 could loose molecular hydrogen. One possibility could be C60H60 f C60H36 + 12H2 ( Q, where Q is the amount of released or absorbed energy. In this particular case for the “standard” icosahedral isomer, we find Q = 4.6 eV. However, for the lowest energy (according to the present calculations) D5d puckered isomer, we get Q = +6.2 eV, which in accordance with the present expectations. All this information cannot be mapped in a single stability index. A triad of numbers is certainly a better choice, but clearly not the best. Nevertheless, this simplified but

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general approach avoids the details and complications of the various ways and channels of destabilization and is a very good compromise between simplicity (and generality) and completeness. As with aromaticity, with “stability” too, the important question is with respect to what? In other words, with respect to which criterion, and compared to what? For instance, on the basis of the NICS(0) criterion of aromaticity, C70 with a NICS(0) value of 27.2 ppm at the B3LYP/TZVP level of theory would be considered more aromatic than benzene with NICS(0) = 7.6 ppm.18 Similarly, based on a HOMOLUMO gap, cubane would seem to be more stable than dodecahedrane. Through this practice it becomes clear that to assess the possibilities of future synthesis of new (unknown) hydrogenated fullerenes one should use more than one “stability criteria” and/or more than one category of structures. To this end, we have constructed three top four lists (in the order from higher to lower) corresponding to cohesive, kinetic, and aromatic criteria. These lists are [C20H20, C180H180, C80H80, and C50H50], [C8H8, C20H20, C60H60, and C50H50], and [C60H2, C50H50, C70H40, C70H36], respectively. It is very interesting to observe that all three of those lists include at least one structure which has been synthesized (the third, the aromaticity, list includes three structures already synthesized). C50H50 is the only one common in all three of them, which is highly suggestive that this fullerane could be soon synthesized. Thus, the search for “stable” structures has brought up very important characteristics of much less known fulleranes, as well as the critical role of puckering through partial endo-hydrogenation in the stability of these structures. The idea of endo-hydrogenation, which is not in general equivalent to puckering, has surfaced many times in the literature since the early 1990s until today,9,10 despite the expected difficulties with possible surface barriers for introducing hydrogen into the cage and the resulting reduction in kinetic stability. However, most of the puckered isomers (for example of C50H50 and C60H60) have higher kinetic stability (HOMOLUMO gaps) compared to the initial fully exo-hydrogenated structures. When puckering is unfavorable (both cohesively and kinetically), depending on the number and site of endo-hydrogenated carbon atoms, we can see spectacular disintegration of the puckered structure as in both C60H60 and C50H50. Furthermore, depending on the way of production and the strategy of synthesis, a (small) amount of hydrogen could be inside the cage from the very beginning. Finally, independently of which stability criterion is used, if we want to have “consistent” comparisons and correlations of “stability”, it becomes clear from the present results that comparisons should be made among as similar as possible structures with similar bonding. Otherwise, we are led to “discrepancies”, such as, for instance, on the basis of the HOMOLUMO gap, cubane (a ladderane) would seem to be more stable than dodecahedrane. If the various stability criteria reflect different aspects of “stability” (or at least, different proportions of them), this could in part explain the lack of overall correlation between them. In this respect the reference structure for fulleranes (and fullerane fragments) is dodecahedrane, whereas the referene structure for ladderanes is cubane. So fulleranes must be compared to dodecahedrane (and all of them have lower binding and/or cohesive energies per C atom). The more specialized conclusions of the present investigation are as follows: 1. Although puckering, facilitated by partial endohydrogenation, is a very important and efficient process for stabilizing 14515



2.

3.

4.

5.

6.

7.

8. 9.

medium and large CnHn fulleranes, contrary to partially hydrogenated C60 and C70 cages, puckered CnHn fulleranes have not as yet been synthesized despite their energetic advantages (in several cases) in binding and cohesive energy. This in part could be attributed to existing barriers for penetration of hydrogen into the cage. Similarly to bare non-hydrogenated fullerenes, the stability of the fully and partially hydrogenated fullerenes is not directly related to their aromaticity (the aromatic electron delocalization), but it is rather accounted for by strain reduction. Among the more- and less-known totally and partially hydrogenated carbon fullerenes, dodecahedrane appears to be the most stable (in terms of binding and cohesive energy, and size of the HOMOLUMO gaps). This is at variance with results for the corresponding isovalent and isostructural hydrogenated silicon cages, for which the large puckered icosahedral Si80H80 and Si180H180 fulleranes are found to be more stable. Among the less known fully hydrogenated fullerenes, the puckered C50H50 cage of D5h symmetry is more stable (as far as binding energy is concerned) than the well-known C60H60 and C70H70 cages. The corresponding isovalent Si50H50 cage, besides Si60H60 and Si70H70, is even more stable than Si20H20. Yet, due to the existing barrier for penetration of hydrogen into the cage, “puckered” cages would not be easily accessible in practice. The embedded P@C50H50 cage of D5h symmetry is the most stable and efficient P-doped fullerene, with relatively large embedding energy and well localized spin in the doping P atom. Among the partially hydrogenated cases examined here, C70H36 and C70H40 appear to be the most stable, based on the cohesive energy criterion. This high stability is largely due to the five linked equatorial benzene-like rings that form a highly conjugated, graphite-like region. Among the fullerene fragments examined here the most stable is the bowl structure F20.1 in Figure 3 with alternating single and double carboncarbon bonds. Yet this is much less stable than the corresponding isoelectronic hydrogenated fullerene but much more stable than all ladderanes in Table 1 (including) cubane. Contrary to fulleranes, puckering is not efficient for “ladderanes”, at least for the ones examined here. Finally, all results presented here, unless otherwise stated, are largely analogous to homologous and isolobal hydrogenated silicon “fullerenes”.

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(9) Dunlap, B. I.; Brenner, D. W.; Mintmire, J. W.; Mowrey, R. C.; White, C. T. J. Phys. Chem. 1991, 95, 5763. (10) Strained Hydrocarbons. Beyond van’t Hoff and Le Bel Hypothesis; Dodziuk, H., Ed.; Wiley-VCH: Weinheim, 2009. (11) Linnolahti, M.; Karttunen, A. J.; Pakkanen, T. A. ChemPhysChem. 2006, 7, 1661. (12) Karttunen, A. J.; Linnolahti, M.; Pakkanen, T. A. J. Phys. Chem. C 2007, 111, 2545. (13) Zdetsis, A. D. Phys. Rev. B 2009, 80, 195417. Zdetsis, A. D. Phys. Rev. B 2009, 79, 195437. (14) Zdetsis, A. D. J. Phys. Chem. C 2010, 114, 10775. (15) Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F.; Frisch, M. J. J. Phys. Chem. 1994, 98, 11623. (16) TURBOMOLE (Version 5.6), Universitat Karlsruhe, 2000. (17) Sch€afer, C.; Huber; Ahlrichs, R. J. Chem. Phys. 1994, 100, 5829. (18) Zdetsis, A. D. J. Chem. Phys. 2007, 127, 214306. (19) Katz, T. J.; Acton, N. J. Am. Chem. Soc. 1973, 95, 2738–2739. (20) Zdetsis, A. D. Phys. Rev. B 2007, 76, 075402. (21) Zdetsis, A. D. Phys. Rev. B 2007, 75, 085409. (22) Grimme, S.; Comp., J. Chem. 2006, 27, 1787. Kruse, H.; Grimme, S. J. Phys. Chem. C 2009, 11, 17006. (23) Koiller, B.; Assali, L. V. C.; Petrilli, H. M.; Capaz, R. B.; Hu, X.; Das Sarma, S. Bull. Am. Phys. Soc. 2010, 55 (2), A35.00002. Cywinski, L.; Witzel, W. M.; Das Sarma, S. Phys. Rev. Lett. 2009, 102, 057601. (24) Book, L. D.; Scuseria, G. E. J. Phys. Chem. 1994, 98, 4283. (25) Hirsch, A.; Brettreich, M. Fullerenes: chemistry and reactions; Wiley-VCH: Weinheim, 2004. (26) Fowler, P. W.; Sandal1, J. P. B.; Austin, S. J.; Manolopoulos, D. E.; Lawrenson, P. D. M.; Smallwood, J. M. Synth. Met. 1996, 77, 97. (27) B€uhl, M.; Hirsch, A. Chem. Rev. 2001, 101, 1153. (28) Schleyer, P. v. R.; Maeker, C.; Dransfeld, A.; Jiao, H.; van Eikema Hommes, N. J. R. J. Am. Chem. Soc. 1997, 118, 6317. (29) Zdetsis, A. D.; Koukaras, E. N.; Garoufalis, C. S. App. Phys. Lett. 2007, 91, 203112. (30) Zdetsis, A. D. J. Chem. Phys. 2007, 127, 014314. (31) Chen, Z.; King, R. B. Chem. Rev. 2005, 105, 3613.

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Structural, Cohesive, Electronic, and Aromatic Properties of Selected

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