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Carborane super-nano-tubes
Chemical Physics Letters 634 (2015) 71–76
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Carborane super-nano-tubes Debojit Bhattacharya a,∗ , Douglas J. Klein a , Josep M. Oliva b a b
MARS, Texas A&M at Galveston, Galveston, TX 77553, USA Instituto de Química-Física “Rocasolano” (CSIC), ES-28006 Madrid, Spain
a r t i c l e
i n f o
Article history: Received 16 February 2015 In final form 26 May 2015 Available online 9 June 2015
a b s t r a c t Nano-structures are naturally sought to be designed from a few especially stable multifunctional units, which can be manipulated into diverse chosen forms. To this end an icosahedral para-carborane unit is here investigated as a basic building block, to form super-carborane nano-tubes. The energetics for differing conceivable forms of the super-nanotubes is investigated, to reveal evidently more stable choices and asymptotic behaviors for long tubes. Further a lower frequency band of exo-carboraneic vibrations is revealed, and interpreted. © 2015 Elsevier B.V. All rights reserved.
1. Introduction The investigation of especially novel nano-structures has become an area of ever-increasing importance. A general idea is to consider different readily available multifunctional molecular units to build up a selection of larger structures. Indeed the icosahedral borane unit was [1] so proposed, as a sort of ‘molecular tinkertoy’, with the unit being fairly rigid, stable, and able to provide a few different angles of coupling – offering more possibilities for 3-dimensional patterned structures than the ubiquitous benzene units. Several choices of different possible simple multipurpose units have been made [2,3]. And occasionally other possibilities for such carborane units have been proposed [4,5]. In the area of nano-technology, different projected [6] nano-devices have been based on fused diamondoid structures, which still entail a severe synthesis problem, especially for the proposed often stressed fused structures – and much experimental effort has been expended [7] to attempt to deal with diamondoid structures (which however in practice have been largely unstressed) – such study fueled by the discovery [8,9] of a natural source of many polymantanes. Here we return to Müller et al.’s [1] unique dodeca-borane (or carborane) units to look at some especially novel structures. Now B12 H12 2− is a well-known [10–13] perfectly stable anion, of an elegant symmetry, of the regular icosahedron. To avoid (unshielded) Coulomb repulsions and thereby facilitate couplings between such icosahedron units, it seems plausible instead to work with (the also well-known [11–15]) neutral (iso-electronic) carborane units C2 B10 H12 , which though the carboranes do not
∗ Corresponding author. E-mail address: [email protected] (D. Bhattacharya). http://dx.doi.org/10.1016/j.cplett.2015.05.058 0009-2614/© 2015 Elsevier B.V. All rights reserved.
achieve full icosahedral symmetry [16], still involve (only very slightly distorted) molecular icosahedra. Indeed there are three isomers depending on where the two C atoms replace B atoms. We focus on the para- (D5d -symmetry) isomer of Figure 1, since with our constructions this typically leads to more highly symmetric super-structures, while also it is more stable than the orthoor meta-isomers (each of C2v -symmetry). Through the use of the para-carborane unit we then seek to form and investigate novel features of nano-structures formed from such a multi-functional unit. While in our earlier work [16] we focused on a ‘uniquely elegant’ icosahedral-symmetry super-carborane of 12 carborane units, here we focus on a more general extended structure, making super-tubes from our para-carborane units. Such super-tubes can be imagined to be useful in different contexts, e.g., as nano-pipes to carry (smaller) molecular material – as these super-tubes have an inside radius similar to the outside radius of a single carborane unit, molecules of slightly smaller size than a carborane unit should fit and be transportable. But also our currently studied super-tubes could conceivably act as the structural scaffolding for a yet larger nano-structure. 2. Present constructions Here from such carborane units we then first seek to form a proto-type class of nano-structures, namely super-nano-tubes of different lengths, with caps on each end. At the zeroth stage (i.e., at the shortest length, L = 0, with only caps or super-caps) we follow our earlier choice [16] taking 12 of these para-carborane units and coupling them to form a giant icosahedron, in such a way that the C · · · C axis of each component carborane unit occurs oriented along a fivefold axis of the giant icosahedron. During each coupling, a pair of B H bonds in neighboring carboranes are replaced by a B B
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Figure 1. The basic building-block unit of para-carborane. Pink, black and yellowishorange colors represent the boron, carbon and hydrogen atoms respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Figure 3. The mode of interlinking between two subsequent super-pentagons. As an aid to the perception of 3-dim structure, the nearest vertices are colored red, followed by rainbow colors (orange, yellow, green, blue and violet) as the distance increases. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
↑
z
z Figure 2. The component pieces of our (H-deleted) super-nanotubes. As an aid to the perception of 3-dim structure, the nearest vertices are colored red, followed by rainbow colors (orange, yellow, green, blue and violet) as the distance increases. The cap ends are colored yellowish green to make them separate from the others. Joining to the four depicted super-components (with inter connections as in Figure 3) gives an L = 2 super-nano-tubes. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
bond (with the pair of H atoms being removed). This is to be done at each of the five B atoms surrounding one of the C atoms of each para-C2 B10 H12 . With this indicated mode of coupling, the result is a new [16] icosahedral symmetry species: a carborane-based supericosahedron. Next we can imagine this icosahedral super-carborane to be split into two equal super-caps which then are to be used to terminate different length L > 0 open-ended super-nanotubes. That is, we investigate the possibility of tubes with components as in Figure 2. This figure shows at the left and right two caps, and in between two pentagonal units, which are super-pentagons each comprised from five carboranes. If there were no intervening super-pentagons, and the two super-caps are interconnected, then the L = 0 supericosahedron of the preceding paragraph is recovered. Now with the super-pentagons, each is to share a common fivefold axis (along with the ends), but successive super-pentagons are to be rotated by 2/10 about this axis. And such a rotational relation is to apply for the end super-cap super-pentagon part adjacent to an internal super-pentagon. Each super-pentagon is imagined to manifest 2-bonds from each carborane unit to carboranes of a neighboring super-pentagon as in Figure 3. A further point regarding the super-pentagons is that they each manifest just C5v symmetry rather than D5h symmetry – as arises because of the chosen orientations of the C-atoms in the constituent para-carboranes. With this additional specification of the C-atom (location) in the constituent para-carboranes, one needs
−
+
z
super-tube axis
z ↓
Figure 4. A side-view of a carborane icosahedron, with the super-nano-tube axis along the direction indicated. Our names for the six choices of para-axes are shown. Note that the (coaxial) nodes at the opposite ends of the + and − axes are hidden behind the − and + nodes shown. A similar situation applies for the ↑ and ↓ nodes.
to go beyond the specifications of the preceding paragraph. For simplicity and higher symmetry we take each para-carborane in a super-pentagon to have a like orientation (of its C-atoms) with respect to the parent super-pentagon, whence there are further choices for the resultant ‘orientation’ of each super-pentagon. This can be understood from the carborane of Figure 1, when for the super-carborane each B- or C-atom is replaced by a para-C2 B10 H12 unit with the two carbons lying on the opposite sides along what is the H-bond axis in Figure 1. The two boron pentagons of Figure 1 then end up in the super-structure having these axes slanted (relative to the super-pentagons) in opposite directions, say − and + for the respective pentagons on the left and right. Further yet, the C-axis of a para-carborane may be tangent to the nano-tube surface formed by the super-tube comprised from a sequence of super-pentagons. That is, for the six axes thru opposite vertices of an icosahedron there are six corresponding choices of the pair of C-atoms in a para-carborane, and thence also for the superpentagons. These six axes may be conveniently identified if we view a carborane from a side, looking toward it and the central axis of a super-pentagon, oriented along the dashed line, all as depicted in Figure 4 where each node of an icosahedron is labelled with one of six indices +, −, z, z¯ , ↑, ↓ such that antipodal nodes have the same index (and label pairs {+ , −}, {z, z¯ }, {↑ , ↓} are interchanged by
D. Bhattacharya et al. / Chemical Physics Letters 634 (2015) 71–76
different symmetry operations (as indicated shortly). The six different sorts of super-pentagons are then to be linked pair-wise (as in Figure 4) down a tube of L such super-pentagons. 3. Pair interactions There clearly are many possibilities for placing L of our superpentagons down a carborane super-nanotube. In fact ≤6L and ≥6L /4, where the factor of 4 arises because of a group C2v rearranging the super-pentagons of a super-nano-tube amongst one another. Indeed if we take the axial (long axis) of a supernanotubes to be the z-axis, then we can denote this group as C2v = {I, C2 , , C2 } with a reflection about the xy-mid-plane of the nano-tube and C2 a twofold rotation about an axis through the tube center normal to the z-axis. Then neighboring super-pentagon pairs are interchanged in accordance with I · = C2 · = (C2 · )(C2 · ) · = ()() C2 · = (C2 · )(C2 · )
⎫ ⎪ ⎪ ⎬ ⎪ ⎪ ⎭
,
, ∈ {+, −, ↑, ↓, z, z¯ }
(1)
The elements of the group then permute the super-pentagons as in Table 1S (in our supporting information). As a result there are just 13 equivalence classes of super-pentagon pairs out of 6 × 6 = 36 total possibilities (as indicated in Table 2S (in our Supporting information), further discussed in the next paragraph). In order to entertain a manageable number of carborane supernanotubes we then propose to seek out and study just the more stable candidates – presuming an additivity of interaction energies amongst the different super-pentagons – keeping the end caps fixed as already described. That is we assume an energy for a lengthL nano-tube with super-pentagons 1 , 2 , . . ., L to be given by
(2) are basic cap and super-pentagon energies, ε where εcap and is an interaction energy between types and super-pentagon units, while n enumerates the super-pentagon pairs. We find 13 distinguishable super-pentagon pairs with interaction energies as in Table 2S. Here the interaction energies ε are taken from the for a -pair with an computed energies average energy for lone super-pentagons. For simplicity the average is taken over single-pentagon species with H-atoms at all C or B atom bonding positions not used within the single-pentagon. . From this one sees (in The result is Table 2S) that the most stable neighbor pair is for =− +. But of course the whole chain of super-pentagons cannot all be made to be =− +, since following such a pair one must have a following / − +). Taking this into account we anticipate pair + (clearly no = the most stable chain to be that from taking alternating + and − super-pentagons. Figure 1S (in our Supporting information) shows the actual geometry of the neighbor pair − + and + − respectively. Furthermore, Figure 2S (in our supporting information) depicts of the super carborane nano-tube (L = 4) as viewed along the z-axis (the axis of the nano-tube). Here our super-nano-tubes are to contain L super-pentagons between two super-caps- somewhat as indicated in Figure 3. An L = 40 super-nano-tube is shown in Figure 5. If left and right caps are denoted by ⊂ and⊃, then this species in Figure 5 might be denoted ⊂· (+ −)20 · ⊃. A general super-nanotube would be denoted ⊂· 1 , 2 , . . ., L · ⊃ with each i , i = 1 to L, taking one of the six axis values indicated in Figure 5.
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Table 1 Schleyer–Williams [18] (so-called) ‘strain’ energies (MM2, in kcal/mol) of supercarborane nano-tubes starting from 4 to 40 super pentagonal carborane units. (Besides strains due to geometric distortions this also includes various non-neighbor interactions). L
Stretch
Bend
Non-1,4 VDW
1,4 VDW
Strain energy
4 8 12 16 20 24 28 32 36 40
2934.5 5628.8 8323.1 11017.3 13653.5 16336.4 19019.3 21702.1 24385.0 27067.9
24766.3 47289.4 69812.6 92335.7 114743.7 137244.2 159744.8 182245.3 204745.9 227246.4
−80.7 −124.8 −168.9 −213.0 −258.5 −303.2 −347.9 −392.6 −437.3 −482.0
−82.9 −148.6 −214.3 −280.1 −343.4 −408.6 −473.8 −539.0 −604.2 −669.4
27537.3 52644.9 77752.4 102860.0 127795.3 152868.8 177942.3 203015.8 228089.3 253162.9
4. Nano-tube computations All the molecules are optimized at the molecular mechanics level keeping in mind their size and shape and comparisons are made of their frequencies, all using Gaussian software [17]. All the frequencies are found to be positive, i.e. no imaginary frequencies are found, thereby indicating stable molecular geometries. On the other hand, ‘strain’ energies (in Table 1) are computed with molecular mechanics (MM2) level for all molecules. Readership might note that, Schleyer and Williams [18] in 1970 presented a ‘group-contribution-like’ scheme for estimation of heats of formation with the higher-order (longer-range) contributions being identified to ‘strain’. But this nomenclature is faulty in the sense that ‘strain’ properly relates to geometry, while ‘stress’ properly relates to force. It may also be noted that there are other counter choices as to how energies should be referenced [19], avoiding the assignment of stress or strain in certain systems. And non-1,4-VWD and 1,4-VWD terms obtained from MM2 run represent non-bonded and bonded van der Waals energies. However, here we utilize the strain energy delivered by the MM2 package [20] we use. The strain energies show a highly linear increase in terms of number of carborane super-pentagon units, in consonance with our additivity presumption (of Eq. (2)), as seen in Figure 3S (in our supporting information), where the excellence of the linear fit is indicated by the correlation coefficient R2 ∼ = 0.9997. We note that the ‘strain’ energies of the super-carborane nano-tubes of length L = 4 to L = 40 increase from 27 537 kcal/mol to 253 162 kcal/mol, whereas the same for the carbon nano-tube having chiral index (n, m) = (10, 10) with tube length = 50 is 1460 kcal/mol. The computations for the super-pentagon pairs (in Table 2S) in the previous section are done by semi-empirical PM6 level, as already discussed in the preceding section, and lead to our energetically preferred choice of alternating + and − super-pentagon units. This calculations gives respective − + and + − interaction energies per super-pentagon pair of −9114.63 and −8884.37 eV (with an average −8998.45 eV), while other choices continue to give higher energies. Further molecular mechanics computational results for normal-mode vibrational frequencies, are depicted in later figures. 5. Stress and strain In the super-carborane [16] structure the bond angles are not quite right. That is, the construction demands inter-unit angles of 60◦ , whereas the angles of two B H bonds at neighboring sites of a regular icosahedral (car-) borane unit are not directed at this angle, but rather at ≈63.3◦ . The consequent stress and strain is apparently handled tolerably well at our super-stage. And as the super-carborane pentagons and caps are the secondary building blocks (carborane is the primary) of our designed systems, we attend to the associated secondary-structure contributions energy
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Figure 5. Our longest super-carborane nano-tubes with L = 40 super-pentagons and two caps.
(Table 2S) of these systems. The strain energy clearly increases as the number of carborane super-pentagons increases. To check the stresses in an experimentally more amenable manner, we turn to computations of frequencies of normal modes of vibration (in Table 2). Thence we have done this, at the molecular mechanics level. In our previous work [16] we found that the lowest frequency super-carborane vibrational force constant is ∼190 cm−1 , while the first vibrational force constant for the simple carborane is ∼790 cm−1 , which entails a wiggling of H atoms grouped by distortions of the attached borons in the boron triangles in the belt of borons around the para-C-axis. In the same way here the super-carborane nano-tubes with L = 4 super-pentagon units lead to a first (i.e., lowest) vibrational frequency ∼101 cm−1 which is almost half that of the super-carborane [16]. A subsequent decrease of the first vibrational force constant is observed as the length L of the species increases along the series. This lowering of the force constants of the super-carborane nanotube series are plausibly associated to stresses arising from the mentioned angle off-set. A further check for our L = 4 case is provided via inspection of the other associated normal vibrational modes, whence we find a fairly dense packing of (normal-mode) vibrational frequencies up to ≈560 cm−1 whereafter there is large gap up to the higher frequency ≈850 cm−1 which we associate (primarily) with internal motions in individual carboranes. Inspection of the highest frequency of our lower energy band reveals it to involve primarily the near-rigid motion of whole C2 B10 H7 units – which is to say, it is the bonds between these units which are stretching and bending, and therefore are evidently weak, because of the indicated angle-off-set stress. Granted such weak inter-carborane coupling, there should be many other additional low-frequency modes: 3 rotational and 3 translational modes for each of our present 22 carborane units, minus 3 overall translation and 3 overall rotation for the super-carborane as a whole, to give (3 + 3) · 22– (3 + 3) = 126 hypothesized low-frequency vibrational modes. Indeed, we find exactly 126 such low-frequency modes ranging from ∼101 cm−1 up to ∼557 cm−1 whereafter there is a jump to ∼850 cm−1 (the 127th normal mode). Examination of the lowest frequency ∼850 cm−1 normal mode after the gap reveals that it involves H-atom wagging internal to individual carboranes. Thence, this L = 4 super-carborane nano-tubes is reasonably tested as a stable possibility, with interior stress related to a band of (126) low-energy normal modes. For longer super-nanotubes this overall pattern of behavior appears to persist, with slight changes in the positions of the upper and lower frequencies of the exo- and intra-nodes. That is, there
is a lower energy band involving 3 rotations and 3 translations of each of the 6 + 5L + 6 carboranes (involved in the 6-carborane units of each cap along with the 5 carboranes of each super-pentagon). But also we subtract off the overall 3 rotations and 3 translations for the super-tube as a whole, thereby leaving a low-energy band of (3 + 3) (6 + 5L + 6) − (3 + 3) = 30L + 66 normal modes involving motions of whole internally near-rigid carborane units. The behavior seems to be similar to that of molecular crystals, where the internal vibrational modes are of high frequency, while the low-frequency (vibrational) modes include dissimilar comparatively inflexible molecules vibrating/rotating against one another. These lower frequency normal modes (mostly entailing motions of internally rigid carboranes) we term exocarboraneic. The lowest exo-carboreneic frequency flow-exo seems to become ever smaller as the system becomes ever larger, and indeed in Figure 4S (in our supporting information) we see that L · flow-exo → 0 in a linear fashion as the tube length L→ ∞, thereby indicating flow-exo ∼ 1/L2 for small L, much as for the confinement of a particle (a phonon) to a box of length L. The remaining higher frequency modes beyond the exo-carboraneic, we term intracarboraneic. Table 2 gives the lower and upper frequencies for both the exo- and intra-carborane sets (or bands) of frequencies – the sequence number i for each frequency is also noted. The asymptotic behavior of the upper exo-frequency as well as both the lower and upper intra-carboraneic frequencies are plotted against 1/L2 in Figure 5S (in our supporting information), to reveal their asymptotic behaviors approaching different finite limits, evidently bounding different phonon bands. A yet further illustration of our ideas is given in the Figure 6, showing discretized densities of states for the L = 40 and the simple carborane (C) cases. In the simple carborane case there is a complete absence of the exo-carboraneic band, which however is clearly seen (between 0 and 590 cm−1 ) for the L = 40 super-carborane (SC) case. Indeed this exo-carbonic band seems to be split into two sub-bends, the lower of which surmise corresponds primarily to rotational motions of individual carborane units, while the upper sub-band corresponds primarily to vibro-translational motions of one carborane against another. The overall vibrational (or phonon) structure is elucidated. Overall bulk distortions of the nano-tubes of course depend collectively on the low-energy normal modes (as well as their frequencies and relative distribution of frequencies). That the bulk
Table 2 The exo-carborane-frequencies (in cm−1 ) lower (fE-C-L ) and upper (fE-C-U ) (where the jumps observed) vibrational modes and also the lower (fI-C-L ) and upper (fI-C-U ) vibrational modes of intra-carborane frequencies of all carborane super-nano-tubes, where, i is the sequence number for vibrational frequencies (in order of increasing frequencies). L
4 8 12 16 20 24 28 32 36 40
Exo-carborane frequencies
Intra-carborane frequencies
Lower (fE-C-L )
Upper (fE-C-U )
Lower (fI-C-L )
Upper (fI-C-U )
101.67 (i = 1) 37.92 (i = 1) 19.33 (i = 1) 11.56 (i = 1) 7.65 (i = 1) 5.43 (i = 1) 4.04 (i = 1) 3.15 (i = 1) 2.47 (i = 1) 2.02 (i = 1)
557.52 (i = 126) 581.01 (i = 246) 583.77 (i = 366) 585.25 (i = 486) 585.73 (i = 606) 585.98 (i = 726) 586.13 (i = 846) 586.22 (i = 966) 586.28 (i = 1086) 586.95 (i = 1206)
853.8 (i = 127) 846.46 (i = 247) 846.05 (i = 367) 845.28 (i = 487) 845.13 (i = 607) 845.05 (i = 727) 844.09 (i = 847) 844.97 (i = 967) 844.93 (i = 1087) 845.05 (i = 1207)
3235.47 (i = 1218) 3231.45 (i = 2298) 3231.36 (i = 3378) 3231.47 (i = 4458) 3231.56 (i = 5538) 3231.52 (i = 6616) 3231.49 (i = 7698) 3231.37 (i = 8778) 3231.29 (i = 9858) 3231.26 (i = 10938)
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Figure 6. Discretized density of states (DOS) plots of the super-carborane nano tubes having 40 pentagonal blocks with two ends (basic carborane halves) in blue color and also the basic carborane unit with red color. Note the different scales for L = 40 and L = 0 on the left and right, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
distortions arise from this lower-energy band indicates that such bulk distortions of the super-tube should be able to be done relatively readily. 6. Conclusions We have studied the possibility of novel nano-tube-structures comprised from para-carborane units. Although they evidently present a severe synthetic challenge, these super-carborane-nanotubes appear to be reasonably stable. Moreover, we have developed and tested an appealing qualitative description of the resulting super-nanotubes. At a first step this entails a simple additivity relation for (strain) energies, such as we use to select the more stable super nano-tubes. At a second step, we find a partitioning of the normal vibrational modes into low-frequency ‘exo-carboraneic’ modes and higher frequency and higher-frequency ‘intra-carboraneic’ modes. Indeed this picture is an elaboration of that found [16] for the super-carborane structure, as corresponds to an L = 0 supernano-tube in our present study. We also have calculated the exterior dimensions of the tube, the tube surface pore size, the cavity dimension for the super-carborane nano-tube, to compare them with the carbon nano-tube having chiral index (n, m) = (10, 10) and tube length = 50. The exterior dimension of both types of tubes did not vary much – ∼13.66 and ∼13.80 A˚ for super-carborane and carbon nano-tube respectively, whereas the interior dimension of the super-carborane nano-tube is ∼5.6 A˚ as viewed from Figures 6S and 7S (in our supporting information). The tube surface pore-sizes of ˚ the super-carborane and carbon nano-tube are ∼3.3 and ∼2.9 A, respectively, as is also evident from the Figures 8S and 9S (in our supporting information). The relative ease of bulk distortions of the super-tubes traces to the fact that the accompanying normal modes are found in the lower energy band, and this in turn traces to the fact that there is a stress in the constructions made. This stress inherent in our constructions entails mismatching of angles. The equilateral supertriangles in the surface of the super-tubes each consist of three carboranes at the vertices of an equilateral super-triangle, then manifesting 60◦ angles, whereas the directrixes from the center of a carborane through adjacent cage (B) atoms is ≈63.3◦ – so that
there is a mismatch in bond angles. This mismatch then quite naturally leads (as indicated) to an increase in flexibility, and also a diminishment in strength. We plausibly surmise that similar substructure additivity relations and similar exo-/intra-carboraneic partitioning extends to other super-structures based on (similarly) interconnecting carborane units. The possibility that such partitioning extends to other super-structures based on other stable units such as C60 -fullerene [4,5] or adamantane should perhaps be investigated. Acknowledgments The authors acknowledge the support of the Welch Foundation of Houston, Texas (via grant BD-0894), and project COOPB20040 (CSIC). DB specially thanks Tamal Goswami for his support while addressing the reviewers’ comments. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.cplett.2015.05.058 References [1] J. Müller, K. Base, T.F. Magnera, J. Michl, J. Am. Chem. Soc. 114 (1992) 9721. [2] J.M. Oliva, L. Serrano-Andres, D.J. Klein, P.v.R. Schleyer, J. Michl, Int. J. Photoenergy 2009 (2009) 292393. [3] J.M. Oliva, Adv. Quantum Chem. 64 (2012) 105. [4] H.-Y. Zhu, D.J. Klein, Croat. Chem. Acta 70 (1997) 519. [5] S.G. Semenov, F.Y. Sigolaev, A.V. Belyakov, J. Struct. Chem. 54 (2013) 960. [6] K.E. Drexler, Engines of Creation – The Coming Era of Nanotechnology, Doubleday, NY, 1989. [7] H. Schwertfeger, A.A. Fokin, P.R. Schreiner, Angew. Chem., Int. Ed. 47 (2008) 1022. [8] J.E. Dahl, J.M. Moldowan, K.E. Peters, G.E. Claypool, M.A. Rooney, G.E. Michael, M.R. Mello, M.L. Kohnen, Nature 399 (1999) 54. [9] P.L.B. de Arujo, G.A. Mansoori, E.S. Arujo, J. Oil, Gas Coal Tech. 5 (2012) 316. [10] J.A. Wunderlich, W.N. Lipscomb, J. Am. Chem. Soc. 82 (1960) 4427. [11] E.L. Mutterties, W.H. Knoth, Polyhedral Boranes, Marcel Dekker, NY, 1968. [12] I.B. Sivaev, V.I. Bregadze, S. Sjöberg, Czech. Chem. Commun. 67 (2002) 679. [13] R.M. Grimes, Carboranes, 2nd ed., Academic Press, NY, 2011. [14] S. Papetti, T.L. Heying, J. Am. Chem. Soc. 86 (1964) 2295.
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Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Carborane super-nano-tubes Debojit Bhattacharya a,∗ , Douglas J. Klein a , Josep M. Oliva b a b
MARS, Texas A&M at Galveston, Galveston, TX 77553, USA Instituto de Química-Física “Rocasolano” (CSIC), ES-28006 Madrid, Spain
a r t i c l e
i n f o
Article history: Received 16 February 2015 In final form 26 May 2015 Available online 9 June 2015
a b s t r a c t Nano-structures are naturally sought to be designed from a few especially stable multifunctional units, which can be manipulated into diverse chosen forms. To this end an icosahedral para-carborane unit is here investigated as a basic building block, to form super-carborane nano-tubes. The energetics for differing conceivable forms of the super-nanotubes is investigated, to reveal evidently more stable choices and asymptotic behaviors for long tubes. Further a lower frequency band of exo-carboraneic vibrations is revealed, and interpreted. © 2015 Elsevier B.V. All rights reserved.
1. Introduction The investigation of especially novel nano-structures has become an area of ever-increasing importance. A general idea is to consider different readily available multifunctional molecular units to build up a selection of larger structures. Indeed the icosahedral borane unit was [1] so proposed, as a sort of ‘molecular tinkertoy’, with the unit being fairly rigid, stable, and able to provide a few different angles of coupling – offering more possibilities for 3-dimensional patterned structures than the ubiquitous benzene units. Several choices of different possible simple multipurpose units have been made [2,3]. And occasionally other possibilities for such carborane units have been proposed [4,5]. In the area of nano-technology, different projected [6] nano-devices have been based on fused diamondoid structures, which still entail a severe synthesis problem, especially for the proposed often stressed fused structures – and much experimental effort has been expended [7] to attempt to deal with diamondoid structures (which however in practice have been largely unstressed) – such study fueled by the discovery [8,9] of a natural source of many polymantanes. Here we return to Müller et al.’s [1] unique dodeca-borane (or carborane) units to look at some especially novel structures. Now B12 H12 2− is a well-known [10–13] perfectly stable anion, of an elegant symmetry, of the regular icosahedron. To avoid (unshielded) Coulomb repulsions and thereby facilitate couplings between such icosahedron units, it seems plausible instead to work with (the also well-known [11–15]) neutral (iso-electronic) carborane units C2 B10 H12 , which though the carboranes do not
∗ Corresponding author. E-mail address: [email protected] (D. Bhattacharya). http://dx.doi.org/10.1016/j.cplett.2015.05.058 0009-2614/© 2015 Elsevier B.V. All rights reserved.
achieve full icosahedral symmetry [16], still involve (only very slightly distorted) molecular icosahedra. Indeed there are three isomers depending on where the two C atoms replace B atoms. We focus on the para- (D5d -symmetry) isomer of Figure 1, since with our constructions this typically leads to more highly symmetric super-structures, while also it is more stable than the orthoor meta-isomers (each of C2v -symmetry). Through the use of the para-carborane unit we then seek to form and investigate novel features of nano-structures formed from such a multi-functional unit. While in our earlier work [16] we focused on a ‘uniquely elegant’ icosahedral-symmetry super-carborane of 12 carborane units, here we focus on a more general extended structure, making super-tubes from our para-carborane units. Such super-tubes can be imagined to be useful in different contexts, e.g., as nano-pipes to carry (smaller) molecular material – as these super-tubes have an inside radius similar to the outside radius of a single carborane unit, molecules of slightly smaller size than a carborane unit should fit and be transportable. But also our currently studied super-tubes could conceivably act as the structural scaffolding for a yet larger nano-structure. 2. Present constructions Here from such carborane units we then first seek to form a proto-type class of nano-structures, namely super-nano-tubes of different lengths, with caps on each end. At the zeroth stage (i.e., at the shortest length, L = 0, with only caps or super-caps) we follow our earlier choice [16] taking 12 of these para-carborane units and coupling them to form a giant icosahedron, in such a way that the C · · · C axis of each component carborane unit occurs oriented along a fivefold axis of the giant icosahedron. During each coupling, a pair of B H bonds in neighboring carboranes are replaced by a B B
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Figure 1. The basic building-block unit of para-carborane. Pink, black and yellowishorange colors represent the boron, carbon and hydrogen atoms respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Figure 3. The mode of interlinking between two subsequent super-pentagons. As an aid to the perception of 3-dim structure, the nearest vertices are colored red, followed by rainbow colors (orange, yellow, green, blue and violet) as the distance increases. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
↑
z
z Figure 2. The component pieces of our (H-deleted) super-nanotubes. As an aid to the perception of 3-dim structure, the nearest vertices are colored red, followed by rainbow colors (orange, yellow, green, blue and violet) as the distance increases. The cap ends are colored yellowish green to make them separate from the others. Joining to the four depicted super-components (with inter connections as in Figure 3) gives an L = 2 super-nano-tubes. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
bond (with the pair of H atoms being removed). This is to be done at each of the five B atoms surrounding one of the C atoms of each para-C2 B10 H12 . With this indicated mode of coupling, the result is a new [16] icosahedral symmetry species: a carborane-based supericosahedron. Next we can imagine this icosahedral super-carborane to be split into two equal super-caps which then are to be used to terminate different length L > 0 open-ended super-nanotubes. That is, we investigate the possibility of tubes with components as in Figure 2. This figure shows at the left and right two caps, and in between two pentagonal units, which are super-pentagons each comprised from five carboranes. If there were no intervening super-pentagons, and the two super-caps are interconnected, then the L = 0 supericosahedron of the preceding paragraph is recovered. Now with the super-pentagons, each is to share a common fivefold axis (along with the ends), but successive super-pentagons are to be rotated by 2/10 about this axis. And such a rotational relation is to apply for the end super-cap super-pentagon part adjacent to an internal super-pentagon. Each super-pentagon is imagined to manifest 2-bonds from each carborane unit to carboranes of a neighboring super-pentagon as in Figure 3. A further point regarding the super-pentagons is that they each manifest just C5v symmetry rather than D5h symmetry – as arises because of the chosen orientations of the C-atoms in the constituent para-carboranes. With this additional specification of the C-atom (location) in the constituent para-carboranes, one needs
−
+
z
super-tube axis
z ↓
Figure 4. A side-view of a carborane icosahedron, with the super-nano-tube axis along the direction indicated. Our names for the six choices of para-axes are shown. Note that the (coaxial) nodes at the opposite ends of the + and − axes are hidden behind the − and + nodes shown. A similar situation applies for the ↑ and ↓ nodes.
to go beyond the specifications of the preceding paragraph. For simplicity and higher symmetry we take each para-carborane in a super-pentagon to have a like orientation (of its C-atoms) with respect to the parent super-pentagon, whence there are further choices for the resultant ‘orientation’ of each super-pentagon. This can be understood from the carborane of Figure 1, when for the super-carborane each B- or C-atom is replaced by a para-C2 B10 H12 unit with the two carbons lying on the opposite sides along what is the H-bond axis in Figure 1. The two boron pentagons of Figure 1 then end up in the super-structure having these axes slanted (relative to the super-pentagons) in opposite directions, say − and + for the respective pentagons on the left and right. Further yet, the C-axis of a para-carborane may be tangent to the nano-tube surface formed by the super-tube comprised from a sequence of super-pentagons. That is, for the six axes thru opposite vertices of an icosahedron there are six corresponding choices of the pair of C-atoms in a para-carborane, and thence also for the superpentagons. These six axes may be conveniently identified if we view a carborane from a side, looking toward it and the central axis of a super-pentagon, oriented along the dashed line, all as depicted in Figure 4 where each node of an icosahedron is labelled with one of six indices +, −, z, z¯ , ↑, ↓ such that antipodal nodes have the same index (and label pairs {+ , −}, {z, z¯ }, {↑ , ↓} are interchanged by
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different symmetry operations (as indicated shortly). The six different sorts of super-pentagons are then to be linked pair-wise (as in Figure 4) down a tube of L such super-pentagons. 3. Pair interactions There clearly are many possibilities for placing L of our superpentagons down a carborane super-nanotube. In fact ≤6L and ≥6L /4, where the factor of 4 arises because of a group C2v rearranging the super-pentagons of a super-nano-tube amongst one another. Indeed if we take the axial (long axis) of a supernanotubes to be the z-axis, then we can denote this group as C2v = {I, C2 , , C2 } with a reflection about the xy-mid-plane of the nano-tube and C2 a twofold rotation about an axis through the tube center normal to the z-axis. Then neighboring super-pentagon pairs are interchanged in accordance with I · = C2 · = (C2 · )(C2 · ) · = ()() C2 · = (C2 · )(C2 · )
⎫ ⎪ ⎪ ⎬ ⎪ ⎪ ⎭
,
, ∈ {+, −, ↑, ↓, z, z¯ }
(1)
The elements of the group then permute the super-pentagons as in Table 1S (in our supporting information). As a result there are just 13 equivalence classes of super-pentagon pairs out of 6 × 6 = 36 total possibilities (as indicated in Table 2S (in our Supporting information), further discussed in the next paragraph). In order to entertain a manageable number of carborane supernanotubes we then propose to seek out and study just the more stable candidates – presuming an additivity of interaction energies amongst the different super-pentagons – keeping the end caps fixed as already described. That is we assume an energy for a lengthL nano-tube with super-pentagons 1 , 2 , . . ., L to be given by
(2) are basic cap and super-pentagon energies, ε where εcap and is an interaction energy between types and super-pentagon units, while n enumerates the super-pentagon pairs. We find 13 distinguishable super-pentagon pairs with interaction energies as in Table 2S. Here the interaction energies ε are taken from the for a -pair with an computed energies average energy for lone super-pentagons. For simplicity the average is taken over single-pentagon species with H-atoms at all C or B atom bonding positions not used within the single-pentagon. . From this one sees (in The result is Table 2S) that the most stable neighbor pair is for =− +. But of course the whole chain of super-pentagons cannot all be made to be =− +, since following such a pair one must have a following / − +). Taking this into account we anticipate pair + (clearly no = the most stable chain to be that from taking alternating + and − super-pentagons. Figure 1S (in our Supporting information) shows the actual geometry of the neighbor pair − + and + − respectively. Furthermore, Figure 2S (in our supporting information) depicts of the super carborane nano-tube (L = 4) as viewed along the z-axis (the axis of the nano-tube). Here our super-nano-tubes are to contain L super-pentagons between two super-caps- somewhat as indicated in Figure 3. An L = 40 super-nano-tube is shown in Figure 5. If left and right caps are denoted by ⊂ and⊃, then this species in Figure 5 might be denoted ⊂· (+ −)20 · ⊃. A general super-nanotube would be denoted ⊂· 1 , 2 , . . ., L · ⊃ with each i , i = 1 to L, taking one of the six axis values indicated in Figure 5.
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Table 1 Schleyer–Williams [18] (so-called) ‘strain’ energies (MM2, in kcal/mol) of supercarborane nano-tubes starting from 4 to 40 super pentagonal carborane units. (Besides strains due to geometric distortions this also includes various non-neighbor interactions). L
Stretch
Bend
Non-1,4 VDW
1,4 VDW
Strain energy
4 8 12 16 20 24 28 32 36 40
2934.5 5628.8 8323.1 11017.3 13653.5 16336.4 19019.3 21702.1 24385.0 27067.9
24766.3 47289.4 69812.6 92335.7 114743.7 137244.2 159744.8 182245.3 204745.9 227246.4
−80.7 −124.8 −168.9 −213.0 −258.5 −303.2 −347.9 −392.6 −437.3 −482.0
−82.9 −148.6 −214.3 −280.1 −343.4 −408.6 −473.8 −539.0 −604.2 −669.4
27537.3 52644.9 77752.4 102860.0 127795.3 152868.8 177942.3 203015.8 228089.3 253162.9
4. Nano-tube computations All the molecules are optimized at the molecular mechanics level keeping in mind their size and shape and comparisons are made of their frequencies, all using Gaussian software [17]. All the frequencies are found to be positive, i.e. no imaginary frequencies are found, thereby indicating stable molecular geometries. On the other hand, ‘strain’ energies (in Table 1) are computed with molecular mechanics (MM2) level for all molecules. Readership might note that, Schleyer and Williams [18] in 1970 presented a ‘group-contribution-like’ scheme for estimation of heats of formation with the higher-order (longer-range) contributions being identified to ‘strain’. But this nomenclature is faulty in the sense that ‘strain’ properly relates to geometry, while ‘stress’ properly relates to force. It may also be noted that there are other counter choices as to how energies should be referenced [19], avoiding the assignment of stress or strain in certain systems. And non-1,4-VWD and 1,4-VWD terms obtained from MM2 run represent non-bonded and bonded van der Waals energies. However, here we utilize the strain energy delivered by the MM2 package [20] we use. The strain energies show a highly linear increase in terms of number of carborane super-pentagon units, in consonance with our additivity presumption (of Eq. (2)), as seen in Figure 3S (in our supporting information), where the excellence of the linear fit is indicated by the correlation coefficient R2 ∼ = 0.9997. We note that the ‘strain’ energies of the super-carborane nano-tubes of length L = 4 to L = 40 increase from 27 537 kcal/mol to 253 162 kcal/mol, whereas the same for the carbon nano-tube having chiral index (n, m) = (10, 10) with tube length = 50 is 1460 kcal/mol. The computations for the super-pentagon pairs (in Table 2S) in the previous section are done by semi-empirical PM6 level, as already discussed in the preceding section, and lead to our energetically preferred choice of alternating + and − super-pentagon units. This calculations gives respective − + and + − interaction energies per super-pentagon pair of −9114.63 and −8884.37 eV (with an average −8998.45 eV), while other choices continue to give higher energies. Further molecular mechanics computational results for normal-mode vibrational frequencies, are depicted in later figures. 5. Stress and strain In the super-carborane [16] structure the bond angles are not quite right. That is, the construction demands inter-unit angles of 60◦ , whereas the angles of two B H bonds at neighboring sites of a regular icosahedral (car-) borane unit are not directed at this angle, but rather at ≈63.3◦ . The consequent stress and strain is apparently handled tolerably well at our super-stage. And as the super-carborane pentagons and caps are the secondary building blocks (carborane is the primary) of our designed systems, we attend to the associated secondary-structure contributions energy
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Figure 5. Our longest super-carborane nano-tubes with L = 40 super-pentagons and two caps.
(Table 2S) of these systems. The strain energy clearly increases as the number of carborane super-pentagons increases. To check the stresses in an experimentally more amenable manner, we turn to computations of frequencies of normal modes of vibration (in Table 2). Thence we have done this, at the molecular mechanics level. In our previous work [16] we found that the lowest frequency super-carborane vibrational force constant is ∼190 cm−1 , while the first vibrational force constant for the simple carborane is ∼790 cm−1 , which entails a wiggling of H atoms grouped by distortions of the attached borons in the boron triangles in the belt of borons around the para-C-axis. In the same way here the super-carborane nano-tubes with L = 4 super-pentagon units lead to a first (i.e., lowest) vibrational frequency ∼101 cm−1 which is almost half that of the super-carborane [16]. A subsequent decrease of the first vibrational force constant is observed as the length L of the species increases along the series. This lowering of the force constants of the super-carborane nanotube series are plausibly associated to stresses arising from the mentioned angle off-set. A further check for our L = 4 case is provided via inspection of the other associated normal vibrational modes, whence we find a fairly dense packing of (normal-mode) vibrational frequencies up to ≈560 cm−1 whereafter there is large gap up to the higher frequency ≈850 cm−1 which we associate (primarily) with internal motions in individual carboranes. Inspection of the highest frequency of our lower energy band reveals it to involve primarily the near-rigid motion of whole C2 B10 H7 units – which is to say, it is the bonds between these units which are stretching and bending, and therefore are evidently weak, because of the indicated angle-off-set stress. Granted such weak inter-carborane coupling, there should be many other additional low-frequency modes: 3 rotational and 3 translational modes for each of our present 22 carborane units, minus 3 overall translation and 3 overall rotation for the super-carborane as a whole, to give (3 + 3) · 22– (3 + 3) = 126 hypothesized low-frequency vibrational modes. Indeed, we find exactly 126 such low-frequency modes ranging from ∼101 cm−1 up to ∼557 cm−1 whereafter there is a jump to ∼850 cm−1 (the 127th normal mode). Examination of the lowest frequency ∼850 cm−1 normal mode after the gap reveals that it involves H-atom wagging internal to individual carboranes. Thence, this L = 4 super-carborane nano-tubes is reasonably tested as a stable possibility, with interior stress related to a band of (126) low-energy normal modes. For longer super-nanotubes this overall pattern of behavior appears to persist, with slight changes in the positions of the upper and lower frequencies of the exo- and intra-nodes. That is, there
is a lower energy band involving 3 rotations and 3 translations of each of the 6 + 5L + 6 carboranes (involved in the 6-carborane units of each cap along with the 5 carboranes of each super-pentagon). But also we subtract off the overall 3 rotations and 3 translations for the super-tube as a whole, thereby leaving a low-energy band of (3 + 3) (6 + 5L + 6) − (3 + 3) = 30L + 66 normal modes involving motions of whole internally near-rigid carborane units. The behavior seems to be similar to that of molecular crystals, where the internal vibrational modes are of high frequency, while the low-frequency (vibrational) modes include dissimilar comparatively inflexible molecules vibrating/rotating against one another. These lower frequency normal modes (mostly entailing motions of internally rigid carboranes) we term exocarboraneic. The lowest exo-carboreneic frequency flow-exo seems to become ever smaller as the system becomes ever larger, and indeed in Figure 4S (in our supporting information) we see that L · flow-exo → 0 in a linear fashion as the tube length L→ ∞, thereby indicating flow-exo ∼ 1/L2 for small L, much as for the confinement of a particle (a phonon) to a box of length L. The remaining higher frequency modes beyond the exo-carboraneic, we term intracarboraneic. Table 2 gives the lower and upper frequencies for both the exo- and intra-carborane sets (or bands) of frequencies – the sequence number i for each frequency is also noted. The asymptotic behavior of the upper exo-frequency as well as both the lower and upper intra-carboraneic frequencies are plotted against 1/L2 in Figure 5S (in our supporting information), to reveal their asymptotic behaviors approaching different finite limits, evidently bounding different phonon bands. A yet further illustration of our ideas is given in the Figure 6, showing discretized densities of states for the L = 40 and the simple carborane (C) cases. In the simple carborane case there is a complete absence of the exo-carboraneic band, which however is clearly seen (between 0 and 590 cm−1 ) for the L = 40 super-carborane (SC) case. Indeed this exo-carbonic band seems to be split into two sub-bends, the lower of which surmise corresponds primarily to rotational motions of individual carborane units, while the upper sub-band corresponds primarily to vibro-translational motions of one carborane against another. The overall vibrational (or phonon) structure is elucidated. Overall bulk distortions of the nano-tubes of course depend collectively on the low-energy normal modes (as well as their frequencies and relative distribution of frequencies). That the bulk
Table 2 The exo-carborane-frequencies (in cm−1 ) lower (fE-C-L ) and upper (fE-C-U ) (where the jumps observed) vibrational modes and also the lower (fI-C-L ) and upper (fI-C-U ) vibrational modes of intra-carborane frequencies of all carborane super-nano-tubes, where, i is the sequence number for vibrational frequencies (in order of increasing frequencies). L
4 8 12 16 20 24 28 32 36 40
Exo-carborane frequencies
Intra-carborane frequencies
Lower (fE-C-L )
Upper (fE-C-U )
Lower (fI-C-L )
Upper (fI-C-U )
101.67 (i = 1) 37.92 (i = 1) 19.33 (i = 1) 11.56 (i = 1) 7.65 (i = 1) 5.43 (i = 1) 4.04 (i = 1) 3.15 (i = 1) 2.47 (i = 1) 2.02 (i = 1)
557.52 (i = 126) 581.01 (i = 246) 583.77 (i = 366) 585.25 (i = 486) 585.73 (i = 606) 585.98 (i = 726) 586.13 (i = 846) 586.22 (i = 966) 586.28 (i = 1086) 586.95 (i = 1206)
853.8 (i = 127) 846.46 (i = 247) 846.05 (i = 367) 845.28 (i = 487) 845.13 (i = 607) 845.05 (i = 727) 844.09 (i = 847) 844.97 (i = 967) 844.93 (i = 1087) 845.05 (i = 1207)
3235.47 (i = 1218) 3231.45 (i = 2298) 3231.36 (i = 3378) 3231.47 (i = 4458) 3231.56 (i = 5538) 3231.52 (i = 6616) 3231.49 (i = 7698) 3231.37 (i = 8778) 3231.29 (i = 9858) 3231.26 (i = 10938)
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Figure 6. Discretized density of states (DOS) plots of the super-carborane nano tubes having 40 pentagonal blocks with two ends (basic carborane halves) in blue color and also the basic carborane unit with red color. Note the different scales for L = 40 and L = 0 on the left and right, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
distortions arise from this lower-energy band indicates that such bulk distortions of the super-tube should be able to be done relatively readily. 6. Conclusions We have studied the possibility of novel nano-tube-structures comprised from para-carborane units. Although they evidently present a severe synthetic challenge, these super-carborane-nanotubes appear to be reasonably stable. Moreover, we have developed and tested an appealing qualitative description of the resulting super-nanotubes. At a first step this entails a simple additivity relation for (strain) energies, such as we use to select the more stable super nano-tubes. At a second step, we find a partitioning of the normal vibrational modes into low-frequency ‘exo-carboraneic’ modes and higher frequency and higher-frequency ‘intra-carboraneic’ modes. Indeed this picture is an elaboration of that found [16] for the super-carborane structure, as corresponds to an L = 0 supernano-tube in our present study. We also have calculated the exterior dimensions of the tube, the tube surface pore size, the cavity dimension for the super-carborane nano-tube, to compare them with the carbon nano-tube having chiral index (n, m) = (10, 10) and tube length = 50. The exterior dimension of both types of tubes did not vary much – ∼13.66 and ∼13.80 A˚ for super-carborane and carbon nano-tube respectively, whereas the interior dimension of the super-carborane nano-tube is ∼5.6 A˚ as viewed from Figures 6S and 7S (in our supporting information). The tube surface pore-sizes of ˚ the super-carborane and carbon nano-tube are ∼3.3 and ∼2.9 A, respectively, as is also evident from the Figures 8S and 9S (in our supporting information). The relative ease of bulk distortions of the super-tubes traces to the fact that the accompanying normal modes are found in the lower energy band, and this in turn traces to the fact that there is a stress in the constructions made. This stress inherent in our constructions entails mismatching of angles. The equilateral supertriangles in the surface of the super-tubes each consist of three carboranes at the vertices of an equilateral super-triangle, then manifesting 60◦ angles, whereas the directrixes from the center of a carborane through adjacent cage (B) atoms is ≈63.3◦ – so that
there is a mismatch in bond angles. This mismatch then quite naturally leads (as indicated) to an increase in flexibility, and also a diminishment in strength. We plausibly surmise that similar substructure additivity relations and similar exo-/intra-carboraneic partitioning extends to other super-structures based on (similarly) interconnecting carborane units. The possibility that such partitioning extends to other super-structures based on other stable units such as C60 -fullerene [4,5] or adamantane should perhaps be investigated. Acknowledgments The authors acknowledge the support of the Welch Foundation of Houston, Texas (via grant BD-0894), and project COOPB20040 (CSIC). DB specially thanks Tamal Goswami for his support while addressing the reviewers’ comments. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.cplett.2015.05.058 References [1] J. Müller, K. Base, T.F. Magnera, J. Michl, J. Am. Chem. Soc. 114 (1992) 9721. [2] J.M. Oliva, L. Serrano-Andres, D.J. Klein, P.v.R. Schleyer, J. Michl, Int. J. Photoenergy 2009 (2009) 292393. [3] J.M. Oliva, Adv. Quantum Chem. 64 (2012) 105. [4] H.-Y. Zhu, D.J. Klein, Croat. Chem. Acta 70 (1997) 519. [5] S.G. Semenov, F.Y. Sigolaev, A.V. Belyakov, J. Struct. Chem. 54 (2013) 960. [6] K.E. Drexler, Engines of Creation – The Coming Era of Nanotechnology, Doubleday, NY, 1989. [7] H. Schwertfeger, A.A. Fokin, P.R. Schreiner, Angew. Chem., Int. Ed. 47 (2008) 1022. [8] J.E. Dahl, J.M. Moldowan, K.E. Peters, G.E. Claypool, M.A. Rooney, G.E. Michael, M.R. Mello, M.L. Kohnen, Nature 399 (1999) 54. [9] P.L.B. de Arujo, G.A. Mansoori, E.S. Arujo, J. Oil, Gas Coal Tech. 5 (2012) 316. [10] J.A. Wunderlich, W.N. Lipscomb, J. Am. Chem. Soc. 82 (1960) 4427. [11] E.L. Mutterties, W.H. Knoth, Polyhedral Boranes, Marcel Dekker, NY, 1968. [12] I.B. Sivaev, V.I. Bregadze, S. Sjöberg, Czech. Chem. Commun. 67 (2002) 679. [13] R.M. Grimes, Carboranes, 2nd ed., Academic Press, NY, 2011. [14] S. Papetti, T.L. Heying, J. Am. Chem. Soc. 86 (1964) 2295.
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