Diamond fragments as building blocks of functional nanostructures

Gregory C. McIntosh,1 Mina Yoon,2 Savas Berber,2 and David Tománek21Defence Technology Agency, Naval Base, Devonport, Auckland, New Zealand

2Physics and Astronomy Department, Michigan State University, East Lansing, Michigan 48824-2320, USA(Received 12 January 2004; revised manuscript received 31 March 2004; published 2 July 2004)

Using density functional theory, we investigate the equilibrium structure, stability, and electronic propertiesof nanostructured, hydrogen-terminated diamond fragments. The equilibrium atomic arrangement and elec-tronic structure of these nanostructures turn out to be very similar to bulk diamond. We find that suchdiamondoids may enter spontaneously into carbon nanotubes. Polymerization inside a nanotube is favoredespecially when boron and nitrogen are substituted for carbon atoms.

DOI: 10.1103/PhysRevB.70.045401 PACS number(s): 81.07.2b, 73.22.2f, 68.65.2k, 61.46.1w

I. INTRODUCTION

In his inspiring presentation entitled “There is Plenty ofRoom at the Bottom”1 in 1959, Richard Feynman pointedout the untapped potential of functional nanostructures, as-sembled with atomic precision, to influence our every-daylife. In the meantime, technological progress has been asso-ciated with a continuous drive towards miniaturization. Re-cent progress in nanoscale electromechanical systems(NEMS’s) suggests that complex functional nanostructures,invisible to the naked human eye, may soon follow suit.2

Large-scale production of such complex nanostructures islikely to occur by hierarchical self-assembly from well-defined structural building blocks,3,4 which can be thought ofas “nano-LEGO”. To fulfill their mission, such nanostruc-tures must be strong and chemically inert in their environ-ment.

Carbon fullerenes6 and nanotubes7 have emerged aspromising candidates for such building blocks, providing a

variety of functionalities. Here, we investigate a new class ofcarbon nanostructures, the diamondoids.5 These nanoscalebuilding blocks are very different, but compare well in sta-bility and light weight with fullerenes and nanotubes. Beingessentially hydrogen-terminated nanosized diamond frag-ments, they may occur in a large variety of shapes, as shownin Fig. 1. The smallest possible diamondoid is adamantane,8

consisting of 10 carbon atoms arranged as a single diamondcage,9 surrounded by 16 hydrogen atoms, as shown in Fig.1(a). Larger diamondoids10–12 are created by connectingmore diamond cages and are categorized according to thenumber of diamond cages they contain. The diamondoidsshown in Fig. 1 contain up to tens of carbon atoms and areonly a few nanometers in diameter.

Traditionally, diamondoids have been known in the oilindustry,13,14 where they occur naturally dissolved in oil andits distilled by-products. At low temperatures and low pres-sures, diamondoids may precipitate from the solution and actas nucleation sites for the formation of sludge, which oftenblocks pipelines.15,16 Only recently, isomerically pure dia-mondoids with up to 11 adamantane cages have been ex-tracted from the sludge5 and are now being considered fornanotechnology applications. The isolated diamondoids oc-cur in very different shapes, and many of them form molecu-lar crystals. These uncommon organic molecules can bechemically functionalized by substituting carbon or hydro-gen atoms at the surface by other atoms or groups to promotethe formation of specific polymers.

Given that diamondoids are essentially hydrogen-terminated diamond fragments, we anticipate that in the ab-sence of significant structural changes, they share the tough-ness and insulating properties with their bulk diamondcounterpart. Our study confirms this anticipation. In the fol-lowing, we carry out a theoretical investigation of diamon-doids usingab initio density functional calculations. We de-termine their equilibrium geometry, in particular thedependence of the bond lengths and bond angles on the sys-tem size, and their electronic density of states(DOS).

Beyond identifying the properties of unmodified isolateddiamondoids, we also explore ways to manipulate them andto connect them together. We find that the interaction be-tween unmodified diamondoids is too weak and does notfavor polymerization to larger structures. Hence, we explorethe possibility of creating specific binding sites by atomic

FIG. 1. Relaxed structures of lower diamondoids, identified ex-perimentally in Ref. 5. Hydrogen atoms, terminating the carbonskeleton, are omitted from the diagrams for clarity.(a) The smallestdiamondoid, adamantane, consisting of a single diamond cage.(b)Diamantane with two diamond cages.(c) Tetramantane with fourdiamond cages.(d) Decamantane with ten diamond cages.

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substitution. We then explore the interaction between un-modified and functionalized diamondoids. In particularcases, we conclude that a nanotube attached to the tip of ascanning probe microscope could also be used to manipulatediamondoids into position on a substrate, similar to the waythis was achieved for adsorbed rare-gas atoms.17

Even more intriguing is the possibility to use a nanotubeas a container for unmodified and functionalized diamon-doids, very much the same as it acts for fullerenes18 andpolymers.19 The nanotube surrounding the encapsulated dia-mondoids may act as a template to connect these moleculesin a well-defined way. In particular, we could envisage thepolymerization of quasilinear polymantanes to an infinitediamondoid wire, enclosed in a nanotube.

II. METHOD OF CALCULATION

Our calculations are based on theab initio density func-tional theory(DFT) within the local density approximation(LDA ). We use Troullier-Martins pseudopotentials to de-scribe the effect of atomic nuclei plus core electrons on thevalence electrons and the Perdew-Zunger-parametrizedexchange-correlation potential, as implemented in theSIESTA

code.20 We used a double-z basis21 and 50 Ry as the energycutoff in plane-wave expansions of the electron density andpotential, which is sufficient to achieve a total energy con-vergence of&1 meV per atom during the self-consistencyiterations.

We performed a full optimization of diamondoid struc-tures CnHm containing up to ten diamond cages. Our opti-mized geometries, some of which are reproduced in Fig. 1,are in good agreement with those inferred experimentally5,22

and theoretically.23,24 Also, our calculated equilibrium C-Cbond length of 1.540 Å in the optimized bulk diamond struc-ture was found to agree with the experimental value.25 Con-strained geometries were used when determining the interac-tion between diamondoids.26

III. PROPERTIES OF ISOLATED DIAMONDOIDS

The lower diamondoids we considered here include ada-mantane, diamantane, triamantane, all four isomers of tetra-

mantane, all nine isomers of pentamantane with a molecularweight of 344 amu, six isomers of hexamantane, two isomersof heptamantane, and one isomer each of octamantane, nona-mantane, and decamantane. With increasing polymantanesize, the number of isomers increases geometrically, makingan exhaustive study of all isomers impractical.5 In our selec-tion of isomers, we focused on those identified experimen-tally in Ref. 5. For each of these diamondoids, we have de-

FIG. 2. (Color online) Elec-tronic structure of an(a) adaman-tane,(b) diamantane,(c) tetraman-tane, and (d) decamantane,depicted in Fig. 1.E=0 corre-sponds to the Fermi level. Thefundamental band gaps are indi-cated in eV.

FIG. 3. Electronic, structural, and cohesive properties of dia-mondoid isomers considered here as a function of the polymantaneorder, reflecting the number of adamantane cages.(a) HOMO-LUMO gaps in the density of states(DOS). (b) C-C bond lengths,with the error bar reflecting the spread of the values within eachsystem.(c) Formation energy per carbon atomDE/n of the CnHm

diamondoids.

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termined the equilibrium structure, the binding energy percarbon atom, and the electronic DOS.

The electronic density of states of the diamondoids pre-sented in Fig. 1 is shown in Fig. 2. The spectrum consists ofdiscrete eigenvalues associated with the finite size of themolecules. With increasing size, the gap between the highestoccupied molecular orbital(HOMO) and the lowest unoccu-pied molecular orbital(LUMO) will converge to the funda-mental gap of diamond as the bulk counterpart of the finitemolecules. In comparison to other atomic clusters, we findthe HOMO-LUMO gap to lie very close to that of bulk dia-mond even for the smallest diamondoids, including adaman-tane, as shown in Fig. 3(a). In conjunction with the fact thatthe LDA usually underestimates the HOMO-LUMO gap, itslarge value of several electron volts suggests thatdiamondoids—similar to bulk diamond27—should appeartransparent in visible light and act as electrical insulators.This is indeed in agreement with observations indiamondoid-based molecular crystals.5

Figure 3 summarizes our results for the equilibrium C-Cbond length, the HOMO-LUMO gap, and the formation en-ergy per carbon atom in all the diamondoid isomers we haveconsidered. The equilibrium C-C bond lengths in the dia-mondoids, depicted in Fig. 3(b), lie very close to the valuefound in bulk diamond. Since also the bond angles in thesestructures lie close to those found in diamond, we concludethat even the smallest diamondoids showsp3-type bonding,which is very different from graphite likesp2 bonding foundin fullerenes and nanotubes. Only in the smaller diamon-doids, including adamantane, diamantane, and triamantane,is the C-C bond length somewhat smaller than in bulk dia-mond, reflecting the small difference between the C-H andC-Cssp3d bonds in hydrogen-terminated carbon atoms. Theerror bars shown reflect mainly the differences between theinequivalent sites in the lower diamondoids and an estimateduncertainty resulting from our optimization procedure in thelarger structures. In agreement with related theoreticalstudies,23,24 we find the hydrogen-terminated small diamon-

FIG. 4. (Color online) Com-parison between structural andelectronic properties of an elon-gated hexamantane isomer(leftpanels) and an infinite diamondoidchain (right panels). The equilib-rium structure is shown in(a) and(d), with the large spheres denot-ing carbon and the small sphereshydrogen atoms. The electronicdensity of states is presented in(b)and (e), with the Fermi level atE=0. The one-dimensional bandstructure of the infinite diamon-doid chain is shown in(f). Thecharge-distribution of electrons inthe highest occupied molecular or-bital (HOMO) and the lowest un-occupied molecular orbital(LUMO) of hexamantane isshown in (c). The correspondingcharge distribution in the top va-lence and bottom conduction bandof the diamondoid chain is shownin (g).

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doids, investigated here, stable with respect to hydrogen de-sorption and surface reconstruction.

The structural resemblance between even the smaller dia-mondoids and diamond suggests that these nanostructureswill also share the desirable toughness and insulating prop-erties with bulk diamond. The latter is indeed the case, assuggested by the large HOMO-LUMO gap we find in all thediamondoids investigated here, shown in Fig. 3(a). In agree-ment with former studies,23,24 we find the HOMO-LUMOgap to decrease monotonically with increasing diamondoidsize. Among the different isomers of a particular polyman-tane, we can observe a subtle trend, which correlates themore elongated structures with somewhat larger HOMO-LUMO gaps than more compact structures.

Figure 3(c) shows the formation energy per carbon atom,DE/n, of the CnHm diamondoids as a function of the diamon-doid size. We define the formation energy byDE/nsCnHmd=fEtotsCnHmd−nEtotsCd−sm/2dEtotsH2dg /n, whereEtotsCd isthe total energy of diamond per atom andEtotsH2d is the totalenergy of a hydrogen molecule.28

According to Fig. 3(c), we find all diamondoids, as wellas bulk diamond, overbound due to underestimating the totalenergy of isolated atoms, a well-documented shortcoming of

the LDA. As suggested by the results in Fig. 3(c), the stabil-ity of the lower polymantanes is inferior to bulk diamond,since a significant fraction of carbon atoms is connected tofewer than four carbon neighbors. An intriguing observationis that the stability is nearly independent of the stacking ar-rangement of adamantane cages, suggesting an isomer-independent binding energy. With increasing size, we ob-serve a monotonic increase in stability towards the bulkdiamond value.

The properties of an elongated hexamantane isomer andan infinite diamondoid chain as its quasi-one-dimensional(quasi-1D) crystalline counterpart are discussed in Fig. 4.Such structural elements could find use in NEMS devicesand, as we discuss in the following sections, could be self-assembled inside carbon nanotubes. Figures 4(a) and 4(d)show the close structural relationship between the finite mol-ecule and the infinite chain, obtained by periodically repeat-ing the unit cell shown in Fig. 4(d). The average C-C bondlength in the infinite diamondoid chain is 1.530±0.008Å,close to the values found for the other diamondoids, given inFig. 3(b).

The electronic density of states of hexamantane is shownin Fig. 4(b). In all respects, including its large HOMO-LUMO gap, this DOS lies close to the results found in the

FIG. 5. (Color online) Struc-ture, interaction energy, and elec-tronic properties of unmodifiedand functionalized diamantanes.(a) Structural arrangement and(b)interaction energy of two unmodi-fied diamantanes C14H20, sepa-rated by distanced. (c) Structuralarrangement and(d) interactionenergy of two chemically func-tionalized diamantanes C13BH19

and C13NH19, with the B and Nsites in the neighboring moleculesfacing each other.(e) Equilibriumstructure and(f) density of statesof C13BH19. (g) Equilibrium struc-ture and(h) density of states ofC13NH19. The dashed lines indi-cate the position of the HOMOand LUMO in the unmodified dia-mantane, shown in Fig. 2(b). Bo-ron (light shading) and nitrogen(dark shading) sites are empha-sized in(c), (e), and(g).

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other diamondoids, depicted in Fig. 2. The electronic spec-trum of the infinite quasi-1D counterpart of hexamantane,shown in Fig. 4(e), is similar to that of hexamantane anddominated by a series of van Hove singularities in the va-lence and conduction regions. The dense sequence of thesesingularities reflects the dense spectrum of relatively flatbands, depicted in Fig. 4(f), which makes this system a wide-gap insulator with an indirect gap. In view of the negativeelectron affinity of diamond,29 combined with a large length-to-diameter aspect ratio, diamondoid chains may even sur-pass carbon nanotubes in applications such as cold cathodesor low-voltage electron emitters in flat panel displays.

In spite of its wide fundamental gap, the infinite diamon-doid chain could possibly acquire conductivity by electron orhole doping. Close inspection of the electronic dispersionrelations in Fig. 4(f) reveals that the bands close to the Fermilevel show an energy dispersion of below 2 eV. To investi-gate the charge delocalization as a prerequisite for conduc-tion, we display the charge distribution of the topmost va-lence and bottom conduction bands in Fig. 4(g) and compare

it to that of the HOMO and LUMO of hexamantane in Fig.4(c).

Results for the infinite chain suggest that the charge asso-ciated with the valence band is localized in pockets nearinteratomic bonds, thus hindering hole transport. This chargedistribution is very similar to that of the HOMO of hexam-antane. The conduction band, on the other hand, consists offour strongly delocalized states located on the outer perim-eter of the structure, which could be used to conduct elec-trons. These extended conduction states find their counterpartin the LUMO of hexamantane, which is similarly delocalizedacross the middle section of this molecule. The bottom of theconduction band is very flat, suggesting that electrons in alightly electron-doped system should have a low mobility.

Due to the wide fundamental gap, chemical doping is un-likely to provide free carriers, since it would require the in-troduction of impurities with a very low ionization potential,likely to introduce trap sites. One possibility of electron dop-ing would involve gating a supported diamondoid chain. Amore likely scenario ofn doping would involve enclosing thediamondoid chain inside a carbon nanotube, as discussed be-low, andn doping the surrounding nanotube.

IV. FUNCTIONALIZED DIAMONDOIDS

Construction of functional elements of diamondoid-basedNEMS devices precludes a controllable method to connectdiamondoids with strong bonds. Chemically unmodified dia-mondoids interact only weakly, leading to the formation ofmolecular crystals.5 This is illustrated in Figs. 5(a) and 5(b),showing the arrangement and binding of two interacting dia-mantane cages.30 The binding energy of two diamantanes,only 0.13 eV in our calculation, is to be considered only arough estimate and lower limit on the real value, mainly dueto the structural constraints imposed in our calculation.26

Still, identifying ways to stabilize the bond is desirable.One way to enhance bonding involves chemical function-

alization of diamondoids in order to create more reactivesites. Obvious choices for substitution are elements close tocarbon in the periodic table, such as boron and nitrogen,which have a similar atomic size as carbon. We also note thatcarbon has been successfully replaced by boron and nitrogenin fullerenes and carbon nanotubes.31 A similar substitutionof terminal carbon atoms by boron and nitrogen in adjacentdiamondoids, shown in Fig. 5(c), should result in a muchstronger polar bond between the modified molecules. This isindeed confirmed by our results shown in Fig. 5(d). Eventhough significantly smaller than the typical bond energy indiamond, the binding energy26 of 1.64 eV between the func-tionalized diamondoids should prevent spontaneous dissocia-tion at room temperature.

Our results for functionalized diamondoids are summa-rized in Figs. 5(e)–5(h). We find that substituting a CH groupin C14H20 by either a boron or a nitrogen atom leads to stablestructures, with a geometry closely related to that of unmodi-fied diamantane. In C13BH19, depicted in Fig. 5(e), the C-Bbond length is somewhat larger than the C-C bond length,suggesting a weaker bond. In C13NH19 on the other hand,shown in Fig. 5(g), the C-N bond is shorter than the C-C

FIG. 6. (Color online) Total charge distribution in(a) C13BH19

and(b) C13NH19 in their equilibrium structure, shown in Figs. 5(e)and 5(g). (c) Total charge distribution and(d) electronic density ofstates of C13BH19 interacting with C13NH19 in the structural ar-rangement depicted in Fig. 5(c).

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bond, suggesting a stronger bond. Substitution of a carbonatom by either boron or nitrogen leads in both cases to im-purity states within the HOMO-LUMO gap of their densityof states, shown in Figs. 5(f) and 5(h).

The effect of atomic substitution on the overall chargedistribution within the functionalized diamondoids is shownin Fig. 6. The Periodic Table would suggest a charge deple-tion at the boron site and a charge accumulation at the nitro-gen site. This is indeed confirmed in Fig. 6(a) for C13BH19and in in Fig. 6(b) for C13NH19.

Combining the excess charge at the nitrogen site inC13NH19, clearly visible by a charge density protrusion inFig. 6(b), with a charge deficit at the boron site in C13BH19,visible in Fig. 6(a), leads to the formation of a polar bond,once the two sites face each other. As seen in Fig. 6(c), wefind the charge cloud at the nitrogen site further extendedtowards the positively charged boron site in the stable com-

plex consisting of the two functionalized diamondoids. Closeinspection of the charge density distribution in the bond re-gion also illustrates the fundamental difference between theweaker, predominantly polar B-N bond, with very littlecharge in the bond region, and covalent C-C bonds with astrong charge accumulation in the bond region.

Similar to the individual functionalized diamondoids, alsothe bonded complex shows a large HOMO-LUMO gap offew eV in the density of states, as seen in Fig. 6(d). Due tothe polar nature of the bond, the total density of states of thecomplex is closely related to that of its components, shownin Figs. 5(f) and 5(h).

V. INTERACTION OF DIAMONDOIDS WITH CARBONNANOTUBES

Since the cross section of carbon nanotubes is compatiblewith the size of diamondoids, nanotubes could be used to

FIG. 7. (Color online.) Ener-getics of a diamantane moleculeentering sn,nd carbon nanotubeswith various diameters. Theend-on and side views of the in-sertion geometry are depicted inthe left panels. The axial separa-tion between the closest end of thediamantane and the nanotube isdenoted byz, with z,0 corre-sponding to the diamantane out-side andz.0 to the diamantaneinside the carbon nanotube.

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manipulate and assemble these molecules to larger struc-tures. Precise deposition and positioning of diamondoidscould be achieved with the help of a carbon nanotube at-tached to the tip of a scanning probe microscope,17,32 whichmay combine its functionality as a storage, deposition, andmanipulation device. Combination of diamondoids withnanotubes may, moreover, lead to functional nanostructuresfor particular applications. Key to all these applications is tounderstand the interaction of diamondoids with carbon nano-tubes.

In the following, we describe the interaction of diaman-tane as a prototype diamondoid withsn,nd armchair carbonnanotubes of different diameter. Aspects of particular interestto us are the energy change associated with the entry of adiamondoid inside a nanotube and the optimum nanotubediameter to maximize the encapsulation energy.

Our results for the entry of diamantane into armchair car-bon nanotubes ranging froms4,4d to s7,7d are presented inFig. 7. Due to computer limitations, we considered finite-length nanotube segments, which have been hydrogen termi-nated at both ends. The encapsulation geometry is depictedin end-on and side views in the left panels of Fig. 7. Thedependence of the diamantane-nanotube interaction energyon the diamantane positionz along the tube axis is presentedin the right panels of Fig. 7.

These energy results suggest that entry of diamantane intoa s4,4d, s5,5d, ands6,6d nanotube is energetically unfavor-able. Nevertheless, the dip in the total energy atz<0 sug-gests the possibility of attaching this molecule to thehydrogen-terminated nanotube end and thus a possibility ofmanipulating diamondoids with a nanotube attached to anSPM tip. In all cases, the diamantane-nanotube binding en-ergy is lower than the bond strength between C13BH19 andC13NH19, shown in Fig. 5(d), suggesting the possibility tomanipulate and position assemblies of connected, function-alized diamondoids without disrupting them.

As seen in Fig. 7, onlysn,nd nanotubes withnù7 arewide enough to accommodate diamantane endohedrallywithout energy investment. The energy of diamantane encap-sulated inside widersn,nd nanotubes is shown in Fig. 8 as afunction of its off-axis displacementy. We find that thes7,7dnanotube has an ideal diameter to contain a single diaman-tane with optimal encapsulation energy. Containment in thes6,6d nanotube is moderately endothermic. Containment inthe s8,8d nanotube is exothermic, but the minimum in theenergy curve is rather flat, suggesting that the diamondoidwould have some degree of lateral freedom and that thes8,8d nanotube is too wide. Nevertheless, the enclosingnanotube should suppress free rotation of the diamondoid,thus facilitating specific reactions, including polymerizationaddressed in Fig. 5. Results very similar to those for diaman-tane are also expected for all higher, linear diamondoids, aswell as the diamond chain, addressed in Fig. 4. The encap-sulation of the smaller adamantane should proceed verysimilar to that of diamantane, with the exception that orien-tational alignment of adamantane with no obvious “long”axis cannot be achieved.

VI. SUMMARY AND CONCLUSIONS

In summary, we performedab initio density functionalcalculations to study the structural and electronic propertiesof unmodified and chemically functionalized polymantanes,as well as their reactivity and interaction with carbon nano-tubes. Our results support the conjecture that the lower poly-mantanes are essentially hydrogen-terminated diamond frag-ments with diamondlike properties. Hence, these systemsmay be used as molecular building blocks of complex func-tional nanostructures, to be found in future NEMS devices.Within computational uncertainty, we find the bond lengthsand angles in the carbon skeletal structure of the diamon-doids to be essentially the same as in bulk diamond. Thesimilarity in bonding between diamondoids and diamond ex-tends also to the bond strength and resistance to deforma-tions. The large HOMO-LUMO gaps in diamondoids are themolecular counterparts of a large fundamantal gap in dia-mond, which is responsible for its optical transparency in thevisible range and its insulating properties. We also find theproperties of hydrogen-terminated diamondoids to approachthose of bulk diamond, as their size increases.

Unmodified diamondoids are nonreactive and interactonly weakly with each other. We found, however, that sub-stituting carbon by boron and nitrogen atoms may createlocalized binding sites in these modified diamondoids and

FIG. 8. (Color online) Energetics of diamantane, enclosed insidea s6,6d, s7,7d, and s8,8d carbon nanotube, as a function of anoff-axis displacementy. The geometry in end-on view is shown inthe left panels.

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provide the possibility of connecting diamondoids by muchstronger, directional bonds. Selective substitution at morethan one carbon site per diamondoid may provide the possi-bility to connect even larger diamondoids into well-definednanostructures for particular applications.

We have found that diamondoids should enter spontane-ously into carbon nanotubes with a wide enough diameter,similar to the spontaneous encapsulation of fullerenes, lead-ing to peapods.18 Being orientationally constrained in thesenanosized containers, they may fuse into long structures, in-cluding a “diamond wire.” Carbon nanotubes can be used notonly to store diamondoids, but also to manipulate them steri-cally, preferably in conjunction with a scanning probe micro-

scope. Even nanotubes that are too narrow to contain a dia-mondoid may be used for such a purpose, since diamondoidspreferentially bind to the reactive open end of a nanotube,which may be attached to the tip of a scanning probe micro-scope.

ACKNOWLEDGMENTS

We thank W. Qureshi, J. E. Dahl, S. G. Liu, and R. M.Carlson for drawing our attention to their results prior topublication. We also thank Noejung Park and Eiji Osawa foruseful discussions. This work has been partly supported byNSF-NIRT Grant No. DMR-0103587.

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