Local and Global Electronic Effects in Single and Double Boron

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J. Phys. Chem. C 2010, 114, 1528–1533

Local and Global Electronic Effects in Single and Double Boron-Doped Carbon Nanotubes Julia Saloni,† Wojciech Kolodziejczyk,‡ Szczepan Roszak,‡ D. Majumdar,† Glake Hill, Jr.,*,† and Jerzy Leszczynski*,† Interdisciplinary Center for Nanotoxicity, Jackson State UniVersity, Jackson, Mississippi 39217, and Institute of Physical and Theoretical Chemistry, Wroclaw UniVersity of Technology, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland ReceiVed: NoVember 7, 2009; ReVised Manuscript ReceiVed: December 14, 2009

The foreign atom doping influences the properties of carbon materials, and it is a possible way of designing materials of desired characteristics. Density functional calculations have been carried out on various isomers of boron-doped (4,0) and (9,0) carbon nanotubes as templates to investigate the doping effect on the structure and electronic properties on such systems. The results indicate that these boron-doped carbon nanotubes show local structural changes, mostly due to the elongation of bonds. The insertion of heteroatoms perturbs the π-conjugation system, which, in effect, destabilizes the material through higher energy cost of formation. The position of the foreign atom controls the new organization of electron density and leads to one of two possible distributions, viz., global (where electron density is distributed over the molecular surface) or local (localized distribution of electron density). This feature, in turn, can influence the bonding of the reactants while interacting with the surface. The charge distribution at a particular boron-doped site always possesses the local characteristics with a positively charged boron atom surrounded by negatively charged carbons. Such a character is also a measure of the driving force for influencing the substitution reaction in the vicinity of boron through an ionic mechanism. I. Introduction 1

Since the first report of carbon nanotubes (CNTs), the unique structural, mechanical, chemical, electronic, and magnetic characteristics of these materials stimulated the search for finding ways to control these properties so that useful designing of nanotube-based nanoscale materials could be achieved.2 The control of nanotube properties can be realized through modification of intrinsic tube topology3 or substitutional doping. The doping, in particular, may influence the characteristics of CNTs in many ways, which include intermolecular interactions4 and covalent sidewall functionalization.5 The substitutional doping could lead to a further possibility. In analogy to semiconducting materials, replacement of carbon by boron in CNTs leads to p-doped CNTs. The metallic behavior of such B-doped multiwalled carbon nanotubes was confirmed by the transport measurement6 as well as by scanning tunneling spectroscopy.7 The first boron-doped CNTs were available soon after the availability of CNT structures;8 however, improved techniques aimed to produce well-calibrated doped CNTs are still under development.9,10 Extensive experimental2,7,11,12 and theoretical13-16 studies are available on such doped materials. The carbon/boron materials, due to their potential applications, are probably the most studied carbons modified by a single element. The boron doping not only modulates the electronic properties of the host CNT system but it also modifies significantly the crystallinity and stiffness of the carbon fibers.17,18 The latter change of CNT property (i.e., stiffness) has an important role in making graphitic systems oxidation resistant.10 The modulation of the electronic properties * To whom correspondence should be addressed. E-mail: jerzy@ icnanotox.org (J.L.), [email protected] (G.H.). † Jackson State University. ‡ Wroclaw University of Technology.

of the B-doped CNTs also led to the investigation of hydrogen adsorption on boron-substituted graphene sheets, which could lead to find the key factors for designing hydrogen storage materials.19,20 Theoretical investigations, which are available on the energetics of the various boron/metal-doped CNTs, are mostly available for regular array structures, that is, in the solid state. On the other hand, theoretical studies of the restricted C/B nanoclusters, providing insight into the nature of the C-B bond, are scarce. The major advantage of studies on restricted systems lies in generating useful information regarding electronic properties that lead to unique chemical behavior, which are otherwise difficult to track in the extended systems. One of these properties is related to the spin densities of the B-doped CNTs, as the doping leads to p-type (hole) systems. In the present paper, the effect of boron doping is investigated for CNTs of restricted sizes [(4,0) and (9,0) zigzag tubes of the chemical formulas C32-nBnH8 and C64-nBnH18 (n ) 1, 2), respectively]. After the initial theoretical studies on the influence of single and double boron doping on the structural, thermodynamic, and electronic properties of such systems, it is shown that the boron substitutions in different positions could be used like a switch to control the spin densities at desired locations in these systems. Furthermore, these properties have an approximately additive nature, depending on boron substitutions, and as a consequence, these results could be used to design nanomaterials of desired chemical and storage (hydrogen) properties. II. Methodological Approach and Computational Details The structural, energetics, and electronic properties of borondoped single-walled carbon nanotubes (BSWCNTs) were performed on two model [(4,0) and (9,0)] zigzag systems of finite length at the density functional level of theories (DFT).21 Both single and double boron substitutions have been investigated

10.1021/jp910625w  2010 American Chemical Society Published on Web 01/05/2010

Electronic Effects in Single and Double B-Doped CNTs

Figure 1. Two-boron-substituted (4,0) carbon nanotube with “end” and “in” boron positions.

by terminating the edges of each model tubes with hydrogen atoms. As indicated in Figure 1s (Supporting Information), in the case of single boron substitutions, only four isomers are possible because of the symmetry of the structures. The double boron substitutions near a particular site were represented by three configurations, viz., neighboring boron atoms and boron atoms separated by one or two carbon atoms (i.e., B-B, B-C-B, and B-C-C-B substitutions), and altogether, fifteen isomers were generated (Figures 2s-4s, Supporting Information). Two more isomers corresponding to the same edge with longer B-B separation (three carbon atom separation) and another isomer with end substitutions on both sides of the (4,0) nanotube (as the model of two independent end centers) were also included (Figure 5s, positions a-c, Supporting Information). The structures of all of these isomers were fully optimized without any symmetry constraints to locate the lowest-energy isomers of these boron-doped nanotubes. Vibrational frequency calculations were carried out on each optimized structure to make sure that they are true minima on the respective energy surfaces (absence of any imaginary frequency). The DFT technique used in the present calculations utilizes the Becke’s22 three parameter functional together with the local correlation part of Vosko et al.23 and the nonlocal part by Lee et al.24 (abbreviated as B3LYP). All of the calculations were carried out using the 6-31G Pople’s basis set25,26 augmented with the d-polarization function for boron and carbon and p-function for hydrogen.27 The calculations were performed for an unrestricted wave function. The restricted open formalism leads to very similar representation of molecular orbitals (Figures 6s and 7s, Supporting Information). Electron spin density values are based on gross Mulliken population analyses, whereas atomic charges were studied through gross Mulliken population and natural bond orbital28 approaches. Atomic spin densities resulting from NBO analysis were also calculated for selected cases, indicating the reasonable agreement and, more importantly, provides the validation of the Mulliken population scheme. The computations have been carried out using the Gaussian 03 code,29 and the graphics in this paper were generated using Gaussview30 and MOLDEN31 programs. III. Results and Discussion a. Structures of Doped Nanocarbons. The structures of (4,0) CNTs are formed through an interconnected array of sixcarbon “boat” fragments. The optimized structures of the hydrogen-terminated boron-doped CNTs show that such a pattern is not altered (Figure 1). Every heavy atom in the hydrogen-terminated region (carbon or boron) forms three deformed edge angles (viz., CBC, HBC, or HCB). The boat skeletons (not connected with boron) on the average have two C-C-C angles of 111° and one of 108° (in one-half of the boat), and they are repeated more or less symmetrically throughout the tube. The boron substitution does not destroy this basic structural skeleton. The main perturbation in the

J. Phys. Chem. C, Vol. 114, No. 3, 2010 1529 geometry comes from elongated B-C bonds due to the distance change from C-C of 1.41 Å to B-C of 1.47 Å. The boroninduced perturbation is of a local nature and only slightly influences adjacent rings. The nanotube doped by two adjacent boron atoms possesses a long B-B bond (1.71 Å); however, the related perturbation is also local in character. The only deformation is that the boron atoms protrude more outside than the average molecular surface of regular (4,0) CNTs. The isomers with boron atoms separated by one or more carbon atoms demonstrate the same kind of deformations. The boat structure in the isomers with boron atoms separated by three carbon atoms is characterized by the same structural parameters as those in the equivalent fragment of singly substituted structure. The out-of-plane dihedral angle of about 34° in the (4,0) CNT boats leads to significant perturbation in the π-bond conjugation. The “building boats”, as defined in Figure 1, in (9,0) doped nanotubes are more planar with an average out-of-plane angle of 20°. As a consequence, the boat skeletons (not connected with boron) possess similar C-C-C angles with an average value of 119°. The B-C distances are, however, comparable with those found in (4,0) CNTs, indicating that the main forces of structural distortions are interatomic distances. The picture of geometric perturbations, due to single and multiple boron doping, indicates that the geometrical parameters maintain reasonable similarity within the considered class of isomers. Experimental observations on boron-doped nanotubes32 as well as for graphite33 have shown that the lattice constants change insignificantly with respect to the regular systems, indicating a negligible change in structural topology. The observed localized structural effects of doping are fully compatible with such observations. b. Energetics. The boron doping of pure carbon nanotubes leads to the energetic destabilization, although it improves some mechanical or chemical properties, such as resistance for oxidation.10 The energetics of doping is monitored here though the energy change of the following substitution reaction 1.

SWCNT(1A) + nB(2P) f Bn-SWCNT(2A or 1A) + nC(3P) (n ) 1, 2) (1) In the above equation, SWCNT represents a hydrogenterminated single-walled carbon nanotube, while Bn-SWCNT is the corresponding boron-doped system. If ESWCNT, EBSWCNT, EB, and EC are, respectively, the energies of SWCNT, BnSWCNT, boron, and carbon atoms, then the energy change ∆E is given by

∆E ) EB-SWCNT + nEC - (ESWCNT + nEB)

(2)

With little rearrangement, eq 2 could be made to look like the formation energy expression (∆EF), used by earlier researchers16,34 while treating the boron-doped carbon nanotubes as a periodic array. Thus, this ∆E could be considered as the energy that is needed during substitutional doping of CNTs under thermodynamic equilibrium. The calculated ∆E (which is equivalent to ∆EF) from eq 2 are presented in Figure 2. According to these results, the doping of a single boron atom increases the energy of the (4,0) CNT by at least 20 kcal/mol. According to earlier studies, boron atoms preferentially substitute carbon atoms at the terminal position of the tube (end position in Figure 1).9 The substitution inside

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Figure 2. Formation energy (∆EF) of the different isomers of (a) singly B-substituted and (b) doubly B-substituted (4,0) CNTs. The minimum ∆EF for the single B substitution (20.6 kcal/mol; Figure 1s, model a, Supporting Information) and the double boron substitution (32.1 kcal/mol; Figure 5s, position c, Supporting Information) are taken as respective reference energies in (a) and (b). The ∆EF of other isomers amounts to the relative energies in such a situation. The blue (square), red (circle), and purple (triangle) markings in (b) represent the ∆EF of the isomers, according to the definition of the x axis.

the tube (in position in Figure 1) costs 14 kcal/mol or slightly higher energy (regarding different internal positions) (Figure 1s, Supporting Information). The above value roughly agrees with one estimated by molecular dynamics simulations.10 The replacement of two atoms in remote sites (Figure 5s, Supporting Information) requires 32.1 kcal/mol. This value takes into account the energy of conjugation leading to the singlet electronic state. The energy of destabilization of distant B centers coupled to the triplet state is almost additive (39 kcal/mol) in comparison with single boron substitution (20 kcal/mol). A direct B-B bond is the characteristic of the least stable moieties. The end B positions are preferred similarly in single-boronsubstituted CNTs. The imposed instability, in comparison with pure carbon structures, is proportional to the number of end and in occupied sites (Figure 1). The end-in difference of ∆E amounts roughly to 10 kcal/mol, when B atoms are separated by at least one carbon atom (Figure 2). The destabilization of doped carbons, as the contents of B increases, is consistent with the observed small quantity of dopant in the available C/B materials.10 The ground electronic states of CNTs with twoboron atom doping are singlets, which are accompanied by lowlying triplet excited states. The excitation energies (∼6 kcal/ mol) indicate that triplets play a significant role in overall properties of boron-doped materials. The presence of the lowlying electronic excited states is in agreement with the EPR studies, and it indicates the presence of a high density of unpaired electrons in B/C moieties.32 c. Electron Spin Density Characteristics. The insertion of a B atom into a carbon NT perturbs not only its geometry but also, more importantly, the electronic structure. Boron constitutes a p-hole in the otherwise well-conjugated π electronic system, and as a consequence, semiconducting and diamagnetic nanotubes become metallic and paramagnetic.12 The doping affects a number of properties, including the chemical reactivity of the surface. The reactivity of a modified nanotube may be related to the electron spin density distribution controlling covalent interactions or atomic charge distribution responsible for ionic interactions. The insertion of boron into a nanotube or graphene system, due to the lack of electrons in the originally saturated system, severely perturbs the conjugation of the π-bond network. Because the manifold of p orbitals is very similar in the pure CNT and in doped ones, the location of unpaired electrons is controlled by the electronegativity of atoms.

Figure 3. Planar projection of the (4,0) boron-doped carbon nanotube at the end position. White circles indicate equivalent atoms. Small letters indicate atoms with an atomic spin density above 0.1 e. The double bond conjugation scheme corresponds to the boron-induced radical on carbon.

1. Single Boron Substitutions. The (4,0) nanotube is composed of four crowns (A, B, C, and D in Figure 3,) which consist of two sets of nonequivalent atoms located on parallel planes (indexes 1 and 2, Figure 3). Such a structure allows four single doped isomers, with boron replacing carbon at A1, A2, B1, or B2 planes. The energetically preferred isomer possesses boron in plane A1 (Figure 4). In this case, the π conjugation leads to the electron density enhancement on planes A1, B2, C2, and D2 (Figure 3). The corresponding electron spin density (ESD) is illustrated in Figure 4. In this case, spin density possesses “global” characteristics, with atoms carrying spin density above 0.1 e distributed on the whole skeleton. The boron atom possesses negligible spin density (0.05 e), when the highest atomic spin density (ASD) is located on a carbon atom separated from boron by the longest distance (atom d in Figure 3). The isomer with boron occupying the B1 plane (Figure 4) also possesses global distribution of electronic density. This behavior is easy to rationalize since the observed distributions fit well to the bond conjugation model illustrated for the selected case in Figure 3. The doping of a boron atom on A2 or B2 planes (Figure 5) leads to the different distribution of ESD, which now possesses a local character (Figure 4). The significant amount of ASD is concentrated on the boron atom (0.19 e). This phenomenon affects the overall topology of spin densities. The similar local distribution is also observed in the case of an isomer possessing boron in the D plane. The position of a radical electron may be rationalized considering possible π conjugation allowing electron density to be localized also on the boron atom.

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Figure 6. Single-occupied molecular orbitals of energetically lowest end and in isomers of (9,0) boron-doped carbon nanotubes. Isovalue surfaces correspond to 0.02 units.

Figure 4. Electron spin density surfaces for single-boron-doped carbon NTs. Isovalue density surfaces are drawn at 0.003 e.

Figure 5. Planar projection of the (4,0) boron-doped carbon nanotube with boron in the A2 (in) position. Small letters indicate atoms with an ASD above 0.1e. The conjugation scheme corresponds to the location of an electron on the boron atom.

The differences in density distribution may lead to different reactivity of the surface of doped carbon nanotubes. Since the end doped CNTs are thermodynamically preferred, the delocalization of ESD will be the important feature of the doped material and will significantly influence material functionalization due to the presence of a foreign atom. Such electron density topology may support the spillover mechanism of molecular hydrogen adsorption.35 A similar effect was observed for functionalized (6,0) nanotubes, resulting in the remarkable delocalization of electrostatic potential.36 The delocalization of electronic density may be illustrated by singly occupied molecular orbitals (Figures 6s and 7s, Supporting Information). The (9,0) single-boron-doped CNTs possess similar properties with global and local ASD distributions as a function of positions of doped atoms. The picture of a singly occupied molecular orbital (Figure 6) illustrates the site dependence of molecular orbital (MO) topology and, in consequence, the dependence of ASD. The symmetry and topology of MOs determine the overall properties

of electronic states and provide the first-order approximation of the density distribution. The examination of the MOs further indicates the availability of global and local orbitals in every series corresponding to a particular isomer. The energy criterion determines the order of orbitals and indirectly governs the geometrical properties of density distribution. The natural bond orbital (NBO) as well as gross Mulliken population analysis of atomic charge indicates similar behavior. These charge characteristics are independent of the position of boron in the nanotube skeleton. The boron atom constitutes a positive center with an atomic charge (NBO) of 0.54 and 0.60 e in A1 (end) and B1 (in) isomers, respectively, and carbon atoms with a complementary negative charge surround this center. The hydrogen of B-H in the end isomer (A1) carries almost no charge. The boron centers, regardless of the structure of isomers, are of local character. Like the (4,0) CNT, atomic charge is also locally perturbed by boron substitutions in (9,0). 2. Double Boron Substitutions. Electronic states of doublesubstituted boron nanotubes are singlets, although the corresponding triplet states are close enough (∆E ) ∼6 kcal/mol) to be considered as competitive ground state and may be available for reactions. The most stable isomer of (4,0) NT possesses boron atoms in the end position separated by the longest possible distance (mainly separation by three carbon atoms, Figure 5s, Supporting Information). Its HOMO possesses global topology, and the electron spin density of the corresponding electronically lowest triplet is also characterized by global distribution and may be roughly considered as the superposition of two independent distributions observed for the single boron end isomer (Figure 7). The isomers with higher separation of boron centers (three carbon atoms) preserve local character, which is visible as the HOMO of local topology (Figure 8s, Supporting Information). The ESD representation for the corresponding triplet electronic state is also of local character (Figure 7). The examination of magnitudes of atomic spin density indicates its approximate additive nature through the superposition of centers with enhancement of electron density in one and concomitant quenching in the other regions. The overall picture however indicates local character of the in-in isomer. The end-in isomer possesses features of both possible (global and local) distributions. The calculated NBO atomic charges indicate the purely local character of boron centers. The charge on boron as well as on its neighbor carbon atoms possesses values similar to centers characterizing singly substituted CNT. The atomic charges are similar regardless of the electronic state considered. The energetically lowest triplet states representing isomers with short distances between boron atoms, which are mainly through B-B, B-C-B (single carbon bridge), and B-C-C-B (double carbon bridge) junctions, possesses boron atoms in the

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Saloni et al. local density. The interaction, due to the presence of boron, leads to some enhancement of density in the area of the molecule, where ESD would not be visible if density is perfectly additive. The atomic charge distribution constitutes a local phenomenon with additive properties. The single C atom separation is sufficient for charges to be additive, with an average NBO charge of boron of 0.55 e and neighbor C atoms of -0.3 e. The carbon atom within the B-C-B bond possesses double negative charge of 0.6 e, again indicating the additive nature of charges. In the case of the B-B bond, boron atoms share a positive total charge of 0.6 e and the overall picture, however, is also of local in character. IV. Conclusions

Figure 7. Electron spin density surface of the triplet electronic state with a long distance (three carbon atoms) between boron atoms for (a) end-end and (b) in-in isomers. Isovalue density surfaces are drawn at 0.003 e.

Figure 8. Electron spin density surfaces for energetically lowest isomers for (a) B-B, (b) B-C-B, and (c) B-C-C-B classes of boron-doped carbon nanotubes. Isovalue surfaces are drawn at 0.003 e.

end position. Although compared to the single-B-doped CNTs, the environment of boron centers is perturbed and the double boron isomers may still be considered as the superposition of simpler single B atom structures. The additive nature of electron spin density is quite explicit and global and local distributions are well visible (Figure 8). The presence of end boron atoms always generates ESD on the corresponding backbone carbon atoms of the nanotube. The in boron atoms introduce enhanced

The doping of carbon nanotubes provides a way to influence the electronic structure of such systems, and this may lead to the controlled enhancement of selected properties. The potential applications of these materials stimulated extensive research of C/B nanotubes. In the present theoretical investigations, density functional calculations (DFT/B3LYP) have been carried out on various isomers of boron-doped (4,0) and (9,0) model carbon nanotubes to investigate the doping effect on the structure and electronic properties on such systems. The insertion of boron into CNTs leads to local structural perturbations of their skeleton due to longer B-C bond length (in the comparison to regular C-C distances in CNT). The doping of pure carbon tubes leads to destabilization of the systems in the sense that the energy cost for their formation is higher than regular CNTs. The higher concentration of B atoms further increases the energy cost (i.e., destabilization) of their formation. This is in agreement with experimental observations with the prediction that the most stable isomers possess boron at the terminal position of the nanotube (the “end” position). The doping of boron severely perturbs the π-conjugation system. The new organization of molecular orbitals depends critically on the position at which the carbon was replaced. In the case of the (4,0) nanotube, the single end doping leads to the global distribution of atomic spin density, whereas the occupation of the A2 plane (Figure 5) results in the local distribution. The other in-doping, considered here, also falls in global or local categories. Considering the nature of MOs and electron density distributions, the effect of insertion of two boron atoms has been found to be approximately additive. The organization of atomic charge, however, always possesses local character with positively charged boron surrounded by negatively charged carbons. Such a character of electron density distribution influences the reactivity of CNT surfaces. Similar global/local electron spin densities and local charge properties were observed in both (4,0) and (9,0) structures, indicating the general nature of such phenomenon. Acknowledgment. This work has been supported by PREM Award No. DMR/0611539, CREST Award No. HRD0833178, and ONR; we also thank the Mississippi Center for Supercomputing Research, the Poznan Supercomputing and Networking Center, and the Wroclaw Centre for Networking and Supercomputing. Supporting Information Available: Figures representing boron-doping positions in BCNT isomers and molecular orbital pictures of restricted and unrestricted DFT wave functions. The supporting figures are indicated in the text by the letter “s”. This material is available free of charge via the Internet at http:// pubs.acs.org.

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