We present an analysis of the dynamics of single-walled carbon nanotube (SWCNT) chirality during growth, using the recently developed local chirality index (LOCI) method [Kim et al. Phys. Rev. Lett. 2011, 107, 175505] in conjunction with quantum chemical molecular dynamics (QM/MD) simulations. Using (5,5) and (8,0) SWCNT fragments attached to an Fe38 catalyst nanoparticle, growth was induced by periodically placing carbon atoms at the edge of the SWCNT. For both armchair and zigzag SWCNTs, QM/MD simulations indicate that defect healing—the process of defect removal during growth—is a necessary, but not sufficient, condition for chirality-controlled SWCNT growth. Time-evolution LOCI analysis shows that healing, while restoring the pristine hexagon structure of the growing SWCNT, also leads to changes in the local chirality of the SWCNT edge region and thus of the entire SWCNT itself. In this respect, we show that zigzag SWCNTs are significantly inferior in maintaining their chirality during growth compared to armchair SWCNTs.

We present the optimization of a genetic algorithm (GA) that is designed to predict the most stable structural isomers of hydrogenated and hydroxylated fullerene cages. Density functional theory (DFT) and density functional tight binding (DFTB) methods are both employed to compute isomer energies. We show that DFTB and DFT levels of theory are in good agreement with each other and that therefore both sets of optimized GA parameters are very similar. As a prototypical fullerene cage, we consider the functionalization of the C20 species, since for this smallest possible fullerene cage it is possible to compute all possible isomer energies for evaluation of the GA performance. An energy decomposition analysis for both C20Hn and C20(OH)n systems reveals that, for only few functional groups, the relative stabilities of different structural isomers may be rationalized simply with recourse to π-Hückel theory. However, upon a greater degree of functionalization, π-electronic effects alone are incapable of describing the interaction between the functional groups and the distorted cage, and both σ- and π-electronic structure must be taken into account in order to understand the relative isomer stabilities.

N-Boryl-substituted carbazoles (carBR2) and (diphenylamino)boranes (Ph2NBR2) with R = Mes (mesityl) and FMes [tris(trifluoromethyl)phenyl] substituents on boron exhibit large UV/vis Stokes shifts. To investigate the substituent effect on the magnitude of the Stokes shifts, we studied the electronic structure and spectroscopic properties of carBR2 and Ph2NBR2 with R = H, Mes, and FMes using hybrid density functional theory (B3LYP) and time-dependent density functional theory (TD-B3LYP) for ground and low-lying excited states. The lowest lying excited state with a nonvanishing oscillator strength is a twisted internal charge transfer (TICT) 1A state in the C2 point group, owing to a single-electron excitation from the nitrogen lone pair to the unoccupied boron pz AO, Nlp → Bpz. Emission from these 1A excited states are predicted to be much brighter than from the energetically close 1B excited states that are not directly related to CT excitation from N to B, due to symmetry. An analysis of geometrical relaxations in the excited state and the state energies relative to the ground state energy of the equilibrium geometry reveals that (a) the carbazole skeleton induces a general red shift in UV/vis spectra, (b) bulky boryl substituents reduce the predicted Stokes shifts of TICT states, and (c) the presence of electron-withdrawing functional groups induces a further general red shift in UV/vis spectra but does not significantly alter Stokes shifts.

Quantum chemical molecular dynamics (QM/MD) simulations of ensembles of C2 molecules on the Ni(111) terrace show that, in the absence of a hexagonal template or step edge, Haeckelite is preferentially nucleated over graphene as a metastable intermediate. The nucleation process is dominated by the swift transition of long carbon chains toward a fully connected sp2 carbon network. Starting from a pentagon as nucleus, pentagons and heptagons condense during ring collapse reactions, which results in zero overall curvature. To the contrary, in the presence of a coronene-like C24 template, hexagonal ring formation is clearly promoted, in agreement with recent suggestions from experiments. In the absence of step edges or molecular templates, graphene nucleation follows Ostwald’s “rule of stages” cascade of metastable states, from linear carbon chains, via Haeckelite islands that finally anneal to graphene.

Combined temperature-programmed desorption and IR studies suggest that absorption cross sections of IR-active vibrations of molecules “strongly” bound to single-wall carbon nanotubes (SWCNTs) are reduced at least by a factor of 10. Quantum chemical simulations show that IR intensities of endohedrally encapsulated molecules are dramatically reduced, and identify dielectric screening by highly polarizable SWCNT sidewalls as the origin of such “screening”. The observed intensity reduction originates from a sizable cancellation of adsorbate dipole moments by mirror charges dynamically induced on the nanotube sidewalls. For exohedrally adsorbed molecules, the dielectric screening is found to be orientation-dependent with a smaller magnitude for adsorption in groove and interstitial sites. The presented results clearly demonstrate and quantify the screening effect of SWCNTs and unequivocally show that IR spectroscopy cannot be applied in a straightforward manner to the study of peapod systems.

The dynamic fullerene self-assembly process during benzene combustion was studied using classical Reactive Force Field (ReaxFF) nonequilibrium molecular dynamics (MD) simulations. In order to drive the combustion process, the hydrogen to carbon (H/C) ratio was gradually reduced during the course of the MD simulations. Target temperatures of 2500 and 3000 K were maintained by using a Berendsen thermostat. Simulation conditions and hydrogen removal strategies were chosen to match closely a previous quantum chemical MD (QM/MD) study based on the density-functional tight-binding (DFTB) potential (Saha et al. ACS Nano 2009, 3, 2241) to allow a comparison between the two different potentials. Twenty trajectories were computed at each target temperature, and hydrocarbon cluster size, CxHy composition, average carbon cluster curvature, carbon hybridization type, and ring count statistics were recorded as a function of time. Similarly as in the QM/MD simulations, only giant fullerene cages in the range from 155 to 212 carbon atoms self-assembled, and no C60 cages were observed. The most notable difference concerned the time required for completing cage self-assembly: Depending on temperature, it takes between 50 and 150 ps in DFTB/MD simulations but never less than 100 ps and frequently several 100s ps in ReaxFF/MD simulations. In the present system, the computational cost of ReaxFF/MD is about 1 order of magnitude lower than that of the corresponding DFTB/MD. Overall, the ReaxFF/MD simulations method paints a qualitatively similar picture of fullerene formation in benzene combustion when compared to direct MD simulations based on the DFTB potential.

Density-functional tight-binding molecular dynamics (DFTB/MD) methods were employed to demonstrate single-walled carbon nanotube (SWNT) nucleation resulting from thermal annealing of SiC nanoparticles. SWNT nucleation in this case is preceded by a change of the SiC structure from a crystalline one, to one in which silicon and carbon are segregated. This structural transformation ultimately resulted in the formation of extended polyyne chains on the SiC nanoparticle surface. These polyyne chains subsequently coalesced, forming an extended sp2-hybridized carbon cap on the SiC nanoparticle. The kinetics of this process were enhanced significantly at higher temperatures (2500 K), compared to lower temperatures (1200 K) and so directly correlated to the surface premelting behavior of the nanoparticle structure. Analysis of the SiC nanoparticle Lindemann index between 1000 and 3000 K indicated that SWNT nucleation at temperatures below 2600 K occurred in the solid, or quasi-solid, phase. Thus, the traditional vapor–liquid–solid mechanism of SWNT growth does not apply in the case of SiC nanoparticles. Instead, we propose that this example of SWNT nucleation constitutes evidence of a vapor–solid–solid process. This conclusion complements our recent observations regarding SWNT nucleation on SiO2 nanoparticles (A. J. Page, K. R. S. Chandrakumar, S. Irle and K. Morokuma, J. Am. Chem. Soc., 2011, 133, 621–628). In addition, similarities between the atomistic SWNT nucleation mechanisms on SiC and SiO2 catalysts provide the first evidence of a catalyst-independent SWNT nucleation mechanism with respect to ‘non-traditional’ SWNT catalyst species.

Ripples naturally occur in graphene sheets. First-principles calculations reveal that, by altering the pyramidalization angles of the carbon atoms, these ripples can be used to direct the chemical reactivity of graphene towards hydrogenation. A fraction of the carbon atoms of a rippled graphene, located around the crests and troughs, show significantly increased reactivity. The remaining carbon atoms have comparable reactivity to those in a flat graphene. To illustrate the increased reactivity, we show that hydrogenation becomes exothermic when the characteristic ratio between the amplitude and wavelength reaches ∼0.55. This finding offers a practical chemical venue for regioselectivity control of graphene functionalization. While the rippling does not directly affect the band gap of the graphene, the rippling-induced hydrogenation does.

Quantum chemical molecular dynamics (QM/MD) simulations of pristine and carbon-doped SiO2 nanoparticles have been performed between 1000 and 3000 K. At temperatures above 1600 K, pristine nanoparticle SiO2 decomposes rapidly, primarily forming SiO. Similarly, carbon-doped nanoparticle SiO2 decomposes at temperatures above 2000 K, primarily forming SiO and CO. Analysis of the physical states of these pristine and carbon-doped SiO2 nanoparticles indicate that they remain in the solid phase throughout decomposition. This process is therefore one of sublimation, as the liquid phase is never entered. Ramifications of these observations with respect to presently debated mechanisms of carbon nanotube growth on SiO2 nanoparticles will be discussed.Graphical abstractDrotjhfklcmbnofResearch highlights► Melting of pristine and carbon-doped nanoparticle SiO2 investigated using QM/MD. ► Sublimation, not liquefaction, of SiO2 and carbon-doped SiO2 observed. ► Primary chemical product of SiO2 sublimation is SiO. ► Primary chemical product of carbon-doped SiO2 sublimation is SiO and CO. ► Sublimation of SiO2 holds ramifications for models of CNT growth on SiO2 catalysts.

Quantum chemical molecular dynamics (QM/MD) simulations using periodic boundary conditions show that hot giant fullerene (GF) cages can both eject and capture C2 molecules dependent on the concentration of noncage carbons in the simulated system, and that the cage size can therefore both increase and decrease under high temperature conditions. The reaction mechanisms for C2 elimination and incorporation involve sp3 carbon defects and polygonal rings larger than hexagons, and are thus closely related to previously described mechanisms (Murry, R. L.; Strout, D. L.; Odom, G. K.; Scuseria, G. E. Nature1993, 366, 665). The atoms constituting the cage are gradually replaced by the two processes, suggesting that a fullerene cage during high-temperature synthesis is a dissipative structure in the sense of Ilya Prigogine’s theory of self-organization in nonequilibrium systems. Explicit inclusion of Lennard-Jones-type helium or argon noble gas atoms is found to increase the GF shrinking rate. Large GFs shrink at a greater rate than small GFs. The simulations suggest that in an idealized, closed system the fullerene cage size may grow to a dynamic equilibrium value that depends on initial cage size, temperature, pressure, and overall carbon concentration, whereas in an open system cage shrinking prevails when noncage carbon density decreases as a function of time.

The synthesis and properties of the phosphonium- and borate-bridged stilbenes are reported. The zwitterionic ladder stilbenes were synthesized by the intramolecular cascade cyclization from the phosphanyl- and boryl-substituted diphenylacetylenes 1. The study of the substituent effects of the phosphanyl and boryl groups revealed the significant dependence of the reactivity on both the nucleophilicity of the phosphanyl group and the electrophilicity of the boryl group. Theoretical calculations indicated that this reaction is initiated by the nucleophilic attack of the phosphanyl group, irrespective of the degree of the electrophilicity of the boryl group, in contrast to the analogous intermolecular reaction promoted by the frustrated Lewis pairs of R3P and B(C6F5)3. Moreover, even in the case of compound 1c, which does not undergo cascade cyclization under thermal conditions, photoexcitation promoted the cyclization to produce the corresponding zwitterionic stilbene 2c, indicative of the potential use as a photoresponsive material. The photophysical properties of a series of zwitterionic stilbenes, 2a–e, also display dependence on the substituents. The fluorescence quantum yields (ΦF) of the stilbenes 2d and 2e, with electron-withdrawing diarylboryl groups, were an order of magnitude higher than those of 2a–c, with a dimesitylboryl group. Time-resolved fluorescence spectroscopy as well as the measurement of ΦF in the polymer matrices revealed that the electron-withdrawing diarylboryl groups significantly retarded the nonradiative decay process from the singlet excited state, resulting in a higher ΦF.

Since their discovery in the early 1990s, single-walled carbon nanotubes (SWNTs) have spawned previously unimaginable commercial and industrial technologies. Their versatility stems from their unique electronic, physical/chemical, and mechanical properties, which set them apart from traditional materials. Many researchers have investigated SWNT growth mechanisms in the years since their discovery. The most prevalent of these is the vapor−liquid−solid (VLS) mechanism, which is based on experimental observations. Within the VLS mechanism, researchers assume that the formation of a SWNT starts with co-condensation of carbon and metal atoms from vapor to form liquid metal carbide. Once the liquid reaches supersaturation, the solid phase nanotubes begin to grow. The growth process is partitioned into three distinct stages: nucleation of a carbon “cap-precursor,” “cap-to-tube” transformation, and continued SWNT growth. In recent years, molecular dynamics (MD) simulations have come to the fore with respect to SWNT growth. MD simulations lead to spatial and temporal resolutions of these processes that are superior to those possible using current experimental techniques, and so provide valuable information regarding the growth process that researchers cannot obtain experimentally. In this Account, we review our own recent efforts to simulate SWNT nucleation, growth, and healing phenomena on transition-metal catalysts using quantum mechanical molecular dynamics (QM/MD) methods. In particular, we have validated each stage of the SWNT condensation mechanism using a self-consistent-charge density-functional tight-binding (SCC-DFTB) methodology. With respect to the nucleation of a SWNT cap-precursor (stage 1), we have shown that the presence of a transition-metal carbide particle is not a necessary prerequisite for SWNT nucleation, contrary to conventional experimental presumptions. The formation and coalescence of polyyne chains on the metal surface occur first, followed by the formation of the SWNT cap-precursor, “ring condensation”, and the creation of an sp2-hybridized carbon structure. In our simulations, the nucleation process takes approximately 400 ps. This first step occurs over a much longer time scale than the second stage of SWNT condensation (approximately 50 ps). We therefore observe SWNT nucleation to be akin to the rate-limiting step of the SWNT formation process. In addition to the QM/MD simulation of various stages of SWNT nucleation, growth, and healing processes, we have determined the effects of temperature, catalyst composition, and catalyst size on the kinetics and mechanism of SWNT growth. With respect to temperature dependence, we observe a “sweet-spot” with respect to the efficiency of SWNT growth. In addition, Ni-catalyzed SWNT growth is observed to be 70−100% faster compared to Fe-catalyzed SWNT growth, depending on the catalyst particle size. We also observe a noticeable increase in SWNT growth rates using smaller catalyst particles. Finally, we review our recent QM/MD investigation of SWNT healing. In particular, we recount mechanisms by which adatom defects, monovacancy defects, and a “5-7 defect” are removed from a nascent SWNT. The effectiveness of these healing mechanisms depends on the rate at which carbon moieties are incorporated into the growing SWNT. Explicitly, we observe that healing is promoted using a slower carbon supply rate. From this rudimentary control of SWNT healing, we propose a route towards chirality-controlled SWNT growth.

Since the discovery of single-walled carbon nanotubes (SWNTs) in the early 1990s, the most commonly accepted model of SWNT growth on traditional catalysts (i.e., transition metals including Fe, Co, Ni, etc.) is the vapor−liquid−solid (VLS) mechanism. In more recent years, the synthesis of SWNTs on nontraditional catalysts, such as SiO2, has also been reported. The precise atomistic mechanism explaining SWNT growth on nontraditional catalysts, however, remains unknown. In this work, CH4 chemical vapor deposition (CVD) and single-walled carbon nanotube (SWNT) nucleation on SiO2 nanoparticles have been investigated using quantum-chemical molecular dynamics (QM/MD) methods. Upon supply of CHx species to the surface of a model SiO2 nanoparticle, CO was produced as the main chemical product of the CH4 CVD process, in agreement with a recent experimental investigation [Bachmatiuk et al., ACS Nano 2009, 3, 4098]. The production of CO occurred simultaneously with the carbothermal reduction of the SiO2 nanoparticle. However, this reduction, and the formation of amorphous SiC, was restricted to the nanoparticle surface, with the core of the SiO2 nanoparticle remaining oxygen-rich. In cases of high carbon concentration, SWNT nucleation then followed, and was driven by the formation of isolated sp2-carbon networks via the gradual coalescence of adjacent polyyne chains. These simulations indicate that the carbon saturation of the SiO2 surface was a necessary prerequisite for SWNT nucleation. These simulations also indicate that a vapor−solid−solid mechanism, rather than a VLS mechanism, is responsible for SWNT nucleation on SiO2. Fundamental differences between SWNT nucleation on nontraditional and traditional catalysts are therefore observed.

Metal-catalyzed SWCNT growth has been modeled using quantum chemical molecular dynamics (QM/MD) in conjunction with feeding of carbon atoms to C40–Fe55 and C40–Ni55 model complexes at 1500 K. The rate of Fe55-catalyzed SWCNT growth determined in this work was 19% slower than the Fe38-catalyzed growth rate. Conversely, Ni55-catalyzed SWCNT growth exhibited a growth rate 69% larger than of Fe55-catalyzed SWCNT growth, a fact consistent with excellent performance of Ni in laser evaporation and carbon-arc experiments. Ni55-catalyzed growth was preceded by the formation of extended polyyne chains at the base of the SWCNT, and so differed fundamentally from Fe55-catalyzed growth. These polyyne chains usually persisted for 10–30 ps. Subsequent polyyne ring condensation resulted in carbon polygon addition at the SWCNT base. The relative stabilities of the Cn carbon cluster moieties on the Fe55 and Ni55 surfaces were consistent with the relative strengths of the Fe–C, Ni–C and C–C interactions. The presence of smaller carbon moieties on the Fe55 surface led to the dissemination of surface iron atoms, and subsequent diffusion of short Cn units through the subsurface region of the catalyst particle. Conversely, the Ni55 catalyst particle was observed to be more stable, remaining intact to a greater extent.

We present reaction pathways for adsorption reactions of NO and NO2 molecules in the vicinity of monovacancy defects on graphite (0001) based on quantum chemical potential energy surfaces (PESs) obtained by B3LYP and dispersion-augmented density-functional tight-binding (DFTB-D) methods. To model the graphite (0001) monovacancy defects, finite-size molecular model systems up to the size of dicircumcoronene (C95H24) were employed. We find that the reactions of NOx on the monodefective graphite surface are initiated by rapid association processes with negligible barriers, leading to nitridation and oxidation of the graphite surface, and eventually producing gaseous COx, NO, and CN species leaving from an even more defective graphite surface. On the basis of the computed reaction pathways, we predict reaction rate constants in the temperature range between 300 and 3000 K using Rice−Ramsperger−Kassel−Marcus theory. High-temperature quantum chemical molecular dynamics simulations at 3000 K based on on-the-fly DFTB-D energies and gradients support the results of our PES studies.

A mechanism describing Ni38-catalyzed single-walled carbon nanotube (SWNT) growth has been elucidated using quantum mechanical molecular dynamics (QM/MD) methods. This mechanism is dominated by the existence of extended polyyne structures bound to the base of the initial SWNT cap-fragment. Polygonal ring formation, and hence SWNT growth itself, was driven by the continual, simultaneous extension of these polyyne chains and subsequent “ring collapse” (i.e., self-isomerization/interaction of these polyyne chains). The rate of the former exceeded that of the latter, and so this mechanism was self-perpetuating. Consequently, the observed kinetics of Ni38-catalyzed SWNT growth were increased substantially compared to those observed using other transition metal catalysts of comparable size.

Structural characterization of nanodiamonds by vibrational spectroscopy requires knowledge of the factors determining the spectra. Raman spectroscopy is widely used to detect the diamond phase in nanodiamond powders and films, but several spectral features are still poorly understood. Here we present a theoretical study of the evolution of diamond hydrocarbon Raman spectra with increasing size, from the adamantane molecule to ∼3 nm large tetrahedral and octahedral particles of Td symmetry, containing up to about 1000 carbon atoms. The self-consistent-charge density functional tight-binding method (SCC-DFTB) was used for the calculation of harmonic first-order Raman spectra. We demonstrate very good agreement with Raman spectra computed by standard density functional theory (DFT) for the smaller model systems. The evolution of the Raman patterns is smooth, and convergence to the bulk limit could clearly be observed in case of the acoustic vibrational modes (ωA = 0 cm−1). We found a simple relationship between nanodiamond size and vibrational frequency, which is analogous to the corresponding equation for the radial breathing mode of single-walled carbon nanotubes. The T2 modes of octahedral diamond hydrocarbons coalesce faster to the bulk optical vibrational mode (in experiment, ωO = 1332 cm−1) than those of tetrahedral particles, consistent with the fact that the bulk/surface ratio is more favorable for octahedral particles. Our simulations unequivocally show that controversial Raman features around 500 and 1150 cm−1 do not originate from the nanodiamond crystals, and that the nanocrystal shape plays an important role in the appearance of the Raman spectra even in the 3 nm domain.Keywords: density functional tight binding; nanodiamonds; Raman intensities; size evolution of Raman spectra; vibrational spectroscopy

Iron-catalyzed SWCNT growth by carbon diffusion starting from a carbon cap has been demonstrated in density-functional tight-binding molecular dynamics simulations. A C40 (5,5) SWCNT cap attached to an Fe38 cluster was employed as initial model system. After 40 carbon atoms were supplied onto the iron surface for 20 ps, dynamics were continued for 160 ps without supply of further carbon feedstock. Growth of the SWCNT sidewall is mainly due to surface-diffusion of short carbon chains, and to a lesser degree due to sub-surface diffusion. Newly created rings consist only of pentagons and hexagons, while heptagons are infrequent and short-lived, which seems to be caused by the slower, more ordered sidewall growth due to the diffusion process.

Quantum chemical molecular dynamics have been employed to investigate the healing of single-walled carbon nanotubes (SWNTs) during growth. In trajectories based on self-consistent-charge density-functional tight-binding (SCC-DFTB) energies and gradients, gas-phase carbon atoms were supplied to the carbon−iron boundary of a model C40-Fe38 complex at two different rates (1 C/0.5 ps and 1 C/10 ps). The lower rate of carbon supply was observed to promote SWNT growth, compared to the higher rate, for the same number of carbon atoms supplied. This promotion of growth was ascribed to the suppression of pentagon and heptagon incorporation in the sp2 carbon network observed at lower carbon supply rates. The most successful example of growth occurred when the respective periods of hexagon and pentagon formation were out of phase and heptagon formation was limited. Higher carbon supply rates tended to result in the encapsulation of the Fe38 cluster by the extended sp2 carbon cap, due to a saturation of pentagon and heptagon defects in the latter. The greater tendency toward hexagon formation found using a lower carbon supply rate was attributed to the relative rates of defect removal and addition from the sp2 carbon cap during the growth process. The defect removal (i.e., healing) process of the sp2 carbon cap occurred via ring isomerization, which resulted in the removal of 5-7, adatom, and monovacancy defects. These healing mechanisms generally occurred over time scales of several picoseconds and depended largely on the presence of the catalyst surface. The healing mechanisms observed in this work represent a possible pathway by which control over the (n, m) chirality of a nascent SWNT is obtained during the growth process.

We present a brief review of the most important efforts aimed at simulating single-walled carbon nanotube (SWNT) nucleation and growth processes using molecular dynamics (MD) techniques reported in the literature. MD simulations allow the spatio-temporal movement of atoms during nonequilibrium growth to be followed. Thus, it is hoped that a successful MD simulation of the entire SWNT formation process will assist in the design of chirality-specific SWNT synthesis techniques. We give special consideration to the role of the metal catalyst particles assumed in standard theories of SWNT formation, and describe the actual metal behavior observed in the reported MD simulations, including our own recent quantum chemical MD simulations. It is concluded that the use of a quantum potential is essential for a qualitatively correct description of the catalytic behavior of the metal cluster, and that carbide formation does not seem to be a necessary requirement for nucleation and growth of SWNTs according to our most recent quantum chemical MD simulations.

The temperature dependence of continued single-walled carbon nanotube (SWNT) growth on an iron cluster is investigated using quantum chemical molecular dynamics simulations based on the density functional tight-binding method. As a model system for continued SWNT growth, a (5,5) armchair-type SWNT seed attached to an iron Fe38 cluster was used. Continuous and rapid supply of C atoms was provided in the vicinity of the nanotube-metal interface area. The simulations were performed at temperatures of 1000, 1500, and 2000 K. The simulations reveal fastest growth at 1500 K, although the differences are moderate. In the observed growth process, formation of polyyne chains at the rim of the nanotube-metal interface efficiently initiates pentagon/hexagon/heptagon ring formations in the carbon sidewall, leading to “lift-off” of the nanotube from the metal cluster. At 1000 K, the SWNT lift-off is suppressed despite the fact that the total number of created rings in the nanotube is comparable to that at 1500 K. In addition, relatively long polyyne chains tend to form extensions from the carbon sidewall to the metal cluster at 1000 K, whereas at 2000 K, deformation of the nanotube becomes more pronounced and diameter narrowing sets in, and polyyne chains at the rim of the nanotube easily dissociate at this high temperature. These physical and chemical events at 1000 and 2000 K can be considered inhibiting factors preventing efficient growth of the nanotube.

The atomic scale details of single-walled carbon nanotube (SWNT) nucleation on metal catalyst particles are elusive to experimental observations. Computer simulation of metal-catalyzed SWNT nucleation is a challenging topic but potentially of great importance to understand the factors affecting SWNT diameters, chirality, and growth efficiency. In this work, we use nonequilibrium density functional tight-binding molecular dynamics simulations and report nucleation of sp2-carbon cap structures on an iron particle consisting of 38 atoms. One C2 molecule was placed every 1.0 ps around an Fe38 cluster for 30 ps, after which a further 410 ps of annealing simulation without carbon supply was performed. We find that sp2-carbon network nucleation and annealing processes occur in three sequential and repetitive stages: (A) polyyne chains on the metal surface react with each other to evolve into a Y-shaped polyyne junction, which preferentially form a five-membered ring as a nucleus; (B) polyyne chains on the first five-membered ring form an additional fused five- or six-membered ring; and (C) pentagon-to-hexagon self-healing rearrangement takes place with the help of short-lived polyyne chains, stabilized by the mobile metal atoms. The observed nucleation process resembles the formation of a fullerene cage. However, the metal particle plays a key role in differentiating the nucleation process from fullerene cage formation, most importantly by keeping the growing cap structure from closing into a fullerene cage and by keeping the carbon edge “alive” for the addition of new carbon material.Keywords: continued carbon nanotube growth; density functional tight binding; iron catalyst nanoparticle; nonequilibrium dynamics; quantum chemical molecular dynamics simulations; self-assembly

We present reaction pathways for adsorption of CO and CO2 molecules in the vicinity of monovacancy defects on graphite (0001) based on B3LYP and dispersion-augmented density-functional tight-binding (DFTB-D) studies of the potential energy surfaces (PES) of these reactions. To model the graphite (0001) monovacancy defects, finite-size molecular model systems up to the size of dicircumcoronene (C95H24) were employed. We find that the CO molecule reacts readily with the monovacancy defects and partially “heals” the carbon hexagon network leading to the formation of a stable epoxide, whereas CO2 oxidizes the defect via a dissociative adsorption pathway following CO elimination. We predict reaction rate constants in the temperature range between 300 and 3000 K using Rice−Ramsperger−Kassel−Marcus theory. Quantum chemical molecular dynamics simulations at 3000 K based on on-the-fly DFTB-D energies and gradients support the results of our PES studies.

Using density-functional tight-binding (DFTB)-based quantum chemical molecular dynamics at 2500 and 3000 K, we have performed simulations of benzene combustion by gradually reducing the hydrogen to carbon (H/C) ratio. The accuracy of DFTB for these simulations was found to be on the order of 7−9 kcal/mol when compared to higher-level B3LYP and G3-like quantum chemical methods in extensive benchmark calculations. Ninety direct-dynamics trajectories were run for up to 225 ps simulation time, during which hydrocarbon cluster size, curvature, and CxHy composition, carbon hybridization type, and ring count statistics were recorded. Giant fullerene cage formation was observed only after hydrogen was completely eliminated from the reaction mixture, with yields of around 50% at 2500 K and 42% at 3000 K. Cage sizes are mostly in the range from 152 to 202 carbon atoms, with the distribution shifting toward larger cages at lower temperature. In contrast to previous simulations of dynamics fullerene assembly from ensembles of C2 molecules, we find that the resulting cages show smaller number of attached carbon chains (antenna) surviving until cage closure. Again, no direct formation pathway for C60 from smaller fragments was observed. Our results challenge the idealized picture of “ordered” growth of PAHs along a route involving only maximally condensed and fully hydrogenated graphene platelets, and favor instead fleeting open-chains with ring structures attached, featuring a large number of hydrogen defects, pentagons, and other nonhexagon ring species.Keywords: benzene combustion; density-functional tight-binding; dynamic self-assembly; fullerene formation; H/C ratio change during combustion; nonequilibrium dynamics; quantum chemical molecular dynamics simulations

Continued growth of a single-walled carbon nanotube (SWNT) on an Fe cluster at 1500 K is demonstrated using quantum chemical molecular dynamics simulations based on the self-consistent-charge density-functional tight-binding (SCC-DFTB) method. In order to deal with charge transfer between carbon and metal particles and the multitude of electronic states, a finite electronic temperature approach is applied. We present trajectories of 45 ps length, where a continuous supply of carbon atoms is directed toward the C−Fe boundary between a 7.2 Å long armchair (5,5) SWNT fragment and an attached Fe38 cluster. The incident carbon atoms react readily at the C−Fe interface to form C- and C2-extensions on the tube rim that attach to the Fe cluster. These bridging sp-hybridized carbon fragments are vibrationally excited and highly mobile and, therefore, become engaged in frequent bond formation and breaking processes between their constituent C and the Fe atoms. The sp-hybridized carbon bridge dynamics and their reactions with the Fe-attached nanotube end bring about formations of new five-, six-, and seven-membered carbon rings extending the tube sidewall, resulting in overall continued growth of the nanotube on the Fe cluster up to nearly twice its length. Due to the random nature of new polygon formation, sidewall growth is observed as an irregular process without clear SWNT chirality preference. Compared to fullerene formation, heptagon formation is considerably promoted.Keywords: continued carbon nanotube growth; density-functional tight-binding; iron catalyst nanoparticle; nonequilibrium dynamics; quantum chemical molecular dynamics simulations; self-assembly

The relationship of reaction energies for CH2/NH/O exo- and endo-[2 + 1] cycloadditions to chiral single-walled carbon nanotube (SWNT) sidewalls with the inverse tube diameter (1/d) was investigated using density functional theory (DFT) and density functional tight binding (DFTB) methods. We considered additions to the three nonequivalent C−C bond types t (bond most parallel to tube axis), d (“diagonal” bond, slightly skewed), and p (bond most perpendicular to tube axis), using hydrogen-terminated (2n,n) SWNT model systems with n = 2−8. Exoadditions are classified into two types, one where the original C−C bond is broken (exo(l)), and one where it remains intact (exo(s)) in the addition complex. Endoadditions are found to always belong to the latter (endo(s)) type. It is found that (a) exoadditions are more exothermic than endo additions, and (b) that exoadditions are more exothermic with larger bond-tube axis angle (p > d > t). A nearly perfect linear relationship between the total reaction energy ΔE and 1/d holds only for individual endo, exo(s) and exo(l) addition series to specific t/d/p bonds, while ΔE, as well as the SWNT deformation energy (DEF) and the interaction energy (INT) between deformed SWNT and deformed addends, are quadratically dependent on 1/d, when both negative (endo) and positive (exo(s)) bond curvatures are considered in linear regression analysis. Energy decomposition analysis shows that for endo- and exo(s)- series the curvature dependence of ΔE is dominated by INT, while for exo(l) series, this quantity is dominated by DEF.

The mechanism and kinetics of single-walled carbon nanotube (SWNT) nucleation from Fe- and Ni-carbide nanoparticle precursors have been investigated using quantum chemical molecular dynamics (QM/MD) methods. The dependence of the nucleation mechanism and its kinetics on environmental factors, including temperature and metal-carbide carbon concentration, has also been elucidated. It was observed that SWNT nucleation occurred via three distinct stages, viz. the precipitation of the carbon from the metal-carbide, the formation of a “surface/subsurface” carbide intermediate species, and finally the formation of a nascent sp2-hybidrized carbon structure supported by the metal catalyst. The SWNT cap nucleation mechanism itself was unaffected by carbon concentration and/or temperature. However, the kinetics of SWNT nucleation exhibited distinct dependences on these same factors. In particular, SWNT nucleation from NixCy nanoparticles proceeded more favorably compared to nucleation from FexCy nanoparticles. Although SWNT nucleation from FexCy and NixCy nanoparticle precursors occurred via an identical route, the ultimate outcomes of these processes also differed substantially. Explicitly, the Nix-supported sp2-hybridized carbon structures tended to encapsulate the catalyst particle itself, whereas the Fex-supported structures tended to form isolated SWNT cap structures on the catalyst surface. These differences in SWNT nucleation kinetics were attributed directly to the relative strengths of the metal−carbon interaction, which also dictates the precipitation of carbon from the nanoparticle bulk and the longevity of the resultant surface/subsurface carbide species. The stability of the surface/subsurface carbide was also influenced by the phase of the nanoparticle itself. The observations agree well with experimentally available data for SWNT growth on iron and nickel catalyst particles.

Ripples naturally occur in graphene sheets. First-principles calculations reveal that, by altering the pyramidalization angles of the carbon atoms, these ripples can be used to direct the chemical reactivity of graphene towards hydrogenation. A fraction of the carbon atoms of a rippled graphene, located around the crests and troughs, show significantly increased reactivity. The remaining carbon atoms have comparable reactivity to those in a flat graphene. To illustrate the increased reactivity, we show that hydrogenation becomes exothermic when the characteristic ratio between the amplitude and wavelength reaches ∼0.55. This finding offers a practical chemical venue for regioselectivity control of graphene functionalization. While the rippling does not directly affect the band gap of the graphene, the rippling-induced hydrogenation does.

Density-functional tight-binding molecular dynamics (DFTB/MD) methods were employed to demonstrate single-walled carbon nanotube (SWNT) nucleation resulting from thermal annealing of SiC nanoparticles. SWNT nucleation in this case is preceded by a change of the SiC structure from a crystalline one, to one in which silicon and carbon are segregated. This structural transformation ultimately resulted in the formation of extended polyyne chains on the SiC nanoparticle surface. These polyyne chains subsequently coalesced, forming an extended sp2-hybridized carbon cap on the SiC nanoparticle. The kinetics of this process were enhanced significantly at higher temperatures (2500 K), compared to lower temperatures (1200 K) and so directly correlated to the surface premelting behavior of the nanoparticle structure. Analysis of the SiC nanoparticle Lindemann index between 1000 and 3000 K indicated that SWNT nucleation at temperatures below 2600 K occurred in the solid, or quasi-solid, phase. Thus, the traditional vapor–liquid–solid mechanism of SWNT growth does not apply in the case of SiC nanoparticles. Instead, we propose that this example of SWNT nucleation constitutes evidence of a vapor–solid–solid process. This conclusion complements our recent observations regarding SWNT nucleation on SiO2 nanoparticles (A. J. Page, K. R. S. Chandrakumar, S. Irle and K. Morokuma, J. Am. Chem. Soc., 2011, 133, 621–628). In addition, similarities between the atomistic SWNT nucleation mechanisms on SiC and SiO2 catalysts provide the first evidence of a catalyst-independent SWNT nucleation mechanism with respect to ‘non-traditional’ SWNT catalyst species.