End-Cap Effects on Vibrational Structures of Finite-Length Carbon Nanotubes

Theoretical understanding of stability of mechanically interlocked carbon nanotubes and their precursors

Dispersion-corrected DFT calculations were performed on (a,a) nanotubes (a = 5-10) attached by a U-shaped functional group consisting of p-xylene-linked double 9,10-di(1,3-dithiol-2-ylidene)-9,10-dihydro anthracene terminated by C_nH_2n chains (n = 6, 8, and 9), and their ring-closing macrocycles containing tubes. The reactant precursors and macrocycles are denoted by UP-n-(a,a) and (a,a)@Cycle-n, respectively. We found that UP-n-(a,a) are energetically preferable relative to the dissociation limit toward a U-shaped functional group (UP-n) and a tube (initial state) due to the attractive CH-π and π-π interactions. The attractive interactions are enhanced by increasing the tube diameters and C_nH_2n chain lengths because UP-n structures can be easily adjusted to interact with the tubes. The stability of (a,a)@Cycle-n and related (a,b)@Cycle-n is sensitive to tube diameters due to the restriction of ring structures. When diameter differences between a Cycle-n and a tube (D-d) are larger than 5 Å, (a,a)@Cycle-n plus C₂H₄ are energetically preferable relative to the initial state. However, the (a,a)@Cycle-n plus C₂H₄ byproduct is always energetically unstable relative to UP-n-(a,a). The DFT calculations found that the energy differences were low at D-d values ranging from 7 to 8 Å, explaining the tube-diameter-selective formation of the mechanically-interlocked tubes, observed experimentally.

Simulation of the Raman spectroscopy of multi-layered carbon nanomaterials

A empirical potential based model for simulating the Raman spectroscopy of layered carbon nanomaterials is introduced.

Importance of the alignment of polar π conjugated molecules inside carbon nanotubes in determining second-order non-linear optical properties

Dispersion-corrected DFT calculations found energetically preferred alignments of certain p,p′-dimethylaminonitrostilbene (DANS) molecules inside an carbon nanotube, and their importance in determining second-order non-linear optical properties.

Anomalous Compression of D5(450)-C100 by Encapsulating La2C2 Cluster instead of La2

We demonstrate that a finite-length (10,0) carbon nanotube (CNT) with two fullerene caps, namely D5(450)-C100, is an ideal prototype to study the mechanical responses of small CNTs upon endohedral metal doping. Encapsulation of a large La2C2 cluster inside D5(450)-C100 induces a 5% axial compression of the cage, as compared with the structure of La2@D5(450)-C100. Detailed crystallographic analyses reveal quantitively the flexibility of the [10]cyclacene-sidewall segment and the rigidity of the pentagon-dominating caps for the first time. The internal C2-unit acts as a molecular spring that attracts the surrounding cage carbon atoms through strong interactions with the two moving lanthanum ions. This is the first crystallographic observation of the axial compression of CNTs caused by the internal stress, which enhances our knowledge about the structural deformation of novel carbon allotropes at the atomic level.

Roles of water molecules in trapping carbon dioxide molecules inside the interlayer space of graphene oxides

Density functional theory (DFT) calculations were employed to investigate the energetics of carbon dioxide migration within hydrated or anhydrous graphene oxides (GOs). When anhydrous GO structures contain a carbon dioxide molecule, the carbon dioxide interacts repulsively with the GO layers to increase the interlayer spacing. The repulsive electrostatic interactions are reduced by the insertion of water molecules into CO2-containing GO structures due to the occurrence of attractive water-layer interactions through hydrogen bonding. Consequently, the interlayer spacings in CO2-containing hydrated structures are shortened compared with those in the anhydrous structures. The results indicate that the intercalated water molecules have the ability to connect the GO layers in the presence of carbon dioxide. Furthermore, the DFT calculations indicated that the GO interlayer spacings, which are influenced by the intercalation of water molecules, control carbon dioxide migration within the GO layers. The importance of the interlayer spacings on the migration of carbon dioxide arises from the occurrence of repulsive interactions between CO2 and oxygen-containing groups attached on the graphene sheets. When the GO interlayer spacings are short due to the presence of intercalated water molecules, the repulsive interactions between carbon dioxide and the GO layers are strong enough to prevent CO2 from migrating from its original position. Such repulsive interactions do not occur during the migration of CO2 within anhydrous GO structures because of the relatively longer interlayer spacing. Accordingly, CO2 migrates within anhydrous GO with a less significant barrier, indicating that carbon dioxide molecules are easily released from the GO.

Key factors in determining the arrangement of π-conjugated oligomers inside carbon nanotubes

Dispersion corrected DFT calculations found different arrangements of π-conjugated oligomers inside a carbon nanotube, dependent on the type of oligomer, which are responsible for determining the oligomers’ electronic properties.

Vibrational Excitation in Electron Transport through Carbon Nanotube Quantum Dots

Electron transport in single-walled carbon nanotubes (SWCNTs) is extremely sensitive to environmental effects. SWCNTs experiencing an inhomogeneous environment are effectively subjected to a disorder potential, which can lead to localized electronic states. An important element of the physical picture of such states localized on the nanometer-scale is the existence of a local vibronic mainfold resulting from the localization-enhanced electron-vibrational coupling. In this Letter, scanning tunneling spectroscopy (STS) is used to study the quantum-confined electronic states in SWCNTs deposited on the Au(111) surface. STS spectra show the vibrational overtones identified as D-band Kekulé vibrational modes and K-point transverse out-of plane phonons. The presence of these vibrational modes in the STS spectra suggests rippling distortion and dimerization of carbon atoms on the SWCNT surface. The present study thus, for the first time, experimentally connects the properties of well-defined localized electronic states to the properties of their associated vibronic states.

Platinum clusters on vacancy-type defects of nanometer-sized graphene patches

Density functional theory calculations found that spin density distributions of platinum clusters adsorbed on nanometer-size defective graphene patches with zigzag edges deviate strongly from those in the corresponding bare clusters, due to strong Pt-C interactions. In contrast, platinum clusters on the pristine patch have spin density distributions similar to the bare cases. The different spin density distributions come from whether underlying carbon atoms have radical characters or not. In the pristine patch, center carbon atoms do not have spin densities, and they cannot influence radical characters of the absorbed cluster. In contrast, radical characters appear on the defective sites, and thus spin density distributions of the adsorbed clusters are modulated by the Pt-C interactions. Consequently, characters of platinum clusters adsorbed on the sp² surface can be changed by introducing vacancy-type defects.

Behavior of Ag3 clusters inside a nanometer-sized space of ZSM-5 zeolite

We found from DFT calculations that Ag-Ag orbital interactions as well as Ag-O electrostatic interactions determine the structures of three silver cations inside a nanometer-sized cavity of ZSM-5 (Ag(3)-ZSM-5) in lower and higher spin states. Both interactions strongly depend on the number of Al atoms substituted for Si atoms on the ZSM-5 framework (ZSM-5(Al(n))), where n ranges from 1 to 3. In smaller n, stronger Ag-Ag orbital interactions and weaker Ag-O electrostatic interactions operate. Accordingly, there are significant dependencies of the structures of three silver cations on the number of Al atoms. In lower spin states of Ag(3)-ZSM-5(Al(1)) and Ag(3)-ZSM-5(Al(2)), D(3h)-like triangle clusters are contained inside ZSM-5 whereas their higher spin states have triangle clusters distorted significantly from the D(3h) structure. In lower spin states, the totally symmetric orbital consisting of 5s(Ag) orbitals is responsible for cluster formation, whereas in higher spin states occupation of a 5s(Ag)-based orbital with one node results in significant distortion of the triangle clusters. The distortion can be partially understood by analogies to Jahn-Teller distortion of the bare D(3h) Ag(3)(+) cluster in the triplet spin state. When n is 3, we found that three silver cations are isolated in a lower spin state and that a linear cluster consisting of two silver cations is formed in a higher spin state. Thus, we demonstrate from DFT calculations that the number of Al atoms can control the properties of three silver cations inside a ZSM-5 cavity. Since the structural and electronic features of the enclosed silver clusters can link to their catalytic properties, the DFT findings can help us to understand the catalytic activity of Ag-ZSM-5.

Toward the development of "nano-QSARs": advances and challenges

The most significant achievements and challenges relating to an application of quantitative structure-activity relationship (QSAR) approach in the risk assessment of nanometer-sized materials are highlighted. Recent advances are discussed in the context of "classical" QSAR methodology. The possible ways for the structural characterization of compounds existing at the nanoscale (at least one dimension of 100 nm or less) are briefly reviewed. The applicability of the existing toxicological data for developing QSAR models is evaluated. Finally, the existing models are presented. The need to develop new interpretative descriptors for the nanosystems is also highlighted. It is suggested that, due to high variability in the molecular structures and different mechanisms of toxicity, individual classes of nanoparticles should be modeled separately.

Nanomaterials – the Next Great Challenge for Qsar Modelers

In this final chapter a new perspective for the application of QSAR in the nanosciences is discussed. The role of nanomaterials is rapidly increasing in many aspects of everyday life. This is promoting a wide range of research needs related to both the design of new materials with required properties and performing a comprehensive risk assessment of the manufactured nanoparticles. The development of nanoscience also opens new areas for QSAR modelers. We have begun this contribution with a detailed discussion on the remarkable physical–chemical properties of nanomaterials and their specific toxicities. Both these factors should be considered as potential endpoints for further nano-QSAR studies. Then, we have highlighted the status and research needs in the area of molecular descriptors applicable to nanomaterials. Finally, we have put together currently available nano-QSAR models related to the physico-chemical endpoints of nanoparticles and their activity. Although we have observed many problems (i.e., a lack of experimental data, insufficient and inadequate descriptors), we do believe that application of QSAR methodology will significantly support nanoscience in the near future. Development of reliable nano-QSARs can be considered as the next challenging task for the QSAR community.

Which do endohedral Ti2C80 metallofullerenes prefer energetically: Ti2@C80 or Ti2C2@C78? A theoretical study

Four possible isomers of the Ti2C80 metallofullerene are discussed in detail at the B3LYP DFT level of theory: two isomers in Ti2@C80 formula with two Ti atoms encapsulated inside a C80 cage and the other two in Ti2C2@C78 formula with a Ti2C2 cluster involved inside a C78 cage. In the encaged Ti2C2 cluster, there are end-on and side-on C2 bridging modes into the two Ti atoms. The optimized end-on cluster has a linear Ti-C-C-Ti array, whereas the side-on cluster has a butterfly-like structure where the two Ti atoms and the C2 unit do not lie in a plane. DFT calculations show that the Ti2C2@C78 molecule with the end-on Ti2C2 cluster is energetically most favorable in the four isomers. Stabilities of the Ti2C80 molecules are essentially dominated by Ti binding sites inside fullerene cages. The Ti atoms bind over the hexagon rings in preference to a junction between hexagon and pentagon rings. In the Ti2C2@C78 molecules, orbital interactions between the Ti2C2 cluster and the outer cage play a significant role in determining the C2 bridging modes into the dititanium center and their relative stabilities.

Molecular vibrations of [n]oligoacenes (n=2−5 and 10) and phonon dispersion relations of polyacene

As model compounds for nanosize carbon clusters, the phonon dispersion curves of polyacene are constructed based on density functional theory calculations for [n]oligoacenes (n=2-5, 10, and 15). Complete vibrational assignments are given for the observed Fourier-transform infrared and Raman spectra of [n]oligoacenes (n=2-5). Raman intensity distributions by the 1064-nm excitation are well reproduced by the polarizability-approximation calculations for naphthalene and anthracene, whereas several bands of naphthacene and pentacene at 1700-1100 cm(-1) are calculated to be enhanced by the resonance Raman effect. It is found from vibronic calculations that the coupled a(g) modes between the Kekulé deformation and joint CC stretching give rise to the Raman enhancements of the Franck-Condon type, and that the b(3g) mode corresponding to the graphite G mode is enhanced by vibronic coupling between the (1)L(a)((1)B(1u)) and (1)B(b)((1)B(2u)) states. The phonon dispersion curves of polyacene provide a uniform foundation for understanding molecular vibrations of the oligoacenes in terms of the phase difference. The mode correlated with the defect-sensitive D mode of the bulk carbon networks is also found for the present one-dimensional system.

Local Modifications of Single-Wall Carbon Nanotubes Induced by Bond Formation with Encapsulated Fullerenes

Defected fullerenes in nanopeapods form bonds with the encapsulating single-walled carbon nanotubes when irradiated by an electron beam leading to changes in the guest (fullerene) and the host (nanotube). Intrinsic reaction coordinate (IRC) analysis based on B3LYP hybrid density functional theory shows that a C1-C59 defect with a single protruding C atom is initially formed from the C60(Ih) cage. The high activation energy for this step (8.37 eV (193.0 kcal/mol)), being assumed to be accessible during irradiation, is lower than that of the Stone-Wales rearrangement on the sp2 network. The binding of the defected fullerene to the nanotube is preferential, orthogonal bonds relative to the tube axis being slightly preferred. Because of the covalent bonds formed between the guest and host, the carbon network on the nanotube is locally perturbed in the vicinity of the binding site. As a result of the new bonds, bisnorcaradiene-like as well as quinonoid-like patterns appear near the binding site. These results are interpreted using orbital interaction and Clar diagram arguments. The changes in the bonding pattern on the nanotube should be significant in further functionalization of carbon nanotubes.

Density Functional Study of the 13C NMR Chemical Shifts in Small-to-Medium-Diameter Infinite Single-Walled Carbon Nanotubes

NMR chemical shifts were calculated for semiconducting (n,0) single-walled carbon nanotubes (SWNTs) with n ranging from 7 to 17. Infinite isolated SWNTs were calculated using a gauge-including projector-augmented plane-wave (GIPAW) approach with periodic boundary conditions and density functional theory (DFT). In order to minimize intertube interactions in the GIPAW computations, an intertube distance of 8 A was chosen. For the infinite tubes, we found a chemical shift range of over 20 ppm for the systems considered here. The SWNT family with lambda = mod(n, 3) = 0 has much smaller chemical shifts compared to the other two families with lambda = 1 and lambda = 2. For all three families, the chemical shifts decrease roughly inversely proportional to the tube's diameter. The results were compared to calculations of finite capped SWNT fragments using a gauge-including atomic orbital (GIAO) basis. Direct comparison of the two types of calculations could be made if benzene was used as the internal (computational) reference. The NMR chemical shifts of finite SWNTs were found to converge very slowly, if at all, to the infinite limit, indicating that capping has a strong effect (at least for the (9,0) tubes) on the calculated properties. Our results suggest that (13)C NMR has the potential for becoming a useful tool in characterizing SWNT samples.

Gate effect of vacancy-type defect of fullerene cages on metal-atom migrations in metallofullerenes

Metal-atom migration outside from a defective fullerene cage of a metallofullerene Gd@C(82) (Ca@C(82)), where the Gd(3+) (Ca(2+)) ion is incorporated inside the C(2)(v)()-C(82) cage, is discussed in detail at the B3LYP DFT level of theory. The metal-atom migrations are initiated by the formation of vacancy-type defects involving two coordinatively unsaturated C atoms. This step, which is assumed to proceed due to energy-particle irradiation, leads to the formation of antibonding orbitals between the two C atoms. Since the antibonding orbitals can interact with vacant d-orbitals of the Gd(3)(+)() ion in an in-phase fashion, the attractive interactions allow the Gd ion to insert into the two C atoms in the defect. As a result, the metal ion passes through the defect under energy-particle irradiation. In contrast, the Ca(2+) ion with the vacant s-orbitals does not have such orbital interactions, and thus, a C-C bond is reformed between the two C atoms, which prohibits the Ca ion from penetrating the defected C(82) cage. DFT calculations nicely demonstrate that the orbital interactions control metal-atom migration around the defect site using their orbital symmetries, and therefore, the vacancy-type defect acts as a "gate" that permits a specific atom to go out from a defected fullerene cage.