A Density Functional Study of the ¹³C NMR Chemical Shifts in Functionalized Single-Walled Carbon Nanotubes

The 13C NMR chemical shifts for functionalized (7,0), (8,0), (9,0), and (10,0) single-walled carbon nanotubes (SWNTs) have been studied computationally using gauge-including projector-augmented plane-wave (GIPAW) density functional theory (DFT). The functional groups NH, NCH3, NCH2OH, and CH2NHCH2 have been considered, and different sites where covalent addition or substitution may occur have been examined. The shifts of the carbons directly attached to the group are sensitive to the bond which has been functionalized and may, therefore, be used to identify whether the group has reacted with a parallel or a diagonal C−C bond. The addition of NH to a parallel bond renders the functionalized carbons formally sp3-hybridized, yielding shifts of around 44 ppm, independent of the SWNT radius. Reaction with a diagonal bond retains the formal sp2 hybridization of the substituted carbons, and their shifts are slightly lower or higher than those of the unsubstituted carbon atoms. The calculated 1H NMR shifts of protons in the functional groups are also dependent upon the SWNT−group interaction. Upon decreasing the degree of functionalization for the systems where the group is added to a parallel bond, the average chemical shift of the unfunctionalized carbons approaches that of the pristine tube. At the same time, the shifts of the functionalized carbons remain independent upon the degree of functionalization. For the SWNTs where N−R attaches to a parallel bond, the average shift of the sp2 carbons was found to be insensitive to the substituent R. Moreover, the shifts of the functionalized sp3 carbons, as well as of the carbons within the group itself, are independent of the SWNT radius. The results indicate that a wealth of knowledge may be obtained from the 13C NMR of functionalized SWNTs

Single-Layered Hittorf’s Phosphorus: A Wide-Bandgap High Mobility 2D Material

We propose here a two-dimensional material based on a single layer of violet or Hittorf’s phosphorus. Using first-principles density functional theory, we find it to be energetically very stable, comparable to other previously proposed single-layered phosphorus structures. It requires only a small energetic cost of approximately 0.04 eV/atom to be created from its bulk structure, Hittorf’s phosphorus, or a binding energy of 0.3–0.4 J/m2 per layer, suggesting the possibility of exfoliation in experiments. We find single-layered Hittorf’s phosphorus to be a wide band gap semiconductor with a direct band gap of approximately 2.5 eV, and our calculations show it is expected to have a high and highly anisotropic hole mobility with an upper bound lying between 3000–7000 cm2 V–1 s–1. These combined properties make single-layered Hittorf’s phosphorus a very good candidate for future applications in a wide variety of technologies, in particular for high frequency electronics, and optoelectronic devices operating in the low wavelength blue color range

Determining the Diameter of Functionalized Single-Walled Carbon Nanotubes with ¹³C NMR: A Theoretical Study

NMR chemical shifts of N–R-functionalized (n, 0) single-walled carbon nanotubes (SWNTs) with n = 11, 13−17 were computed from first principles. The chemical shifts of functionalized carbons at a bond diagonal to the SWNT axis are strongly dependent upon the C−C distance in the C−NR−C moiety. This distance, in turn, is sensitive to the SWNT radius. Monitoring these shifts could therefore help to determine the diameter distribution within a sample. Proton shifts are also reported

Determining the Diameter of Functionalized Single-Walled Carbon Nanotubes with ¹³C NMR: A Theoretical Study

NMR chemical shifts of N–R-functionalized (n, 0) single-walled carbon nanotubes (SWNTs) with n = 11, 13−17 were computed from first principles. The chemical shifts of functionalized carbons at a bond diagonal to the SWNT axis are strongly dependent upon the C−C distance in the C−NR−C moiety. This distance, in turn, is sensitive to the SWNT radius. Monitoring these shifts could therefore help to determine the diameter distribution within a sample. Proton shifts are also reported

Density Functional Study of the ¹³C NMR Chemical Shifts in Single-Walled Carbon Nanotubes with Stone−Wales Defects

The 13C NMR chemical shifts of (7,0), (8,0), (9,0), and (10,0) single-walled carbon nanotubes (SWNTs) with Stone−Wales (SW) defects have been studied computationally using a gauge-including projector-augmented plane-wave (GIPAW) density functional theory (DFT) method. A SW-defect substantially broadens the NMR signal of a particular tube, however, in general the average shift of the non-defect carbons does not differ greatly from that of the pristine species. “Parallel” orientations of the defect site yields shifts at around 150−160 ppm from atoms in the defect site which are separated from the rest of the NMR signal. Therefore, the results indicate that 13C NMR might be able to detect the presence of, and perhaps even quantify the concentration of SW defects found in SWNTs. Differences in the NMR obtained for two defect orientations are analyzed by comparing the shifts of the defect atoms with those of planar and bent structures of the azupyrene molecule. Representative visualizations for the shielding tensors of the (8,0) SWNT with and without defects are also reported

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 Å 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 λ = mod(n, 3) = 0 has much smaller chemical shifts compared to the other two families with λ = 1 and λ = 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 13C NMR has the potential for becoming a useful tool in characterizing SWNT samples

<i>Ab Initio</i> Quality NMR Parameters in Solid-State Materials Using a High-Dimensional Neural-Network Representation

Nuclear magnetic resonance (NMR) spectroscopy is one of the most powerful experimental tools to probe the local atomic order of a wide range of solid-state compounds. However, due to the complexity of the related spectra, in particular for amorphous materials, their interpretation in terms of structural information is often challenging. These difficulties can be overcome by combining molecular dynamics simulations to generate realistic structural models with an <i>ab initio</i> evaluation of the corresponding chemical shift and quadrupolar coupling tensors. However, due to computational constraints, this approach is limited to relatively small system sizes which, for amorphous materials, prevents an adequate statistical sampling of the distribution of the local environments that is required to quantitatively describe the system. In this work, we present an approach to efficiently and accurately predict the NMR parameters of very large systems. This is achieved by using a high-dimensional neural-network representation of NMR parameters that are calculated using an <i>ab initio</i> formalism. To illustrate the potential of this approach, we applied this neural-network NMR (NN-NMR) method on the ¹⁷O and ²⁹Si quadrupolar coupling and chemical shift parameters of various crystalline silica polymorphs and silica glasses. This approach is, in principal, general and has the potential to be applied to predict the NMR properties of various materials

Density Functional Theory Calculations of Hydrogen-Bond-Mediated NMR <i>J</i> Coupling in the Solid State

A recently developed method for calculating NMR J coupling in solid-state systems is applied to calculate hydrogen-bond-mediated 2hJNN couplings across intra- or intermolecular N−H···N hydrogen bonds in two 6-aminofulvene-1-aldimine derivatives and the ribbon structure formed by a deoxyguanosine derivative. Excellent quantitative agreement is observed between the calculated solid-state J couplings and those previously determined experimentally in two recent spin-echo magic-angle-spinning NMR studies (Brown, S. P.; et al. Chem. Commun.2002, 1852−1853 and Pham, T. N.; et al. Phys. Chem. Chem. Phys. 2007, 9, 3416−3423). For the 6-aminofulvene-1-aldimines, the differences in 2hJNN couplings in pyrrole and triazole derivatives are reproduced, while for the guanosine ribbons, an increase in 2hJNN is correlated with a decrease in the N−H···N hydrogen-bond distance. J couplings are additionally calculated for isolated molecules of the 6-aminofulevene-1-aldimines extracted from the crystal with and without further geometry optimization. Importantly, it is shown that experimentally observed differences between J couplings determined by solution- and solid-state NMR are not solely due to differences in geometry; long-range electrostatic effects of the crystal lattice are shown to be significant also. J couplings that are yet to be experimentally measured are calculated. Notably, 2hJNO couplings across N−H···O hydrogen bonds are found to be of a similar magnitude to 2hJNN couplings, suggesting that their utilization and quantitative determination should be experimentally feasible

Density Functional Theory Calculations of Hydrogen-Bond-Mediated NMR <i>J</i> Coupling in the Solid State

A recently developed method for calculating NMR J coupling in solid-state systems is applied to calculate hydrogen-bond-mediated 2hJNN couplings across intra- or intermolecular N−H···N hydrogen bonds in two 6-aminofulvene-1-aldimine derivatives and the ribbon structure formed by a deoxyguanosine derivative. Excellent quantitative agreement is observed between the calculated solid-state J couplings and those previously determined experimentally in two recent spin-echo magic-angle-spinning NMR studies (Brown, S. P.; et al. Chem. Commun.2002, 1852−1853 and Pham, T. N.; et al. Phys. Chem. Chem. Phys. 2007, 9, 3416−3423). For the 6-aminofulvene-1-aldimines, the differences in 2hJNN couplings in pyrrole and triazole derivatives are reproduced, while for the guanosine ribbons, an increase in 2hJNN is correlated with a decrease in the N−H···N hydrogen-bond distance. J couplings are additionally calculated for isolated molecules of the 6-aminofulevene-1-aldimines extracted from the crystal with and without further geometry optimization. Importantly, it is shown that experimentally observed differences between J couplings determined by solution- and solid-state NMR are not solely due to differences in geometry; long-range electrostatic effects of the crystal lattice are shown to be significant also. J couplings that are yet to be experimentally measured are calculated. Notably, 2hJNO couplings across N−H···O hydrogen bonds are found to be of a similar magnitude to 2hJNN couplings, suggesting that their utilization and quantitative determination should be experimentally feasible

Density Functional Theory Calculations of Hydrogen-Bond-Mediated NMR <i>J</i> Coupling in the Solid State

A recently developed method for calculating NMR J coupling in solid-state systems is applied to calculate hydrogen-bond-mediated 2hJNN couplings across intra- or intermolecular N−H···N hydrogen bonds in two 6-aminofulvene-1-aldimine derivatives and the ribbon structure formed by a deoxyguanosine derivative. Excellent quantitative agreement is observed between the calculated solid-state J couplings and those previously determined experimentally in two recent spin-echo magic-angle-spinning NMR studies (Brown, S. P.; et al. Chem. Commun.2002, 1852−1853 and Pham, T. N.; et al. Phys. Chem. Chem. Phys. 2007, 9, 3416−3423). For the 6-aminofulvene-1-aldimines, the differences in 2hJNN couplings in pyrrole and triazole derivatives are reproduced, while for the guanosine ribbons, an increase in 2hJNN is correlated with a decrease in the N−H···N hydrogen-bond distance. J couplings are additionally calculated for isolated molecules of the 6-aminofulevene-1-aldimines extracted from the crystal with and without further geometry optimization. Importantly, it is shown that experimentally observed differences between J couplings determined by solution- and solid-state NMR are not solely due to differences in geometry; long-range electrostatic effects of the crystal lattice are shown to be significant also. J couplings that are yet to be experimentally measured are calculated. Notably, 2hJNO couplings across N−H···O hydrogen bonds are found to be of a similar magnitude to 2hJNN couplings, suggesting that their utilization and quantitative determination should be experimentally feasible