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.     

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.     

Unraveling the 13C NMR chemical shifts in single-walled carbon nanotubes: dependence on diameter and electronic structure

The atomic specificity afforded by nuclear magnetic resonance (NMR) spectroscopy could enable detailed mechanistic information about single-walled carbon nanotube (SWCNT) functionalization as well as the noncovalent molecular interactions that dictate ground-state charge transfer and separation by electronic structure and diameter. However, to date, the polydispersity present in as-synthesized SWCNT populations has obscured the dependence of the SWCNT (13)C chemical shift on intrinsic parameters such as diameter and electronic structure, meaning that no information is gleaned for specific SWCNTs with unique chiral indices. In this article, we utilize a combination of (13)C labeling and density gradient ultracentrifugation (DGU) to produce an array of (13)C-labeled SWCNT populations with varying diameter, electronic structure, and chiral angle. We find that the SWCNT isotropic (13)C chemical shift decreases systematically with increasing diameter for semiconducting SWCNTs, in agreement with recent theoretical predictions that have heretofore gone unaddressed. Furthermore, we find that the (13)C chemical shifts for small diameter metallic and semiconducting SWCNTs differ significantly, and that the full-width of the isotropic peak for metallic SWCNTs is much larger than that of semiconducting nanotubes, irrespective of diameter.     

Density functional calculations of NMR chemical shifts and ESR g-tensors

An overview is given on recent advances of density functional theory (DFT) as applied to the calculation of nuclear magnetic resonance (NMR) chemical shifts and electron spin resonance (ESR) g-tensors. This is a new research area that has seen tremendous progress and success recently; we try to present some of these developments. DFT accounts for correlation effects efficiently. Therefore, it is the only first-principle method that can handle NMR calculations on large systems like transition-metal complexes. Relativistic effects become important for heavier element compounds; here we show how they can be accounted for. The ESR g-tensor is related conceptually to the NMR shielding, and results of g-tensor calculations are presented. DFT has been very successful in its application to magnetic properties, for metal complexes in particular. However, there are still certain shortcomings and limitations, e.g., in the exchange-correlation functional, that are discussed as well. Received: 24 October 1997 / Accepted: 19 December 1997     

Theoretical study of the 13C NMR spectroscopy of single-walled carbon nanotubes

The 13C NMR spectroscopy of armchair and zigzag single-walled carbon nanotubes has been investigated theoretically. Spectra for (4,4), (5,5), (6,6), (6,0), (9,0), and (10,0) nanotubes have been simulated based on ab initio calculations of model systems. The calculations predict a dominant band arising from the carbon atoms in the "tube" with smaller peaks at higher chemical shifts arising from the carbon atoms of the caps. The dominant band lies in the range of 128 and 138 ppm. Its position depends weakly on the length, width, and chirality of the tubes. The calculations demonstrate how structural information may be gleaned from relatively low-resolution nanotube 13C NMR spectra.     

Quantum-chemical calculations of NMR chemical shifts of organic molecules: XIV. Solvation effects in calculations of chemical shifts in 13C NMR spectra of chlorine-containing compounds

Analysis of precision factors in calculations of ¹³C NMR chemical shifts in the series of saturated and unsaturated organochlorine compounds was performed in the framework of the method of electron density functional theory GIAO-DFT-KT3/pcS-2 in the gas phase and with accounting for solvent effect by the polarized continuum model IEF-PCM. The accounting for solvation effects in calculations of ¹³C NMR chemical shifts within the framework of the IEF-PCM model is not fundamental for organochlorine compounds, yet it considerably improves the precision of calculations up to 2.5 ppm.     

Density functional computation of 49Ti NMR chemical shifts

49Ti chemical shifts of TiX4 (X = Cl, Br, F), TiClnMe(4-n) (n = 0-3), Ti(C5H5)2X2 (X = F, Cl, Br) and Ti(CO)6(2-) were computed, using geometries optimized with the gradient-corrected BP86 density functional, at the GIAO (gauge-including atomic orbitals)-Hartree-Fock, BPW91, and B3LYP levels. For this set of compounds, substituent effects on delta(49Ti) are reasonably well described with all methods considered; judged from mean absolute deviations from experiment, B3LYP performs best. Zero-point corrections to the delta(49Ti) values, evaluated from a perturbational approach based on vibrationally averaged effective geometries, turn out to be fairly small. Electric field gradients computed with the B3LYP functional do not correlate with trends in 49Ti NMR linewidths. Attempts are reported to correlate the delta(49Ti) values of Ti[YC(O)CHC(O)Y]2Cl2 (Y = H, Me, CF3, CN, F, Cl and Br) with the rate-limiting propagation barrier for ethylene polymerization using catalysts derived from these precursors.     

Density functional theory calculation of (29)Si NMR chemical shifts of organosiloxanes

Density functional theory at the B3LYP/6-311++G(d,p) level is applied to calculate the (29)Si NMR chemical shifts of a variety of organosiloxane moieties including monomers or precursors for polymerization and representative segments of organosiloxane polymers or thin films. The calculated shifts of two linear dimethylsiloxane compounds, hexamethylcyclotrisiloxane (D3) and octamethylcyclotetrasiloxane (D4), compare well with their known values, having an average error of 3.4 ppm. The same method is applied to structures believed to occur in organosilicate glass thin films deposited using hot-filament chemical vapor deposition (HFCVD) from D3 and D4. The chemical shift at -15 ppm is identified as a cross-linking Si-Si bond between two strained D groups and has not previously been reported. Retention of the strained ringed structure in HFCVD films deposited from D3 is confirmed. The rings are bonded to the matrix through either Si-O or Si-Si bonds, with the latter only becoming prevalent when higher filament temperatures are employed. The strained ring structure is also observed in films deposited from a precursor with a larger unstrained ring structure, D4. These observations suggest that the known gas-phase conversion pathways of D4 to D3 and dimethylsilanone as well as the methyl abstraction reaction from D3 operate in the HFCVD reaction chemistry.     

DFT calculations of 1H and 13C NMR chemical shifts in transition metal hydrides

Transition metal hydrides are of great interest in chemistry because of their reactivity and their potential use as catalysts for hydrogenation. Among other available techniques, structural properties in transition metal (TM) complexes are often probed by NMR spectroscopy. In this paper we will show that it is possible to establish a viable methodological strategy in the context of density functional theory, that allows the determination of 1H NMR chemical shifts of hydride ligands attached to transition metal atoms in mononuclear systems and clusters with good accuracy with respect to experiment. 13C chemical shifts have also been considered in some cases. We have studied mononuclear ruthenium complexes such as Ru(L)(H)(dppm)2 with L = H or Cl, cationic complex [Ru(H)(H2O)(dppm)2]+ and Ru(H)2(dppm)(PPh3)2, in which hydride ligands are characterized by a negative 1H NMR chemical shift. For these complexes all calculations are in relatively good agreement compared to experimental data with errors not exceeding 20% except for the hydrogen atom in Ru(H)2(dppm)(PPh3)2. For this last complex, the relative error increases to 30%, probably owing to the necessity to take into account dynamical effects of phenyl groups. Carbonyl ligands are often encountered in coordination chemistry. Specific issues arise when calculating 1H or 13C NMR chemical shifts in TM carbonyl complexes. Indeed, while errors of 10 to 20% with respect to experiment are often considered good in the framework of density functional theory, this difference in the case of mononuclear carbonyl complexes culminates to 80%: results obtained with all-electron calculations are overall in very satisfactory agreement with experiment, the error in this case does not exceed 11% contrary to effective core potentials (ECPs) calculations which yield errors always larger than 20%. We conclude that for carbonyl groups the use of ECPs is not recommended, although their use could save time for very large systems, for instance in cluster chemistry. The reliance of NMR chemical shielding on dynamical effects, such as intramolecular rearrangements or trigonal twists, is also examined for H2Fe(CO)4, K+[HFe(CO)](-), HMn(CO)5 and HRe(CO)5. The accuracy of the theory is also examined for complexes with two dihydrogen ligands (Tp*RuH(H2)2 and [FeH(H2)(DMPE)2]+) and a ruthenium cluster, [H3Ru4(C6H6)4(CO)]+. It is shown that for all complexes studied in this work, the effect of the ligands on the chemical shielding of hydrogen coordinated to metal is suitably calculated, thus yielding a very good correlation between experimental chemical shifts and theoretical chemical shielding.     

NMR chemical shifts of molecules encapsulated in single walled carbon nanotubes

We present density functional theory calculations of the nuclear magnetic resonance spectroscopy of molecules encapsulated within single walled carbon nanotubes. Ring currents in the nanotube induce shifts in the chemical shift of the nuclei comprising the encapsulated molecule. These changes in the chemical shifts are shown to have characteristic dependence on the chirality of the surrounding nanotubes.     

Structure validation of natural products by quantum-mechanical GIAO calculations of 13C NMR chemical shifts

Geometry optimization and GIAO (gauge including atomic orbitals) (13)C NMR chemical shift calculations at Hartree-Fock level, using the 6-31G(d) basis set, are proposed as a tool to be applied in the structural characterization of new organic compounds, thus providing useful support in the interpretation of experimental NMR data. Parameters related to linear correlation plots of computed versus experimental (13)C NMR chemical shifts for fourteen low-polar natural products, containing 10-20 carbon atoms, were employed to assess the reliability of the proposed structures. A comparison with the hybrid B3LYP method was carried out to evaluate electron correlation contributions to the calculation of (13)C NMR chemical shifts and, eventually, to extend the applicability of such computational methods to the interpretation of NMR spectra in apolar solutions. The method was tested by studying three examples of revised structure assignments, analyzing how the theoretical (13)C chemical shifts of both correct and incorrect structures matched the experimental data.     

Quantum-chemical calculations of NMR chemical shifts of organic molecules: XII. Calculation of the 13C NMR chemical shifts of fluoromethanes at the DFT level

Calculation was carried out of chemical shifts in ¹³C NMR spectra for a series of fluoromethanes CH _n F_4?n (n = 0–4) by the methods of the electron density functional theory GIAO-DFT taking in consideration the solvent effect in the framework of the polarizable continuum model Tomasi IEF-PCM. The best results were obtained at the use of Keal-Tozer KT3 functional combined with Pople standard basis sets 6-311G(d,p) and 6-311++G(d,p), and also with Jensen special set pcS-2 containing tight p-functions. The optimum reference in the calculation of chemical shifts in ¹³C NMR spectra for the fluoromethanes series is TMS.     

13C NMR study on the methoxy carbon chemical shifts in chloro-substituted anisoles and guaiacols

The ¹³C NMR chemical shifts of methoxy carbons in chlorinated anisoles and guaiacols have been measured for acetone-d₆ solutions. Multiple linear regression analysis, and also ‘simple sum rule’ calculations, have been used to estimate the effects of the chlorine atoms (the position and degree of substitution) on the chemical shifts. The most important effects have shown to be due to the chlorine atoms adjacent to the methoxy and hydroxy substituents. For chlorinated guaiacols, the greatest effect is due to the chlorine atom adjacent to the methoxy group. For chlorinated anisoles, the substituents adjacent to the methoxy group (2,6-disubstitution) cause large effects. For both groups of compounds, the chemical shifts are also greatly influenced by the number of chlorine substituents. Using the three most important independent variables, the average differences between the observed and calculated chemical shifts are ca 0.2 ppm for anisoles and 0.1 ppm for guaiacols. For chloroguaiacols, the corresponding difference was only 0.1 ppm when calculations were performed using single substituent effects.     

Prediction of 13C NMR chemical shifts in substituted naphthalenes

The prediction of the ¹³C NMR signals for derivatives of naphthalene has been investigated using mathematical modeling techniques. Two empirical multiple regression models which utilize the field, resonance, and Charton's steric parameters together with molar refractivity were developed, one for α- and the other for β-substituted naphthalene derivatives. In the α case the model had a correlation coefficient of observed versus predicted line positions of r = 0.973 with a standard deviation of 2.2 ppm while in the β case r = 0.979 with the standard deviation being 2.3 ppm. The database consisted of 3152 signals from 394 naphthalene derivatives. We also report the use of the Taft steric parameter in place of the Charton steric parameter in the above- mentioned prediction equations. Received: 19 June 1998 / Accepted: 20 October 1998 / Published online: 16 March 1999     

A predictive tool for assessing (13)C NMR chemical shifts of flavonoids

Herein are presented the (1)H and (13)C NMR data for seven monohydroxyflavones (3-, 5-, 6-, 7-, 2'-, 3'-, and 4'-hydroxyflavone), five dihydroxyflavones (3,2'-, 3,3'-, 3,4'-, 3,6-, 2',3'-dihydroxyflavone), a trihydroxyflavone (apigenin; 5,7,4'-trihydroxyflavone), a tetrahydroxyflavone (luteolin; 5,7,3',4'-tetrahydroxyflavone), and three glycosylated hydroxyflavones (orientin; luteolin-6C-beta-D-glucoside, homoorientin; luteolin-8C-beta-D-glucoside, vitexin; apigenin-8C-beta-D-glucoside). When these NMR spectra are compared, it is possible to assess the impact of flavone modification and to elucidate detailed structural and electronic information for these flavonoids. A simple predictive tool for assigning flavonoid (13)C chemical shifts, which is based on the cumulative differences between the monohydroxyflavones and flavone (13)C chemical shifts, is demonstrated. The tool can be used to accurately predict (13)C flavonoid chemical shifts and it is expected to be useful for rapid assessment of flavonoid (13)C NMR spectra and for assigning substitution patterns in newly isolated flavonoids.     

Density functional theory study of 13C NMR chemical shift of chlorinated compounds

The use of the standard density functional theory (DFT) leads to an overestimation of the paramagnetic contribution and underestimation of the shielding constants, especially for chlorinated carbon nuclei. For that reason, the predictions of chlorinated compounds often yield too high chemical shift values. In this study, the WC04 functional is shown to be capable of reducing the overestimation of the chemical shift of Cl‐bonded carbons in standard DFT functionals and to show a good performance in the prediction of ¹³C NMR chemical shifts of chlorinated organic compounds. The capability is attributed to the minimization of the contributions that intensively increase the chemical shift in the WC04. Extensive computations and analyses were performed to search for the optimal procedure for WC04. The B3LYP and mPW1PW91 standard functionals were also used to evaluate the performance. Through detailed comparisons between the basis set effects and the solvent effects on the results, the gas‐phase GIAO/WC04/6‐311+G(2d,p)//B3LYP/6‐31+G(d,p) was found to be specifically suitable for the prediction of ¹³C NMR chemical shifts of chlorides in both chlorinated and non‐chlorinated carbons. Further tests with eight molecules in the probe set sufficiently confirmed that WC04 was undoubtedly effective for accurately predicting ¹³C NMR chemical shifts of chlorinated organic compounds. Copyright © 2012 John Wiley & Sons, Ltd.     

Density functional study of super cell N-doped (10,0) zigzag single-walled carbon nanotubes as CO sensor

N-doped SWCNT with different concentration of doped nitrogen atoms were investigated through density functional theory (DFT) calculations for detecting CO molecule. The CO molecule was adsorbed to different sites of the modified nanotubes and their geometric structures and electronic properties were investigated after full optimization. A significant change can be observed in adsorption energies and electronic properties of N-doped SWCNT after CO adsorption. By increasing the number of nitrogen atoms in each unit cell, these properties change more obviously. So these modified nanotubes can be used as CO sensors.     

NMR detection of single-walled carbon nanotubes in solution

The detection of nanotube carbons in solution by (13)C NMR is reported. The highly soluble sample was from the functionalization of (13)C-enriched single-walled carbon nanotubes (SWNTs) with diamine-terminated oligomeric poly(ethylene glycol) (PEG(1500N)). The ferromagnetic impurities due to the residual metal catalysts were removed from the sample via repeated magnetic separation. The nanotube carbon signals are broad but partially resolved into two overlapping peaks, which are tentatively assigned to nanotube carbons on semiconducting (upfield) and metallic (downfield) SWNTs. The solid-state NMR signals of the same sample are similarly resolved. Mechanistic and practical implications of the results are discussed.     

Computational studies of 13C NMR chemical shifts of saccharides

The (13)C NMR chemical shifts for alpha-D-lyxofuranose, alpha-D-lyxopyranose (1)C(4), alpha-D-lyxopyranose (4)C(1), alpha-D-glucopyranose (4)C(1), and alpha-D-glucofuranose have been studied at ab initio and density-functional theory levels using TZVP quality basis set. The methods were tested by calculating the nuclear magnetic shieldings for tetramethylsilane (TMS) at different levels of theory using large basis sets. Test calculations on the monosaccharides showed B3LYP(TZVP) and BP86(TZVP) to be cost-efficient levels of theory for calculation of NMR chemical shifts of carbohydrates. The accuracy of the molecular structures and chemical shifts calculated at the B3LYP(TZVP) level is comparable to those obtained at the MP2(TZVP) level. Solvent effects were considered by surrounding the saccharides by water molecules and also by employing a continuum solvent model. None of the applied methods to consider solvent effects was successful. The B3LYP(TZVP) and MP2(TZVP)(13)C NMR chemical shift calculations yielded without solvent and rovibrational corrections an average deviation of 5.4 ppm and 5.0 ppm between calculated and measured shifts. A closer agreement between calculated and measured chemical shifts can be obtained by using a reference compound that is structurally reminiscent of saccharides such as neat methanol. An accurate shielding reference for carbohydrates can be constructed by adding an empirical constant shift to the calculated chemical shifts, deduced from comparisons of B3LYP(TZVP) or BP86(TZVP) and measured chemical shifts of monosaccharides. The systematic deviation of about 3 ppm for O(1)H chemical shifts can be designed to hydrogen bonding, whereas solvent effects on the (1)H NMR chemical shifts of C(1)H were found to be small. At the B3LYP(TZVP) level, the barrier for the torsional motion of the hydroxyl group at C(6) in alpha-D-glucofuranose was calculated to 7.5 kcal mol(-1). The torsional displacement was found to introduce large changes of up to 10 ppm to the (13)C NMR chemical shifts yielding uncertainties of about +/-2 ppm in the chemical shifts.