- Email: [email protected]
DFT study of zigzag (n, 0) single-walled carbon nanotubes: 13C NMR chemical shifts
Journal of Molecular Graphics and Modelling 67 (2016) 14–19
Contents lists available at ScienceDirect
Journal of Molecular Graphics and Modelling journal homepage: www.elsevier.com/locate/JMGM
DFT study of zigzag (n, 0) single-walled carbon nanotubes: 13 C NMR chemical shifts b ´ Teobald Kupka a,∗ , Michal Stachów a , Leszek Stobinski , Jakub Kaminsky´ c,∗ a b c
University of Opole, Faculty of Chemistry, 48, Oleska Street, 45-052 Opole, Poland Faculty of Chemical and Process Engineering, Warsaw University of Technology, Wary´ nskiego 1, 00-645 Warsaw, Poland Institute of Organic Chemistry and Biochemistry, Academy of Sciences of the Czech Republic, Flemingovo nam. 2, 166 10 Prague, Czech Republic
a r t i c l e
i n f o
Article history: Received 4 February 2016 Received in revised form 14 April 2016 Accepted 19 April 2016 Available online 3 May 2016 Keywords: Zigzag SWCNT Cyclacenes Theoretical modeling DFT NMR
a b s t r a c t 13 C NMR chemical shifts of selected finite-size models of pristine zigzag single walled carbon nanotubes (SWCNTs) with a diameter of ∼0.4–0.8 nm and length up to 2.2 nm were studied theoretically. Results for finite SWCNTs models containing 1, 4 and 10 adjacent bamboo-type units were compared with data obtained for infinite tubes in order to estimate the reliability of small finite models in predicting magnetic properties of real-size nanotubes and to assess their tube-length dependence. SWCNTs were fully optimized using unrestricted density functional theory (DFT-UB3LYP/6-31G*). Cyclacenes, as the shortest models of open-ended zigzag SWCNTs, with systematically varying diameter were calculated as well. GIAO NMR calculations on the SWCNT and cyclacene models were performed using the BHandH density ´ functional combined with relatively small STO-3Gmag basis set, developed by Leszczynski and coworkers for accurate description of magnetic properties. Regular changes of carbon 13 C chemical shifts along the tube axis of real size (6, 0) and (9, 0) zigzag carbon nanotubes were shown. The 13 C NMR shifts according to increasing diameter calculated for zigzag (n, 0, n = 5–10) cyclacenes followed the trends observed for zigzag (n, 0) SWCNTs. The results for 4-units long SWCNTs match reasonably well with the data obtained for infinite zigzag (n, 0) SWCNTs, especially to those with bigger diameter (n = 8-15). The presence of rim hydrogens obviously affects theoretical 13 C chemical shieldings and shifts in cyclacenes and thus cyclacenes can provide only approximate estimation of 13 C NMR parameters of real-size SWCNTs. The NMR properties predicted for the longest 10-units long models of SWCNTs reliably correspond to results obtained for infinite nanotubes. They were thus able to accurately predict also recently reported experimental chemical shift of chiral (6, 5) SWCNT. © 2016 Elsevier Inc. All rights reserved.
1. Introduction Fullerenes [1], carbon nanotubes (CNTs [2–4]) and recently graphenes [5] have paved their way to basic and applied science in recent twenty five years of nanoscience development. These ordered carbon allotropes are considered promising materials for many applications ranging from hybrid or future quantum electronics to a rational development of intelligent composites [4]. Thus, pristine CNTs, as well as functionalized tubes, are used in several fields of research and industry [4,6,7]. For example, the CNTs can serve as reactors for nanoscale chemical reactions due to their favorable tubular morphology [8]. Open-ended SWCNTs have been a subject of many model studies in nanocarbon
∗ Corresponding authors. E-mail addresses: [email protected], [email protected] (T. Kupka), ´ [email protected] (J. Kaminsky). http://dx.doi.org/10.1016/j.jmgm.2016.04.008 1093-3263/© 2016 Elsevier Inc. All rights reserved.
chemistry. For example, encapsulation of simple molecules inside the carbon nanotube has attracted the attention of scientists resulting to numerous studies on interaction of small molecules or atoms with interior, as well as exterior of the tube or proton transfer studies [9–13]. Carbon nanotubes could be viewed as a graphene sheet (or a flat set of conjugated benzene rings forming a honey comb pattern) rolled along a chiral vector Ch into a tube [4]. The chiral vector Ch = na1 + ma2 depends on the lattice vectors a1 , a2 . Typically, a short notation (n, m) is used to describe zigzag (n, 0), armchair (n, n) and chiral (n, m) types of single wall carbon nanotubes. Originally, the (n, m) tubes with newly defined parameter = mod(n − m, 3) = 0 were considered as metallic [14], however, due to the curvature effects and s-p hybridization in SWCNTs with extremely small diameters, the rule is broken and e.g. (5, 0) SWCNT is considered metallic according to theoretical predictions [15].
T. Kupka et al. / Journal of Molecular Graphics and Modelling 67 (2016) 14–19
15
Scheme 1. Schematic structures of selected zigzag (n, 0) cyclacenes (n = 4–16) and (n, 0) zigzag SWCNTs used in calculations (n = 5– 9, with diameter in nm).
Nevertheless, dividing SWCNTs to families according to their value is still reasonable and will be used in this work. Unfortunately, SWCNTs are produced as mixtures of tubes, difficult to separate and characterize [4]. Commercial SWCNTs are produced in diameters ranging from a fraction of nanometer (∼0.3 nm) to tens of nanometers. In addition, the ultra-thin SWCNTs [16] were reported inside the zeolite structural channels [17], aluminum oxide [18] and inside larger multi-walled carbon nanotubes [19]. Although experimental characterization of commercial samples is essential in nanotechnology, no simple method is available so far. Instead, a combination of several spectroscopic and microscopic techniques is used in characterization of technical SWCNTs. Therefore, a highly challenging structural and spectroscopic characterization of SWCNTs is usually performed employing several techniques. Raman spectroscopy is widely used to support X-ray and microscopic determination of SWCNTs diameter since the Raman active radial breathing mode vibration (RBM) frequency is inversely proportional to the tube diameter [19–21]. Also a number of experimental and theoretical NMR works on SWCNTs and closely related fullerenes has been published [22–24] [25–31]. Recently, we reported on the impact of –OH and –COOH end substituents on structural changes, RBM, 13 C NMR chemical shifts (␦) and HOMO-LUMO gaps of ultra-thin (4, 0) zigzag, (5, 5) armchair and (8, 2) chiral SWCNTs [32–36]. Due to growing demand for well-characterized nanomaterials and insufficient use of spectroscopic techniques for their characterization (e.g. NMR) we propose in this study theoretical modeling of NMR parameters for finite SWCNT models of a size near to real SWCNTs to support their experimental analysis [22–24,26,28–30]. The main goal of the present study is an accurate theoretical modeling of 13 C NMR chemical shifts of selected finite models of zigzag SWCNTs of diameters common in commercial samples using density functional theory (DFT). Obtained results will be critically compared with available experimental data or with previously reported calculations on infinite SWCNTs. The idea of using finite models is also driven by future aims at NMR studies on one-end functionalized SWCNTs, where the use of periodic calculations on infinite SWCNTs is limited. The finite models could also be utilized for modeling of properties of chiral SWCNTs that is still often computationally expensive procedure if the periodic calculations on infinite models are employed. Enormous computational demands of calculations on infinite chiral tubes are caused due to large unit crystal cells containing often several hundreds of heavy atoms. Standard calculations with the usual periodic boundary conditions (PBC) are not easily compatible with helical symmetry so far. An algorithm comprising infinitely propagated helicity compatible with commonly used Molecular Dynamic software was developed in our group [37]. Nevertheless, we are
not aware of any helical symmetry propagating PBC code working at QM level and plane waves. Thus, suitable finite models can be a relatively cheap alternative providing results with a precision described in this work. Note, that the size of our finite models is considerably wider than reported before [26–30,36,38] (up to n = 15) and this should also enable better observations of convergence patterns of SWCNTs’ parameters in accordance with their diameter. The current study should also make possible a better interpretation of observed experimental 13 C NMR chemical shifts of SWCNTs.
2. Computational methodology Three distinct model systems were chosen—zigzag type cyclacenes and open-end finite zigzag SWCNTs consisting of 4 or 10 “bamboo” units [36,39–42] (Scheme 1). These models were constructed by increasing their diameter from 0.4 to 0.8 nm (10units SWCNTs), and even up to 1.3 nm for 4-units SWCNTs and cyclacenes. The length of models range from 0.3 nm for cyclacenes to 0.9 nm for 4-units SWCNTs or even 2.2 nm for 10-units SWCNTs. All structural calculations were performed using Gaussian 09 program [43] and the unrestricted wavefunction approximation of the Becke three-parameter Lee-Yang-Parr exchange-correlation functional (UB3LYP [44–46]) combined with the 6-31G* basis set. The method together with unrestricted approach was suggested earlier for better description of open-shell singlet states in polyaromatic systems [47–49]. This approach was successfully applied in our previous studies on polyaromatic molecules [15,50]. Besides, we applied loose symmetry and tight SCF and optimization thresholds with a very fine computational grid (GRID = 150,590) during the optimization [43]. The calculations of vibrational frequencies were performed for optimized geometries to ensure the minimum on the potential energy surface for the studied systems [40]. The gauge including atomic orbital [51,52] (GIAO) calculations of nuclear isotropic shieldings for optimized UB3LYP/6-31G* geometries were performed using the BHandH [43,44] functional and the STO-3Gmag basis set [53]. The BHandH [44] density functional and a modified basis set were successful in calculating carbon nuclear shieldings (and chemical shifts) in earlier studies on hydrocarbons, small molecules or nanocarbons [15,36,50,54–57]. The STO-3Gmag basis set was developed for accurate description ´ of magnetic properties with a reasonable effort. Leszczynski and coworkers’ idea of STO-3Gmag basis set arises from an extension of standard STO-3G basis set by functions obtained from analytical first-order corrections using the Green’s function [53]. This modified STO-3G basis set shows a very good accuracy, comparable to Jensen’s pcS-2 basis set [58], dedicated to accurate prediction of nuclear shieldings, while being half the size of the latter [50]. Benzene nuclear isotropic shielding (o ), calculated at the same level
16
T. Kupka et al. / Journal of Molecular Graphics and Modelling 67 (2016) 14–19
Fig. 1. 13 C NMR chemical shifts (ppm) along the tube axis calculated at the BHandH/STO-3Gmag level for (6, 0) and (9, 0) zigzag SWCNTs (10 bamboo units). Lines connecting the points are provided to show trends.
of theory, was used as secondary reference for chemical shift (␦i ) calculation of i-th carbon atom according to the formula [36]: ıi = o − i + 128.5
(1)
Additionally, for comparison of our NMR data for finite models results with periodic calculations on infinite length (n, 0) SWCNTs, with n = 7–15, using the Gauge Including Projector Augmented Waves [59] (GIPAW) approach based on CASTEP code [60] were taken from the literature. 3. Results and discussion We have recently reported on 13 C NMR chemical shifts for individual atoms in ultra-thin (4, 0) SWCNT calculated at the B3LYP/pcS-2 level of theory [36,42,50]. In case of such ultra-thin open-ended zigzag SWCNTs the carbon chemical shifts converged toward 175 ± 5 ppm for interior carbon atoms of the nanotube consisting of 10 “bamboo” units. A very high value (deshielding) of carbon chemical shift in this model was most likely caused by extreme structural strain and deformation of sp2 hybridized carbon atoms due to a high curvature. This also explains the fact that the experimentally observed ultra-thin carbon nanotubes exist only in confined spaces [19]. In the current study of 13 C chemical shift change along the tube axis we first selected two zigzag SWCNTs, (6, 0) and (9, 0) tubes, with the length of 10 “bamboo” units (see Scheme 1) corresponding to 2.15 nm. Thus, a realistic diameter described in experimental works [25–29,31] was chosen. The 13 C chemical shift changes for two types of carbon atoms, Ai and Bi , along the tube axis in (6, 0) and (9, 0) SWCNTs are compared in Fig. 1. It is important to note that
chemical shifts along the tube length are not the same for carbon atoms at both ends. Thus, the carbon atoms labeled A1 and A11 are C H and C types, respectively. On the contrary, atoms B1 and B11 are C and C H types. For both models significant differences of carbon chemical shifts at the rim (A1 atom) and the interior (C6 atom) of the tube are observed (about 20 and 15 ppm for Ai , and 25 and 15 ppm for Bi carbons respectively). Besides, significantly larger oscillations of carbon chemical shifts along the tube axis are observed for more strained structure (the smaller diameter one, compare results in ref [42]). In fact, the convergence of carbon chemical shifts start from the two rims (ends) of the tube and decays in an exponential-like way toward the middle of the tube. However, for these CNTs of different diameter, the convergence of carbon chemical shifts at about 125 and 130 ppm for atoms near the middle of the tube length is observed for the (6, 0) and (9, 0) zigzag SWCNTs (Fig. 1). Interestingly, for smaller diameter (6, 0) tube the presence of tube end (rim effect) is reflected farther from the end − at the fifth carbon layer (see an about 3 ppm difference of chemical shift between full and empty circle) and is significantly smaller for larger (9, 0) SWCNT (only about 1 ppm at the four carbon layer). A model of SWCNT consisting of 10 “bamboo units” with three “ribbons” (labeled 5, 6 and 7) of carbon atoms in the middle of its length and perpendicular to tube axis, is shown schematically in Fig. 2. The 6th ribbon is located in the middle of tube length and is the least affected by rims. Thus, chemical shifts of the 6th ribbon (after averaging) will be used to study the impact of tube diameter on chemical shift of tube interior. This chemical shift can be considered as an approximation of predicted NMR signal for very long tubes. If one closely looks at earlier studies on theoretical NMR descriptions of infinitely long (n, 0) SWCNTs [22–27] (some presented in Table 1), it can be seen a decreasing trend of chemical shifts upon enlarging CNTs diameter. Data published for different DFT functionals match each other; they are only vertically shifted. Several irregularities can be found on that trend addressed to metallic SWCNTs. Thus, it is more convenient to compare metallic and semiconducting SWCNTs separately. Published data also reveal that 13 C NMR shifts for metallic SWCNTs of certain diameter are substantially lower than those of comparably wide semiconducting SWCNTs. Nevertheless, the trend of changes of ␦ with increasing tube diameter is similar (smooth decreasing) for both metallic and semiconducting zigzag (n, 0) SWCNTs. Table 1 compares averaged carbon chemical shifts for studied zigzag (n, 0) 4-units and 10-units long SWCNT models (for the 10units model 13 C signals of atoms of the 6th “ribbon” – see Fig. 2 – were averaged), as well as zigzag (n, 0) cyclacenes. The latter models can be considered as the shortest SWCNT tubes formed by rim atoms only, e.g. by C1- and C2-type atoms (according to Scheme 1). The zigzag patterns of changes of C1 and C2 ␦ upon increasing the
Fig. 2. Model of SWCNT formed by ten “bamboo units” with three selected “ribbons” of carbon atoms in the middle of length. ribbon are considered the least affected by the tube end effects.
13
C NMR chemical shift values for the 6th
T. Kupka et al. / Journal of Molecular Graphics and Modelling 67 (2016) 14–19
17
Table 1 The BHandH/STO-3Gmag predicted 13 C NMR chemical shifts (␦ in ppm) for model zigzag (n, 0) SWCNTs, cyclacenes and for a chiral (6, 5) SWCNT. Results of periodic calculations for infinite length SWCNTs are also included. Zigzag (n, 0)
Diameter (nm)
␦ (13 C NMR) Cyclacenea
(5, 0) (6, 0) (7, 0) (8, 0) (9, 0) (10, 0) (11, 0) (12, 0) (13,0) (14,0) (15,0) RMSDd
0.39 0.47 0.55 0.63 0.71 0.78 0.86 0.94 1.02 1.10 1.18
e
This work Exp.f
0.77 0.77
4-units SWCNTa
C1
C2
Average
142.9 147.1 132.9 140.8 128.5 137.2 122.5 135.2 120.8 133.8 134.0
162.3 160.8 153.7 149.8 152.6 146.0 154.2 142.8 157.0 140.4 168.7
152.6 154.0 143.3 145.3 140.6 141.6 138.4 139.0 138.9 137.1 151.4 19.6 Chiral (6, 5) SWCNT
144.8 142.5 123.9 136.6 122.0 130.4 127.5 130.4 129.2 133.1 136.7 11.0
10-units SWCNTa
158.2 124.7 139.8 134.1 130.9 129.6
Infinite SWCNT PW91b
PBEc
140.3 134.3 122.7 130.5 126.9 117.7 125.4 123.5 118.5
136.4 130.8 120.9 126.9 124.0 116.8 122.6 120.5 114.7
5.7
130.0 129.0
a
BHandH/STO-3Gmag predicted 13 C chemical shifts of carbon atoms in the middle part of the tube. Chemical shifts of infinite SWCNTs calculated using the gauge-including projector augmented plane-wave (GIPAW) approach and benzene as the secondary reference taken from Ref. [61]. c Chemical shifts of infinite SWCNTs calculated using the GIPAW approach and benzene as the secondary reference taken from ref. [23]. d RMSD calculated from ı of infinite SWCNT taken from Ref. [23]. e The VSXC/STO-3Gmag chemical shift as averaged values of atoms in the middle of the tube length and calculated for the B3LYP/6-31G* optimized short chiral (6, 5) SWCNT formed by 5 units (see Ref. [36]). f Ref. [25]. b
diameter of cyclacene (n = 4–15) are roughly mirror images. Nevertheless a slowly decreasing trend is clear. Obviously, the differences cancel out when the C1 and C2 shifts are averaged. This trend converges as a decreasing exponential to ∼135 ppm (see Fig. S1 in Supplementary data). The predicted chemical shifts for 10-units SWCNT model are rather scattered for tubes with small diameters, but decrease in smooth exponential way for wider models (n ≥ 7, see Fig. S2). Similar limiting value is predicted from CASTEP calculations on infinite SWCNTs (see Fig. S2). It is in general more difficult to model metallic than semiconducting tubes (see results for n = 15 in Fig. S2 in the Supplementary data). Closer inspection of data in Table 1 reveals that while cyclacenes represent rather rough model of real-size SWCNTs providing only general trends with large deviation from the CASTEP values, 4-units long SWCNTs provide already a reasonably precise approximation. The RMSD error drops from ∼20 ppm for cyclacene model (if compared to infinitely long tubes) to ∼11 ppm. The error continuously decreases for 10-units long SWCNTs to ∼6 ppm. Note however, that only values for (n, 0; n = 7–10) SWCNT were achieved here and were compared with available reported data for infinite SWCNTs. More detailed analysis can be made upon comparing data from Fig. 3 presenting calculated 13 C shifts according to SWCNT’s family. We can see, that problematic for models used here are especially metallic SWCNTs ( = 0 family) with larger diameters. Thus, the decreasing trend for metallic SWCNT is broken at (12, 0) value and ␦ values start to increase again (both for cyclacenes and 4-units long SWCNTs). Lai et al. [61] reported similar trends of chemical shifts with increasing diameter for metallic SWCNTs. Within the = 1 family of semiconducting SWCNTs the (13, 0) cyclacene also provides too large value of chemical shift, but the 4-units long model already provides the value much closer to the reference and correctly following the decreasing trend. Such trend for = 2 family is reproduced more or less well by all models, but obviously better by the 4-units long SWCNT models. The theoretical results gathered in Table 1 are compared with recently reported 13 C solid state magic angle spinning experimental results (MAS NMR) for a chiral (6, 5) SWCNT [25]. The observed chemical shift for (6, 5) chiral SWCNT sample (of similar diameter
of 0.77 nm) is very closely reproduced by our calculated values for a model (9, 0) zigzag nanotube of similar diameter and a finite model of chiral tube. The obtained results indicate a possibility of predicting carbon chemical shift for single wall carbon nanotubes differing by diameter. In addition, it seems that nanotube character (zigzag or chiral) is of less importance for the studied NMR shifts. This is in good agreement with recent calculations by Zurek et al. [22–24] and advanced experimental studies [25]. Zurek and coworkers [22–24], Besley et al. [26] and Engtrakul et al. [25] also observed a decreasing 13 C NMR chemical shift upon enlarging CNTs diameter. Thus, our results gathered in Table 1 for both finite lengths tubes and infinite models (obtained with CASTEP method) indicate a similar decrease of chemical shift with increasing diameter of zigzag (n, 0) SWCNTs and cyclacenes. However, the zigzag-like pattern of changes is not very regular and smooth. In case of open ended (5, 5) armchair SWCNTs (C40 to C180 molecules with unsaturated dangling bonds) Wang and coworkers [62] observed a similar zigzag-like pattern of 13 C NMR chemical shifts along the tube axis. However, the sp type carbon atoms at the rim showed much higher shift (about 200 ppm) and the remaining shifts for carbon atoms further from the rim were significantly lower. 4. Conclusion Three types of finite model systems, including cyclic acenes and zigzag (n, 0) SWCNTs, were chosen to study the 13 C NMR chemical shifts of real-size SWCNTs using the DFT methodology. The UB3LYP/6-31G* level of theory was used to fully optimize the structure and calculate vibrational frequencies. The size of studied carbon nanosystems varied from 5 to 15 conjugated benzene rings and the length for nanotubes was up to 2.15 nm (10 “bamboo” units). Carbon nuclear magnetic shieldings, recalculated to chemical shifts using benzene as the secondary reference, were obtained at the BHandH/STO-3Gmag level of theory. A convergence of carbon chemical shifts for atoms along the tube axis for the inner part of the SWCNT was examined. The calculated carbon chemical shifts for interior atoms of the (6, 5) chiral and similar-size (9,
18
T. Kupka et al. / Journal of Molecular Graphics and Modelling 67 (2016) 14–19
Fig. 3. Calculated 13 C chemical shifts ␦ of various SWCNT models (cyclacenes – red circles, 4-units long SWCNTs – black triangles, 10-units long SWCNTs – blue squares and infinite SWCNTs taken from Ref. [63]) as a function of the optimized diameter. Plots show trends separately for metallic ( = 0) and semiconducting SWCNTs ( = 1, 2). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
0) zigzag nanotubes were close to experimentally observed value for the (6, 5) chiral SWCNT. Calculations of 13 C NMR shifts performed using models of different lengths revealed that cyclacenes represent rather rough model of real-size SWCNTs. It provided only general trends with large deviation from the infinite-SWCNT values, while calculations based on the 4-units long SWCNTs provided a reasonably precise approximation of infinitely long tubes with the RMSD error of about 11 ppm. It can be assumed that the error drops even lower to ∼6 ppm if the 10-units long SWCNT model is used. This study demonstrates a possibility to use finite models to make realistic predictions of 13 C chemical shifts with the accuracy comparable to periodic calculations on infinite SWCNTs.
Acknowledgements The National Center for Research and Development (projects no. PBS1/A5/15/2012) and The Faculty of Chemistry, University of Opole (Grant 8/WCH/2016-S) are acknowledged. The Czech Science Foundation (14-03564S,) is also acknowledged. Access to computing and storage facilities owned by parties and projects contributing to the National Grid Infrastructure MetaCentrum, provided under the program “Projects of Large Infrastructure for Research, Development, and Innovations” (LM2010005), is greatly appreciated, as well as access to the CERIT-SC computing and storage facilities provided under the program Center CERIT Scientific Cloud, part of the Operational Program Research and Development for Innovations, reg. no. CZ. 1.05/3.2.00/08.0144. Michał Stachów is a recipient of a Ph. D. fellowship from a project funded by the European Social Fund ‘Uniwersytecki Program Stypendialny 2014–2015’. The Supercomputing and Networking Center ACK CYFRONET AGH in Krakow (grant MNiSW/SGI3700/UOpolski/061/2008 and PL-Grid infrastructure) and the Supercomputing and Networking Center in Wrocław are also acknowledged.
Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.jmgm.2016.04. 008.
References [1] H.W. Kroto, J.R. Heath, S.C. O’Brien, R.F. Curl, R.E. Smalley, C60: Buckminsterfullerene, Nature 318 (1985) 162–163. [2] S. Iijima, Helical microtubules of graphitic carbon, Nature 354 (1991) 56–58. [3] A. Iijima, T. Ichihashi, Single-shell carbon nanotubes of 1-nm diameter, Nature 363 (1993) 603–605. [4] R. Saito, M.S. Dresselhaus, G. Dresselhaus, Physical Properties of Carbon Nanotubes, Imperial College Press, London, 1998. [5] K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, et al., Electric field in atomically thin carbon films, Science 306 (2004) 666–669. ´ [6] Y.F. Hsiou, Y.J. Yang, L. Stobinski, W. Kuo, C.D. Chen, Controlled placement and electrical contact properties of individual multiwalled carbon nanotubes on patterned silicon chips, Appl. Phys. Lett. 84 (2004) 984–986. ´ [7] C.-H. Chen, W.-J. Liou, H.-M. Lin, S.-H. Wu, A. Mikołajczuk, L. Stobinski, et al., Carbon nanotube-supported bimetallic palladium–gold electrocatalysts for electro-oxidation of formic acid, Phys. Status Solidi A. Appl. Mater. Sci. 207 (2010) 1160–1165. [8] X. Pan, X. Bao, The effects of confinement inside carbon nanotubes on catalysis, Acc. Chem. Res. 44 (2011) 553–562. [9] A. Chutia, I. Hamada, M. Tokuyama, Role of lone pair and -orbital interaction in formation of water nanostructures confined in carbon nanotubes, Chem. Phys. Lett. 550 (2012) 118–124. [10] A. Alexiadis, S. Kassinos, The density of water in carbon nanotubes, Chem. Eng. Sci. 63 (2008) 2047–2056. [11] F. Zhu, K. Schulten, Water and proton conduction through carbon nanotubes as models for biological channels, Biophys. J. 85 (2003) 236–244. [12] J. Hu, T.W. Odom, C.M. Lieber, Chemistry and physics in one dimension: synthesis and properties of nanowires and nanotubes, Acc. Chem. Res. 32 (1999) 435–445. ´ [13] P. Okrasinski, Z. Latajka, C. Hättig, Theoretical study on noncovalent interactions in the carbon nanotube–formic acid dimer system, J. Phys. Chem. C 118 (2014) 4483–4488. [14] X. Lu, Z. Chen, Curved pi conjugation, aromaticity and the related chemistry of small fullerenes, Chem. Rev. 105 (2005) 3643–3696. ´ [15] T. Kupka, M. Stachów, E. Chełmecka, K. Pasterny, L. Stobinski, DFT calculations of structures, 13 C NMR chemical shifts and Raman RBM mode of simple models of ultra small diameter (4.0) zigzag hydroxylated single wall carbon nanotubes, Synth. Metals 162 (2012) 573–583. [16] Y.F. Chan, H.Y. Peng, Z.K. Tang, N. Wang, Transmission electron microscopy study of single-walled 0.4 nm carbon nanotubes, Chem. Phys. Lett. 369 (2003) 541–548. [17] N. Wang, G.D. Li, Z.K. Tang, Mono-sized and single-walled 4 Å carbon nanotubes, Chem. Phys. Lett. 339 (2001) 47–52. [18] T. Kyotani, B.K. Pradhan, A. Tomita, Synthesis of carbon nanotube composites in nanochannels of an anodic aluminum oxide film, Bull. Chem. Soc. Jpn. 72 (1999) 1957–1970. [19] L. Ci, Z. Zhou, D. Tang, X. Yan, Y. Liang, D. Liu, et al., Double wall carbon nanotubes with an inner diameter of 0.4 nm, Chem. Vap. Depos. 9 (2003) 119–121.
T. Kupka et al. / Journal of Molecular Graphics and Modelling 67 (2016) 14–19 [20] H. Kuzmany, W. Plank, M. Hulman, C. Kramberger, A. Gruneis, T. Pichler, et al., Determination of SWCNT diameters from the Raman response of the radial breathing mode, Eur. Phys. J. B 22 (2001) 307–320. [21] J. Kürti, V. Zólyomi, M. Kertesz, G. Sun, The geometry and the radial breathing mode of carbon nanotubes: beyond the ideal behaviour, New J. Phys. 5 (2003) 125.1–125.21. [22] E. Zurek, J. Autschbach, Density functional calculations of the 13 C NMR chemical shifts in (9,0) single-walled carbon nanotubes, J. Am. Chem. Soc. 126 (2004) 13079–13088. [23] E. Zurek, C.J. Pickard, B. Walczak, J. Autschbach, Density functional theory studies of the 13 C NMR chemical shifts in small-to-medium-diameter infinite single-walled carbon nanotubes, J. Phys. Chem. A. 110 (2006) 11995–12004. [24] E. Zurek, J. Autschbach, NMR computations for carbon nanotubes from first principles: present status and future directions, Int. J. Quantum Chem. 109 (2009) 3343–3367. [25] C. Engtrakul, M.F. Davies, K. Mistry, B.A. Larsen, A.C. Dillon, M.J. Heben, et al., Solid-state 13 C NMR assignment of carbon resonances on metallic and semiconducting single-walled carbon nanotubes, J. Am. Chem. Soc. 132 (2010) 9956–9957. [26] N.A. Besley, J.J. Titman, M.D. Wright, Theoretical study of the 13 C NMR spectroscopy of single-walled carbon nanotubes, J. Am. Chem. Soc. 127 (2005) 17948–17953. [27] N.A. Besley, A. Noble, NMR chemical shifts of molecules encapsulated in single walled carbon nanotubes, J. Chem. Phys. 128 (2008) 101102–101104. [28] T. Kar, B. Adkim, X. Duan, R. Pachter, Open-ended modified single-wall carbon nanotubes: a theoretical study of the effects of purification, Chem. Phys. Lett. 423 (2006) 126–130. [29] T. Kar, S. Scheiner, A.K. Roy, Reliability of approximate methods to study tip-functionalized single-wall carbon nanotubes, J. Phys.Chem. C. 116 (2012) 25401–25406. [30] S. Kar, S. Scheiner, A.K. Roy, H.F. Bettinger, Unusual low-vibrational C O mode of COOH can distinguish between carboxylated zigzag and armchair single-wall carbon nanotubes, J. Phys. Chem. C 116 (2012) 26072–26083. [31] C. Engtrakul, V.M. Irurzun, E.L. Gjersing, J.M. Holt, B.A. Larsen, D.E. Resasco, et al., Unraveling the 13 C NMR chemical shifts in single-walled carbon nanotubes: dependence on diameter and electronic structure, J. Am. Chem. Soc. 134 (2012) 4850–4856. ´ [32] T. Kupka, E. Chełmecka, K. Pasterny, M. Stachów, L. Stobinski, DFT calculations of structures, 13 C NMR chemical shifts and Raman RBM mode of simple models of small diameter (4.0) zigzag carboxylated single wall carbon nanotubes, Magn. Reson. Chem. 50 (2012) 142–151. ´ [33] E. Chełmecka, K. Pasterny, T. Kupka, L. Stobinski, OH-functionalized open-ended armchair single-wall carbon nanotubes (SWCNT) studied by density functional theory, J. Mol. Model. 18 (2012) 1463–1472. ´ [34] E. Chełmecka, K. Pasterny, T. Kupka, L. Stobinski, DFT studies of COOH tip-functionalized zigzag and armchair single wall carbon nanotubes, J. Mol. Model. 18 (2012) 2241–2246. ´ [35] E. Chełmecka, K. Pasterny, T. Kupka, L. Stobinski, Density functional theory studies of OH-modified open-ended single-wall zigzag carbon nanotubes (SWCNTs), J. Mol. Struct. (Theochem.) 948 (2010) 93–98. ´ ´ [36] T. Kupka, M. Stachów, E. Chełmecka, K. Pasterny, M. Stobinska, L. Stobinski, et al., Efficient modeling of NMR parameters in carbon nanosystems, J. Chem. Theor. Comput. 9 (2013) 4275–4286. [37] J. Kessler, P. Bouˇr, Molecular dynamics with periodic boundary conditions, J. Comput. Chem. 35 (2014) 1552–1559. [38] J. Beheshtian, A.A. Peyghan, Z. Bagheri, Carbon nanotube functionalization with carboxylic derivatives: a DFT study, J. Mol. Model. 19 (2012) 391–396. [39] B. Esser, F. Rominger, R. Gleiter, Synthesis of [6.8]3cyclacene: conjugated belt and model for an unusual type of carbon nanotube, J. Am. Chem. Soc. 130 (2008) 6716–6717. [40] B. Esser, A. Bandyopadhyay, F. Rominger, R. Gleiter, From metacyclophanes to cyclacenes, Chem. Eur. J. 15 (2009) 3368–3379. [41] U. Girreser, D. Giuffrida, F.H. Kohnke, J.P. Matthias, D. Philp, J.F. Stoddart, The structure-directed synthesis of cyclacene and polyacene derivatives, Pure Appl. Chem. 65 (1993) 119–125. ´ [42] T. Kupka, M. Stachów, M. Nieradka, L. Stobinski, DFT calculation of structures and NMR chemical shifts of simple models of small diameter zigzag single wall carbon nanotubes (SWCNTs), Magn. Reson. Chem. 49 (2011) 549–557.
19
[43] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, et al., Gaussian 09, Rev. D.01, Gaussian, Inc, Wallingford, CT, USA, 2009. [44] A.D. Becke, A new mixing of Hartree-Fock and local density-functional theories, J. Chem. Phys. 98 (1993) 1372–1377. [45] C. Lee, W. Yang, R.G. Parr, Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density, Phys. Rev. B 37 (1988) 785–789. [46] B. Miehlich, A. Savin, H. Stoll, H. Preuss, Results obtained with the correlation-energy density functionals of Becke and Lee, Yang and Parr, Chem. Phys. Lett. 157 (1989) 200–206. [47] C. Lepetit, C. Zou, R. Chauvin, Total carbo-mer of benzene, its carbo trannulene form and the zigzag nanotube thereof, J. Org. Chem. 71 (2006) 6317–6324. [48] M. Bendikov, M. Duong, H.M. Starkey, K.N. Houk, E.A. Carter, F. Wudl, Oligocenes: theoretical prediction of open-shell singlet diradical ground states, J. Am. Chem. Soc. 126 (2004) 7416–7417. [49] D.H. Ess, E.R. Johnson, X. Hu, W. Yang, Singlet-triplet energy gaps from diradicals from fractional-spin density-functional theory, J. Phys. Chem. A 115 (2011) 76–83. ´ T. Pluta, Convergence of [50] T. Kupka, M. Stachów, M. Nieradka, J. Kaminsky, nuclear magnetic shieldings in the Kohn-Sham limit for several small molecules, J. Chem. Theor. Comput. 6 (2010) 1580–1589. [51] R. Ditchfield, Self-consistent perturbation theory of diamagnetism I. A gauge-invariant LCAO method for N.M.R. chemical shifts, Mol. Phys. 27 (1974) 789–807. [52] K. Wolinski, J.F. Hinton, P. Pulay, Efficient implementation of the gauge-independent atomic orbital method for NMR chemical shift calculations, J. Am. Chem. Soc. 112 (1990) 8251–8260. [53] E. Voronkov, V. Rossikhin, S. Okovytyy, A. Shatckih, V. Bolshakov, J. Leszczynski, Novel physically adapted STO## -3G basis sets. Efficiency for prediction of second-order electric and magnetic properties of aromatic hydrocarbons. I, J. Quantum Chem. 112 (2012) 2444–2449. [54] T. Kupka, Complete basis set prediction of methanol isotropic nuclear magnetic shieldings and indirect nuclear spin-spin coupling constants (SSCC) using polarization-consistent and XPZ basis sets and B3LYP and BHandH density functionals, Magn. Reson. Chem. 47 (2009) 674–683. ´ M. Budˇesˇ ínsky, ´ S. Taubert, P. Bouˇr, M. Straka, Fullerene C70 [55] J. Kaminsky, characterization by 13 C NMR and the importance of the solvent and dynamics in spectral simulations, Phys. Chem. Chem. Phys. 15 (2013) 9223–9230. ´ [56] A. Buczek, M. Makowski, M. Jewginski, R. Latajka, T. Kupka, M.A. Broda, Toward engineering efficient peptidomimetics. Screening conformational landscape of two modified dehydroaminoacids, Biopolymers 101 (2014) 28–40. [57] K. Radula-Janik, T. Kupka, K. Ejsmont, Z. Daszkiewicz, S.P. Sauer, Halogen effect on structure and 13 C NMR chemical shift of 3,6-disubstituted-N-alkyl carbazoles, Magn. Reson. Chem. 51 (2013) 630–635. [58] F. Jensen, Basis set convergence of nuclear magnetic shielding constants calculated by density functional methods, J. Chem. Theor. Comput. 4 (2008) 719–727. [59] C.J. Pickard, F. Mauri, All-electron magnetic response with pseudopotentials: NMR chemical shifts, Phys. Rev. B 63 (2001) 245101. [60] M.D. Segall, P.J.D. Lindan, M.J. Probert, C.J. Pickard, P.J. Hasnip, S.J. Clark, et al., First-principles simulation: ideas, illustrations and the CASTEP code, J. Phys. Condens. Matter 14 (2002) 2717–2744. [61] L. Lai, J. Lu, W. Song, M. Ni, L. Wang, G. Luo, et al., First-principles calculation of 13 C NMR chemical shifts of infinite single-walled carbon nanotubes: new data for large-diameter and four-helical nanotubes, J. Phys. Chem. C 112 (2008) 16417–16421. [62] L.V. Liu, W.Q. Tian, Y.K. Chen, Y.A. Zhang, Y.A. Wang, Theoretical studies on structures, 13 C NMR chemical shifts, aromaticity, and chemical reactivity of finite-length open-ended armchair single-walled carbon nanotubes, Nanoscale 2 (2010) 254–261. [63] Y. Matsuda, J. Tahir-Kheli, W.A. Goddard, Definitive band gaps for single-wall carbon nanotubes, J. Phys. Chem. Lett. 1 (2010) 2946–2950.
Contents lists available at ScienceDirect
Journal of Molecular Graphics and Modelling journal homepage: www.elsevier.com/locate/JMGM
DFT study of zigzag (n, 0) single-walled carbon nanotubes: 13 C NMR chemical shifts b ´ Teobald Kupka a,∗ , Michal Stachów a , Leszek Stobinski , Jakub Kaminsky´ c,∗ a b c
University of Opole, Faculty of Chemistry, 48, Oleska Street, 45-052 Opole, Poland Faculty of Chemical and Process Engineering, Warsaw University of Technology, Wary´ nskiego 1, 00-645 Warsaw, Poland Institute of Organic Chemistry and Biochemistry, Academy of Sciences of the Czech Republic, Flemingovo nam. 2, 166 10 Prague, Czech Republic
a r t i c l e
i n f o
Article history: Received 4 February 2016 Received in revised form 14 April 2016 Accepted 19 April 2016 Available online 3 May 2016 Keywords: Zigzag SWCNT Cyclacenes Theoretical modeling DFT NMR
a b s t r a c t 13 C NMR chemical shifts of selected finite-size models of pristine zigzag single walled carbon nanotubes (SWCNTs) with a diameter of ∼0.4–0.8 nm and length up to 2.2 nm were studied theoretically. Results for finite SWCNTs models containing 1, 4 and 10 adjacent bamboo-type units were compared with data obtained for infinite tubes in order to estimate the reliability of small finite models in predicting magnetic properties of real-size nanotubes and to assess their tube-length dependence. SWCNTs were fully optimized using unrestricted density functional theory (DFT-UB3LYP/6-31G*). Cyclacenes, as the shortest models of open-ended zigzag SWCNTs, with systematically varying diameter were calculated as well. GIAO NMR calculations on the SWCNT and cyclacene models were performed using the BHandH density ´ functional combined with relatively small STO-3Gmag basis set, developed by Leszczynski and coworkers for accurate description of magnetic properties. Regular changes of carbon 13 C chemical shifts along the tube axis of real size (6, 0) and (9, 0) zigzag carbon nanotubes were shown. The 13 C NMR shifts according to increasing diameter calculated for zigzag (n, 0, n = 5–10) cyclacenes followed the trends observed for zigzag (n, 0) SWCNTs. The results for 4-units long SWCNTs match reasonably well with the data obtained for infinite zigzag (n, 0) SWCNTs, especially to those with bigger diameter (n = 8-15). The presence of rim hydrogens obviously affects theoretical 13 C chemical shieldings and shifts in cyclacenes and thus cyclacenes can provide only approximate estimation of 13 C NMR parameters of real-size SWCNTs. The NMR properties predicted for the longest 10-units long models of SWCNTs reliably correspond to results obtained for infinite nanotubes. They were thus able to accurately predict also recently reported experimental chemical shift of chiral (6, 5) SWCNT. © 2016 Elsevier Inc. All rights reserved.
1. Introduction Fullerenes [1], carbon nanotubes (CNTs [2–4]) and recently graphenes [5] have paved their way to basic and applied science in recent twenty five years of nanoscience development. These ordered carbon allotropes are considered promising materials for many applications ranging from hybrid or future quantum electronics to a rational development of intelligent composites [4]. Thus, pristine CNTs, as well as functionalized tubes, are used in several fields of research and industry [4,6,7]. For example, the CNTs can serve as reactors for nanoscale chemical reactions due to their favorable tubular morphology [8]. Open-ended SWCNTs have been a subject of many model studies in nanocarbon
∗ Corresponding authors. E-mail addresses: [email protected], [email protected] (T. Kupka), ´ [email protected] (J. Kaminsky). http://dx.doi.org/10.1016/j.jmgm.2016.04.008 1093-3263/© 2016 Elsevier Inc. All rights reserved.
chemistry. For example, encapsulation of simple molecules inside the carbon nanotube has attracted the attention of scientists resulting to numerous studies on interaction of small molecules or atoms with interior, as well as exterior of the tube or proton transfer studies [9–13]. Carbon nanotubes could be viewed as a graphene sheet (or a flat set of conjugated benzene rings forming a honey comb pattern) rolled along a chiral vector Ch into a tube [4]. The chiral vector Ch = na1 + ma2 depends on the lattice vectors a1 , a2 . Typically, a short notation (n, m) is used to describe zigzag (n, 0), armchair (n, n) and chiral (n, m) types of single wall carbon nanotubes. Originally, the (n, m) tubes with newly defined parameter = mod(n − m, 3) = 0 were considered as metallic [14], however, due to the curvature effects and s-p hybridization in SWCNTs with extremely small diameters, the rule is broken and e.g. (5, 0) SWCNT is considered metallic according to theoretical predictions [15].
T. Kupka et al. / Journal of Molecular Graphics and Modelling 67 (2016) 14–19
15
Scheme 1. Schematic structures of selected zigzag (n, 0) cyclacenes (n = 4–16) and (n, 0) zigzag SWCNTs used in calculations (n = 5– 9, with diameter in nm).
Nevertheless, dividing SWCNTs to families according to their value is still reasonable and will be used in this work. Unfortunately, SWCNTs are produced as mixtures of tubes, difficult to separate and characterize [4]. Commercial SWCNTs are produced in diameters ranging from a fraction of nanometer (∼0.3 nm) to tens of nanometers. In addition, the ultra-thin SWCNTs [16] were reported inside the zeolite structural channels [17], aluminum oxide [18] and inside larger multi-walled carbon nanotubes [19]. Although experimental characterization of commercial samples is essential in nanotechnology, no simple method is available so far. Instead, a combination of several spectroscopic and microscopic techniques is used in characterization of technical SWCNTs. Therefore, a highly challenging structural and spectroscopic characterization of SWCNTs is usually performed employing several techniques. Raman spectroscopy is widely used to support X-ray and microscopic determination of SWCNTs diameter since the Raman active radial breathing mode vibration (RBM) frequency is inversely proportional to the tube diameter [19–21]. Also a number of experimental and theoretical NMR works on SWCNTs and closely related fullerenes has been published [22–24] [25–31]. Recently, we reported on the impact of –OH and –COOH end substituents on structural changes, RBM, 13 C NMR chemical shifts (␦) and HOMO-LUMO gaps of ultra-thin (4, 0) zigzag, (5, 5) armchair and (8, 2) chiral SWCNTs [32–36]. Due to growing demand for well-characterized nanomaterials and insufficient use of spectroscopic techniques for their characterization (e.g. NMR) we propose in this study theoretical modeling of NMR parameters for finite SWCNT models of a size near to real SWCNTs to support their experimental analysis [22–24,26,28–30]. The main goal of the present study is an accurate theoretical modeling of 13 C NMR chemical shifts of selected finite models of zigzag SWCNTs of diameters common in commercial samples using density functional theory (DFT). Obtained results will be critically compared with available experimental data or with previously reported calculations on infinite SWCNTs. The idea of using finite models is also driven by future aims at NMR studies on one-end functionalized SWCNTs, where the use of periodic calculations on infinite SWCNTs is limited. The finite models could also be utilized for modeling of properties of chiral SWCNTs that is still often computationally expensive procedure if the periodic calculations on infinite models are employed. Enormous computational demands of calculations on infinite chiral tubes are caused due to large unit crystal cells containing often several hundreds of heavy atoms. Standard calculations with the usual periodic boundary conditions (PBC) are not easily compatible with helical symmetry so far. An algorithm comprising infinitely propagated helicity compatible with commonly used Molecular Dynamic software was developed in our group [37]. Nevertheless, we are
not aware of any helical symmetry propagating PBC code working at QM level and plane waves. Thus, suitable finite models can be a relatively cheap alternative providing results with a precision described in this work. Note, that the size of our finite models is considerably wider than reported before [26–30,36,38] (up to n = 15) and this should also enable better observations of convergence patterns of SWCNTs’ parameters in accordance with their diameter. The current study should also make possible a better interpretation of observed experimental 13 C NMR chemical shifts of SWCNTs.
2. Computational methodology Three distinct model systems were chosen—zigzag type cyclacenes and open-end finite zigzag SWCNTs consisting of 4 or 10 “bamboo” units [36,39–42] (Scheme 1). These models were constructed by increasing their diameter from 0.4 to 0.8 nm (10units SWCNTs), and even up to 1.3 nm for 4-units SWCNTs and cyclacenes. The length of models range from 0.3 nm for cyclacenes to 0.9 nm for 4-units SWCNTs or even 2.2 nm for 10-units SWCNTs. All structural calculations were performed using Gaussian 09 program [43] and the unrestricted wavefunction approximation of the Becke three-parameter Lee-Yang-Parr exchange-correlation functional (UB3LYP [44–46]) combined with the 6-31G* basis set. The method together with unrestricted approach was suggested earlier for better description of open-shell singlet states in polyaromatic systems [47–49]. This approach was successfully applied in our previous studies on polyaromatic molecules [15,50]. Besides, we applied loose symmetry and tight SCF and optimization thresholds with a very fine computational grid (GRID = 150,590) during the optimization [43]. The calculations of vibrational frequencies were performed for optimized geometries to ensure the minimum on the potential energy surface for the studied systems [40]. The gauge including atomic orbital [51,52] (GIAO) calculations of nuclear isotropic shieldings for optimized UB3LYP/6-31G* geometries were performed using the BHandH [43,44] functional and the STO-3Gmag basis set [53]. The BHandH [44] density functional and a modified basis set were successful in calculating carbon nuclear shieldings (and chemical shifts) in earlier studies on hydrocarbons, small molecules or nanocarbons [15,36,50,54–57]. The STO-3Gmag basis set was developed for accurate description ´ of magnetic properties with a reasonable effort. Leszczynski and coworkers’ idea of STO-3Gmag basis set arises from an extension of standard STO-3G basis set by functions obtained from analytical first-order corrections using the Green’s function [53]. This modified STO-3G basis set shows a very good accuracy, comparable to Jensen’s pcS-2 basis set [58], dedicated to accurate prediction of nuclear shieldings, while being half the size of the latter [50]. Benzene nuclear isotropic shielding (o ), calculated at the same level
16
T. Kupka et al. / Journal of Molecular Graphics and Modelling 67 (2016) 14–19
Fig. 1. 13 C NMR chemical shifts (ppm) along the tube axis calculated at the BHandH/STO-3Gmag level for (6, 0) and (9, 0) zigzag SWCNTs (10 bamboo units). Lines connecting the points are provided to show trends.
of theory, was used as secondary reference for chemical shift (␦i ) calculation of i-th carbon atom according to the formula [36]: ıi = o − i + 128.5
(1)
Additionally, for comparison of our NMR data for finite models results with periodic calculations on infinite length (n, 0) SWCNTs, with n = 7–15, using the Gauge Including Projector Augmented Waves [59] (GIPAW) approach based on CASTEP code [60] were taken from the literature. 3. Results and discussion We have recently reported on 13 C NMR chemical shifts for individual atoms in ultra-thin (4, 0) SWCNT calculated at the B3LYP/pcS-2 level of theory [36,42,50]. In case of such ultra-thin open-ended zigzag SWCNTs the carbon chemical shifts converged toward 175 ± 5 ppm for interior carbon atoms of the nanotube consisting of 10 “bamboo” units. A very high value (deshielding) of carbon chemical shift in this model was most likely caused by extreme structural strain and deformation of sp2 hybridized carbon atoms due to a high curvature. This also explains the fact that the experimentally observed ultra-thin carbon nanotubes exist only in confined spaces [19]. In the current study of 13 C chemical shift change along the tube axis we first selected two zigzag SWCNTs, (6, 0) and (9, 0) tubes, with the length of 10 “bamboo” units (see Scheme 1) corresponding to 2.15 nm. Thus, a realistic diameter described in experimental works [25–29,31] was chosen. The 13 C chemical shift changes for two types of carbon atoms, Ai and Bi , along the tube axis in (6, 0) and (9, 0) SWCNTs are compared in Fig. 1. It is important to note that
chemical shifts along the tube length are not the same for carbon atoms at both ends. Thus, the carbon atoms labeled A1 and A11 are C H and C types, respectively. On the contrary, atoms B1 and B11 are C and C H types. For both models significant differences of carbon chemical shifts at the rim (A1 atom) and the interior (C6 atom) of the tube are observed (about 20 and 15 ppm for Ai , and 25 and 15 ppm for Bi carbons respectively). Besides, significantly larger oscillations of carbon chemical shifts along the tube axis are observed for more strained structure (the smaller diameter one, compare results in ref [42]). In fact, the convergence of carbon chemical shifts start from the two rims (ends) of the tube and decays in an exponential-like way toward the middle of the tube. However, for these CNTs of different diameter, the convergence of carbon chemical shifts at about 125 and 130 ppm for atoms near the middle of the tube length is observed for the (6, 0) and (9, 0) zigzag SWCNTs (Fig. 1). Interestingly, for smaller diameter (6, 0) tube the presence of tube end (rim effect) is reflected farther from the end − at the fifth carbon layer (see an about 3 ppm difference of chemical shift between full and empty circle) and is significantly smaller for larger (9, 0) SWCNT (only about 1 ppm at the four carbon layer). A model of SWCNT consisting of 10 “bamboo units” with three “ribbons” (labeled 5, 6 and 7) of carbon atoms in the middle of its length and perpendicular to tube axis, is shown schematically in Fig. 2. The 6th ribbon is located in the middle of tube length and is the least affected by rims. Thus, chemical shifts of the 6th ribbon (after averaging) will be used to study the impact of tube diameter on chemical shift of tube interior. This chemical shift can be considered as an approximation of predicted NMR signal for very long tubes. If one closely looks at earlier studies on theoretical NMR descriptions of infinitely long (n, 0) SWCNTs [22–27] (some presented in Table 1), it can be seen a decreasing trend of chemical shifts upon enlarging CNTs diameter. Data published for different DFT functionals match each other; they are only vertically shifted. Several irregularities can be found on that trend addressed to metallic SWCNTs. Thus, it is more convenient to compare metallic and semiconducting SWCNTs separately. Published data also reveal that 13 C NMR shifts for metallic SWCNTs of certain diameter are substantially lower than those of comparably wide semiconducting SWCNTs. Nevertheless, the trend of changes of ␦ with increasing tube diameter is similar (smooth decreasing) for both metallic and semiconducting zigzag (n, 0) SWCNTs. Table 1 compares averaged carbon chemical shifts for studied zigzag (n, 0) 4-units and 10-units long SWCNT models (for the 10units model 13 C signals of atoms of the 6th “ribbon” – see Fig. 2 – were averaged), as well as zigzag (n, 0) cyclacenes. The latter models can be considered as the shortest SWCNT tubes formed by rim atoms only, e.g. by C1- and C2-type atoms (according to Scheme 1). The zigzag patterns of changes of C1 and C2 ␦ upon increasing the
Fig. 2. Model of SWCNT formed by ten “bamboo units” with three selected “ribbons” of carbon atoms in the middle of length. ribbon are considered the least affected by the tube end effects.
13
C NMR chemical shift values for the 6th
T. Kupka et al. / Journal of Molecular Graphics and Modelling 67 (2016) 14–19
17
Table 1 The BHandH/STO-3Gmag predicted 13 C NMR chemical shifts (␦ in ppm) for model zigzag (n, 0) SWCNTs, cyclacenes and for a chiral (6, 5) SWCNT. Results of periodic calculations for infinite length SWCNTs are also included. Zigzag (n, 0)
Diameter (nm)
␦ (13 C NMR) Cyclacenea
(5, 0) (6, 0) (7, 0) (8, 0) (9, 0) (10, 0) (11, 0) (12, 0) (13,0) (14,0) (15,0) RMSDd
0.39 0.47 0.55 0.63 0.71 0.78 0.86 0.94 1.02 1.10 1.18
e
This work Exp.f
0.77 0.77
4-units SWCNTa
C1
C2
Average
142.9 147.1 132.9 140.8 128.5 137.2 122.5 135.2 120.8 133.8 134.0
162.3 160.8 153.7 149.8 152.6 146.0 154.2 142.8 157.0 140.4 168.7
152.6 154.0 143.3 145.3 140.6 141.6 138.4 139.0 138.9 137.1 151.4 19.6 Chiral (6, 5) SWCNT
144.8 142.5 123.9 136.6 122.0 130.4 127.5 130.4 129.2 133.1 136.7 11.0
10-units SWCNTa
158.2 124.7 139.8 134.1 130.9 129.6
Infinite SWCNT PW91b
PBEc
140.3 134.3 122.7 130.5 126.9 117.7 125.4 123.5 118.5
136.4 130.8 120.9 126.9 124.0 116.8 122.6 120.5 114.7
5.7
130.0 129.0
a
BHandH/STO-3Gmag predicted 13 C chemical shifts of carbon atoms in the middle part of the tube. Chemical shifts of infinite SWCNTs calculated using the gauge-including projector augmented plane-wave (GIPAW) approach and benzene as the secondary reference taken from Ref. [61]. c Chemical shifts of infinite SWCNTs calculated using the GIPAW approach and benzene as the secondary reference taken from ref. [23]. d RMSD calculated from ı of infinite SWCNT taken from Ref. [23]. e The VSXC/STO-3Gmag chemical shift as averaged values of atoms in the middle of the tube length and calculated for the B3LYP/6-31G* optimized short chiral (6, 5) SWCNT formed by 5 units (see Ref. [36]). f Ref. [25]. b
diameter of cyclacene (n = 4–15) are roughly mirror images. Nevertheless a slowly decreasing trend is clear. Obviously, the differences cancel out when the C1 and C2 shifts are averaged. This trend converges as a decreasing exponential to ∼135 ppm (see Fig. S1 in Supplementary data). The predicted chemical shifts for 10-units SWCNT model are rather scattered for tubes with small diameters, but decrease in smooth exponential way for wider models (n ≥ 7, see Fig. S2). Similar limiting value is predicted from CASTEP calculations on infinite SWCNTs (see Fig. S2). It is in general more difficult to model metallic than semiconducting tubes (see results for n = 15 in Fig. S2 in the Supplementary data). Closer inspection of data in Table 1 reveals that while cyclacenes represent rather rough model of real-size SWCNTs providing only general trends with large deviation from the CASTEP values, 4-units long SWCNTs provide already a reasonably precise approximation. The RMSD error drops from ∼20 ppm for cyclacene model (if compared to infinitely long tubes) to ∼11 ppm. The error continuously decreases for 10-units long SWCNTs to ∼6 ppm. Note however, that only values for (n, 0; n = 7–10) SWCNT were achieved here and were compared with available reported data for infinite SWCNTs. More detailed analysis can be made upon comparing data from Fig. 3 presenting calculated 13 C shifts according to SWCNT’s family. We can see, that problematic for models used here are especially metallic SWCNTs ( = 0 family) with larger diameters. Thus, the decreasing trend for metallic SWCNT is broken at (12, 0) value and ␦ values start to increase again (both for cyclacenes and 4-units long SWCNTs). Lai et al. [61] reported similar trends of chemical shifts with increasing diameter for metallic SWCNTs. Within the = 1 family of semiconducting SWCNTs the (13, 0) cyclacene also provides too large value of chemical shift, but the 4-units long model already provides the value much closer to the reference and correctly following the decreasing trend. Such trend for = 2 family is reproduced more or less well by all models, but obviously better by the 4-units long SWCNT models. The theoretical results gathered in Table 1 are compared with recently reported 13 C solid state magic angle spinning experimental results (MAS NMR) for a chiral (6, 5) SWCNT [25]. The observed chemical shift for (6, 5) chiral SWCNT sample (of similar diameter
of 0.77 nm) is very closely reproduced by our calculated values for a model (9, 0) zigzag nanotube of similar diameter and a finite model of chiral tube. The obtained results indicate a possibility of predicting carbon chemical shift for single wall carbon nanotubes differing by diameter. In addition, it seems that nanotube character (zigzag or chiral) is of less importance for the studied NMR shifts. This is in good agreement with recent calculations by Zurek et al. [22–24] and advanced experimental studies [25]. Zurek and coworkers [22–24], Besley et al. [26] and Engtrakul et al. [25] also observed a decreasing 13 C NMR chemical shift upon enlarging CNTs diameter. Thus, our results gathered in Table 1 for both finite lengths tubes and infinite models (obtained with CASTEP method) indicate a similar decrease of chemical shift with increasing diameter of zigzag (n, 0) SWCNTs and cyclacenes. However, the zigzag-like pattern of changes is not very regular and smooth. In case of open ended (5, 5) armchair SWCNTs (C40 to C180 molecules with unsaturated dangling bonds) Wang and coworkers [62] observed a similar zigzag-like pattern of 13 C NMR chemical shifts along the tube axis. However, the sp type carbon atoms at the rim showed much higher shift (about 200 ppm) and the remaining shifts for carbon atoms further from the rim were significantly lower. 4. Conclusion Three types of finite model systems, including cyclic acenes and zigzag (n, 0) SWCNTs, were chosen to study the 13 C NMR chemical shifts of real-size SWCNTs using the DFT methodology. The UB3LYP/6-31G* level of theory was used to fully optimize the structure and calculate vibrational frequencies. The size of studied carbon nanosystems varied from 5 to 15 conjugated benzene rings and the length for nanotubes was up to 2.15 nm (10 “bamboo” units). Carbon nuclear magnetic shieldings, recalculated to chemical shifts using benzene as the secondary reference, were obtained at the BHandH/STO-3Gmag level of theory. A convergence of carbon chemical shifts for atoms along the tube axis for the inner part of the SWCNT was examined. The calculated carbon chemical shifts for interior atoms of the (6, 5) chiral and similar-size (9,
18
T. Kupka et al. / Journal of Molecular Graphics and Modelling 67 (2016) 14–19
Fig. 3. Calculated 13 C chemical shifts ␦ of various SWCNT models (cyclacenes – red circles, 4-units long SWCNTs – black triangles, 10-units long SWCNTs – blue squares and infinite SWCNTs taken from Ref. [63]) as a function of the optimized diameter. Plots show trends separately for metallic ( = 0) and semiconducting SWCNTs ( = 1, 2). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
0) zigzag nanotubes were close to experimentally observed value for the (6, 5) chiral SWCNT. Calculations of 13 C NMR shifts performed using models of different lengths revealed that cyclacenes represent rather rough model of real-size SWCNTs. It provided only general trends with large deviation from the infinite-SWCNT values, while calculations based on the 4-units long SWCNTs provided a reasonably precise approximation of infinitely long tubes with the RMSD error of about 11 ppm. It can be assumed that the error drops even lower to ∼6 ppm if the 10-units long SWCNT model is used. This study demonstrates a possibility to use finite models to make realistic predictions of 13 C chemical shifts with the accuracy comparable to periodic calculations on infinite SWCNTs.
Acknowledgements The National Center for Research and Development (projects no. PBS1/A5/15/2012) and The Faculty of Chemistry, University of Opole (Grant 8/WCH/2016-S) are acknowledged. The Czech Science Foundation (14-03564S,) is also acknowledged. Access to computing and storage facilities owned by parties and projects contributing to the National Grid Infrastructure MetaCentrum, provided under the program “Projects of Large Infrastructure for Research, Development, and Innovations” (LM2010005), is greatly appreciated, as well as access to the CERIT-SC computing and storage facilities provided under the program Center CERIT Scientific Cloud, part of the Operational Program Research and Development for Innovations, reg. no. CZ. 1.05/3.2.00/08.0144. Michał Stachów is a recipient of a Ph. D. fellowship from a project funded by the European Social Fund ‘Uniwersytecki Program Stypendialny 2014–2015’. The Supercomputing and Networking Center ACK CYFRONET AGH in Krakow (grant MNiSW/SGI3700/UOpolski/061/2008 and PL-Grid infrastructure) and the Supercomputing and Networking Center in Wrocław are also acknowledged.
Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.jmgm.2016.04. 008.
References [1] H.W. Kroto, J.R. Heath, S.C. O’Brien, R.F. Curl, R.E. Smalley, C60: Buckminsterfullerene, Nature 318 (1985) 162–163. [2] S. Iijima, Helical microtubules of graphitic carbon, Nature 354 (1991) 56–58. [3] A. Iijima, T. Ichihashi, Single-shell carbon nanotubes of 1-nm diameter, Nature 363 (1993) 603–605. [4] R. Saito, M.S. Dresselhaus, G. Dresselhaus, Physical Properties of Carbon Nanotubes, Imperial College Press, London, 1998. [5] K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, et al., Electric field in atomically thin carbon films, Science 306 (2004) 666–669. ´ [6] Y.F. Hsiou, Y.J. Yang, L. Stobinski, W. Kuo, C.D. Chen, Controlled placement and electrical contact properties of individual multiwalled carbon nanotubes on patterned silicon chips, Appl. Phys. Lett. 84 (2004) 984–986. ´ [7] C.-H. Chen, W.-J. Liou, H.-M. Lin, S.-H. Wu, A. Mikołajczuk, L. Stobinski, et al., Carbon nanotube-supported bimetallic palladium–gold electrocatalysts for electro-oxidation of formic acid, Phys. Status Solidi A. Appl. Mater. Sci. 207 (2010) 1160–1165. [8] X. Pan, X. Bao, The effects of confinement inside carbon nanotubes on catalysis, Acc. Chem. Res. 44 (2011) 553–562. [9] A. Chutia, I. Hamada, M. Tokuyama, Role of lone pair and -orbital interaction in formation of water nanostructures confined in carbon nanotubes, Chem. Phys. Lett. 550 (2012) 118–124. [10] A. Alexiadis, S. Kassinos, The density of water in carbon nanotubes, Chem. Eng. Sci. 63 (2008) 2047–2056. [11] F. Zhu, K. Schulten, Water and proton conduction through carbon nanotubes as models for biological channels, Biophys. J. 85 (2003) 236–244. [12] J. Hu, T.W. Odom, C.M. Lieber, Chemistry and physics in one dimension: synthesis and properties of nanowires and nanotubes, Acc. Chem. Res. 32 (1999) 435–445. ´ [13] P. Okrasinski, Z. Latajka, C. Hättig, Theoretical study on noncovalent interactions in the carbon nanotube–formic acid dimer system, J. Phys. Chem. C 118 (2014) 4483–4488. [14] X. Lu, Z. Chen, Curved pi conjugation, aromaticity and the related chemistry of small fullerenes, Chem. Rev. 105 (2005) 3643–3696. ´ [15] T. Kupka, M. Stachów, E. Chełmecka, K. Pasterny, L. Stobinski, DFT calculations of structures, 13 C NMR chemical shifts and Raman RBM mode of simple models of ultra small diameter (4.0) zigzag hydroxylated single wall carbon nanotubes, Synth. Metals 162 (2012) 573–583. [16] Y.F. Chan, H.Y. Peng, Z.K. Tang, N. Wang, Transmission electron microscopy study of single-walled 0.4 nm carbon nanotubes, Chem. Phys. Lett. 369 (2003) 541–548. [17] N. Wang, G.D. Li, Z.K. Tang, Mono-sized and single-walled 4 Å carbon nanotubes, Chem. Phys. Lett. 339 (2001) 47–52. [18] T. Kyotani, B.K. Pradhan, A. Tomita, Synthesis of carbon nanotube composites in nanochannels of an anodic aluminum oxide film, Bull. Chem. Soc. Jpn. 72 (1999) 1957–1970. [19] L. Ci, Z. Zhou, D. Tang, X. Yan, Y. Liang, D. Liu, et al., Double wall carbon nanotubes with an inner diameter of 0.4 nm, Chem. Vap. Depos. 9 (2003) 119–121.
T. Kupka et al. / Journal of Molecular Graphics and Modelling 67 (2016) 14–19 [20] H. Kuzmany, W. Plank, M. Hulman, C. Kramberger, A. Gruneis, T. Pichler, et al., Determination of SWCNT diameters from the Raman response of the radial breathing mode, Eur. Phys. J. B 22 (2001) 307–320. [21] J. Kürti, V. Zólyomi, M. Kertesz, G. Sun, The geometry and the radial breathing mode of carbon nanotubes: beyond the ideal behaviour, New J. Phys. 5 (2003) 125.1–125.21. [22] E. Zurek, J. Autschbach, Density functional calculations of the 13 C NMR chemical shifts in (9,0) single-walled carbon nanotubes, J. Am. Chem. Soc. 126 (2004) 13079–13088. [23] E. Zurek, C.J. Pickard, B. Walczak, J. Autschbach, Density functional theory studies of the 13 C NMR chemical shifts in small-to-medium-diameter infinite single-walled carbon nanotubes, J. Phys. Chem. A. 110 (2006) 11995–12004. [24] E. Zurek, J. Autschbach, NMR computations for carbon nanotubes from first principles: present status and future directions, Int. J. Quantum Chem. 109 (2009) 3343–3367. [25] C. Engtrakul, M.F. Davies, K. Mistry, B.A. Larsen, A.C. Dillon, M.J. Heben, et al., Solid-state 13 C NMR assignment of carbon resonances on metallic and semiconducting single-walled carbon nanotubes, J. Am. Chem. Soc. 132 (2010) 9956–9957. [26] N.A. Besley, J.J. Titman, M.D. Wright, Theoretical study of the 13 C NMR spectroscopy of single-walled carbon nanotubes, J. Am. Chem. Soc. 127 (2005) 17948–17953. [27] N.A. Besley, A. Noble, NMR chemical shifts of molecules encapsulated in single walled carbon nanotubes, J. Chem. Phys. 128 (2008) 101102–101104. [28] T. Kar, B. Adkim, X. Duan, R. Pachter, Open-ended modified single-wall carbon nanotubes: a theoretical study of the effects of purification, Chem. Phys. Lett. 423 (2006) 126–130. [29] T. Kar, S. Scheiner, A.K. Roy, Reliability of approximate methods to study tip-functionalized single-wall carbon nanotubes, J. Phys.Chem. C. 116 (2012) 25401–25406. [30] S. Kar, S. Scheiner, A.K. Roy, H.F. Bettinger, Unusual low-vibrational C O mode of COOH can distinguish between carboxylated zigzag and armchair single-wall carbon nanotubes, J. Phys. Chem. C 116 (2012) 26072–26083. [31] C. Engtrakul, V.M. Irurzun, E.L. Gjersing, J.M. Holt, B.A. Larsen, D.E. Resasco, et al., Unraveling the 13 C NMR chemical shifts in single-walled carbon nanotubes: dependence on diameter and electronic structure, J. Am. Chem. Soc. 134 (2012) 4850–4856. ´ [32] T. Kupka, E. Chełmecka, K. Pasterny, M. Stachów, L. Stobinski, DFT calculations of structures, 13 C NMR chemical shifts and Raman RBM mode of simple models of small diameter (4.0) zigzag carboxylated single wall carbon nanotubes, Magn. Reson. Chem. 50 (2012) 142–151. ´ [33] E. Chełmecka, K. Pasterny, T. Kupka, L. Stobinski, OH-functionalized open-ended armchair single-wall carbon nanotubes (SWCNT) studied by density functional theory, J. Mol. Model. 18 (2012) 1463–1472. ´ [34] E. Chełmecka, K. Pasterny, T. Kupka, L. Stobinski, DFT studies of COOH tip-functionalized zigzag and armchair single wall carbon nanotubes, J. Mol. Model. 18 (2012) 2241–2246. ´ [35] E. Chełmecka, K. Pasterny, T. Kupka, L. Stobinski, Density functional theory studies of OH-modified open-ended single-wall zigzag carbon nanotubes (SWCNTs), J. Mol. Struct. (Theochem.) 948 (2010) 93–98. ´ ´ [36] T. Kupka, M. Stachów, E. Chełmecka, K. Pasterny, M. Stobinska, L. Stobinski, et al., Efficient modeling of NMR parameters in carbon nanosystems, J. Chem. Theor. Comput. 9 (2013) 4275–4286. [37] J. Kessler, P. Bouˇr, Molecular dynamics with periodic boundary conditions, J. Comput. Chem. 35 (2014) 1552–1559. [38] J. Beheshtian, A.A. Peyghan, Z. Bagheri, Carbon nanotube functionalization with carboxylic derivatives: a DFT study, J. Mol. Model. 19 (2012) 391–396. [39] B. Esser, F. Rominger, R. Gleiter, Synthesis of [6.8]3cyclacene: conjugated belt and model for an unusual type of carbon nanotube, J. Am. Chem. Soc. 130 (2008) 6716–6717. [40] B. Esser, A. Bandyopadhyay, F. Rominger, R. Gleiter, From metacyclophanes to cyclacenes, Chem. Eur. J. 15 (2009) 3368–3379. [41] U. Girreser, D. Giuffrida, F.H. Kohnke, J.P. Matthias, D. Philp, J.F. Stoddart, The structure-directed synthesis of cyclacene and polyacene derivatives, Pure Appl. Chem. 65 (1993) 119–125. ´ [42] T. Kupka, M. Stachów, M. Nieradka, L. Stobinski, DFT calculation of structures and NMR chemical shifts of simple models of small diameter zigzag single wall carbon nanotubes (SWCNTs), Magn. Reson. Chem. 49 (2011) 549–557.
19
[43] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, et al., Gaussian 09, Rev. D.01, Gaussian, Inc, Wallingford, CT, USA, 2009. [44] A.D. Becke, A new mixing of Hartree-Fock and local density-functional theories, J. Chem. Phys. 98 (1993) 1372–1377. [45] C. Lee, W. Yang, R.G. Parr, Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density, Phys. Rev. B 37 (1988) 785–789. [46] B. Miehlich, A. Savin, H. Stoll, H. Preuss, Results obtained with the correlation-energy density functionals of Becke and Lee, Yang and Parr, Chem. Phys. Lett. 157 (1989) 200–206. [47] C. Lepetit, C. Zou, R. Chauvin, Total carbo-mer of benzene, its carbo trannulene form and the zigzag nanotube thereof, J. Org. Chem. 71 (2006) 6317–6324. [48] M. Bendikov, M. Duong, H.M. Starkey, K.N. Houk, E.A. Carter, F. Wudl, Oligocenes: theoretical prediction of open-shell singlet diradical ground states, J. Am. Chem. Soc. 126 (2004) 7416–7417. [49] D.H. Ess, E.R. Johnson, X. Hu, W. Yang, Singlet-triplet energy gaps from diradicals from fractional-spin density-functional theory, J. Phys. Chem. A 115 (2011) 76–83. ´ T. Pluta, Convergence of [50] T. Kupka, M. Stachów, M. Nieradka, J. Kaminsky, nuclear magnetic shieldings in the Kohn-Sham limit for several small molecules, J. Chem. Theor. Comput. 6 (2010) 1580–1589. [51] R. Ditchfield, Self-consistent perturbation theory of diamagnetism I. A gauge-invariant LCAO method for N.M.R. chemical shifts, Mol. Phys. 27 (1974) 789–807. [52] K. Wolinski, J.F. Hinton, P. Pulay, Efficient implementation of the gauge-independent atomic orbital method for NMR chemical shift calculations, J. Am. Chem. Soc. 112 (1990) 8251–8260. [53] E. Voronkov, V. Rossikhin, S. Okovytyy, A. Shatckih, V. Bolshakov, J. Leszczynski, Novel physically adapted STO## -3G basis sets. Efficiency for prediction of second-order electric and magnetic properties of aromatic hydrocarbons. I, J. Quantum Chem. 112 (2012) 2444–2449. [54] T. Kupka, Complete basis set prediction of methanol isotropic nuclear magnetic shieldings and indirect nuclear spin-spin coupling constants (SSCC) using polarization-consistent and XPZ basis sets and B3LYP and BHandH density functionals, Magn. Reson. Chem. 47 (2009) 674–683. ´ M. Budˇesˇ ínsky, ´ S. Taubert, P. Bouˇr, M. Straka, Fullerene C70 [55] J. Kaminsky, characterization by 13 C NMR and the importance of the solvent and dynamics in spectral simulations, Phys. Chem. Chem. Phys. 15 (2013) 9223–9230. ´ [56] A. Buczek, M. Makowski, M. Jewginski, R. Latajka, T. Kupka, M.A. Broda, Toward engineering efficient peptidomimetics. Screening conformational landscape of two modified dehydroaminoacids, Biopolymers 101 (2014) 28–40. [57] K. Radula-Janik, T. Kupka, K. Ejsmont, Z. Daszkiewicz, S.P. Sauer, Halogen effect on structure and 13 C NMR chemical shift of 3,6-disubstituted-N-alkyl carbazoles, Magn. Reson. Chem. 51 (2013) 630–635. [58] F. Jensen, Basis set convergence of nuclear magnetic shielding constants calculated by density functional methods, J. Chem. Theor. Comput. 4 (2008) 719–727. [59] C.J. Pickard, F. Mauri, All-electron magnetic response with pseudopotentials: NMR chemical shifts, Phys. Rev. B 63 (2001) 245101. [60] M.D. Segall, P.J.D. Lindan, M.J. Probert, C.J. Pickard, P.J. Hasnip, S.J. Clark, et al., First-principles simulation: ideas, illustrations and the CASTEP code, J. Phys. Condens. Matter 14 (2002) 2717–2744. [61] L. Lai, J. Lu, W. Song, M. Ni, L. Wang, G. Luo, et al., First-principles calculation of 13 C NMR chemical shifts of infinite single-walled carbon nanotubes: new data for large-diameter and four-helical nanotubes, J. Phys. Chem. C 112 (2008) 16417–16421. [62] L.V. Liu, W.Q. Tian, Y.K. Chen, Y.A. Zhang, Y.A. Wang, Theoretical studies on structures, 13 C NMR chemical shifts, aromaticity, and chemical reactivity of finite-length open-ended armchair single-walled carbon nanotubes, Nanoscale 2 (2010) 254–261. [63] Y. Matsuda, J. Tahir-Kheli, W.A. Goddard, Definitive band gaps for single-wall carbon nanotubes, J. Phys. Chem. Lett. 1 (2010) 2946–2950.