Chlorophenol sorption on multi-walled carbon nanotubes: DFT modeling and structure–property relationship analysis
The presence of chlorophenols in drinking water can be hazardous to human health. Understanding the mechanisms of adsorption under specific experimental conditions would be beneficial when developing methods to remove toxic substances from drinking water during water treatment in order to limit human exposure to these contaminants. In this study, we investigated the sorption of chlorophenols on multi-walled carbon nanotubes using a density functional theory (DFT) approach. This was applied to study selected interactions between six solvents, five types of nanotubes, and six chlorophenols. Experimental data were used to construct structure–adsorption relationship (SAR) models that describe the recovery process. Specific interactions between solvents and chlorophenols were taken into account in the calculations by using novel specific mixture descriptors.
KeywordsChlorophenols Carbon nanotubes Adsorption DFT Structure–property relationship Pollutants
Chlorophenols are found in many preservative agents, fungicides, pesticides, antiseptics, and disinfectants, and they are also employed as intermediates in many industrial processes [1, 2, 3, 4, 5, 6, 7]. For instance, chlorophenols possessing two or more chlorines are used as or are converted into pesticides . Mono- and dichlorophenols are produced when wastewater is treated with chlorine, or during the bleaching of wood pulp in the paper production process . They are occasionally also found in drinking water as by-products of the chlorination of natural organic matter during disinfection. Previously published research papers have proven that chlorophenols are hazardous to human health [4, 9, 10] and persistent when released into the environment (water/soil).
There are 19 known chlorophenols. The most toxic of them (2-chlorophenol, 2,4-dichlorophenol, and 2,4,6-trichlorophenol) are included in the European Union and the U.S. Environmental Protection Agency (EPA) lists of priority pollutants and hazardous substances [8, 11]. Their adverse effects on health have also been outlined in various reports. For instance, 2,4,6-trichlorophenol has been linked to multiple types of lymphoma and leukemia in male rats and hepatic tumors in mice .
The best way to reduce exposure to these toxic substances is to develop more efficient methods of removing them from the environment, especially from drinking water, although there are already numerous ways of removing chlorophenols from water. For instance, sorption on activated carbon is an effective technology that is routinely used to remove trace metals and trace organics such as chlorophenols from water . Most recently, many studies have focused on replacing common activated carbon with nanosized materials [13, 14, 15]. It is widely known that the sorbent should be chosen according to the physicochemical properties of the analyte . Carbon nanotubes (CNTs) have ordered structures, high aspect ratios, are ultra-lightweight, and have high electrical and thermal conductivities as well as high surface areas . This combination of desirable physiochemical attributes of CNTs makes them highly attractive potential sorbents.
There are two types of CNTs: single-walled CNTs (SWCNTs) consist of condensed benzene rings rolled up into tubular structures; multi-walled CNTs (MWCNTs) consist of multiple SWCNTs located concentrically inside one another. The sidewalls of CNTs can also be functionalized (via adsorption) to increase the sorption activity of the CNT or change the charge on its surface. For example, the aforementioned properties of CNTs change when they are exposed to benzene compounds, O2, H2, NO2, NH3, and COOH groups .
One way to measure how effectively an aromatic adheres to the sidewall of a CNT is to estimate the intermolecular, adsorption, and dispersive forces between the CNT and aromatic molecules with the structural components of the molecules involved in the adsorption process. For instance, it was determined using density functional theory (DFT) and semi-empirical theory that dispersive and π–π stacking interactions predominate between aromatic molecules and graphene/CNTs. These dispersive forces increase with the number of aromatic rings present . Another study revealed that geometry is a key factor in chlorobenzene adsorption, as are electrophilicity (a powerful conceptual DFT descriptor of toxicity in chlorobenzenes ) and interaction energy. The results obtained revealed that, for the adsorption of chlorobenzene onto a (5,5) SWCNT or a graphene sheet, the interaction strength increases as the chlorine content increases . Woods et al.  determined that simple benzene derivatives are adsorbed on a CNT through an interaction between the π orbitals of the benzene ring and the CNT. Additionally, upon simulating the adsorption of organic pollutants on (8,0) SWCNTs in water using DFT with the M05-2X functional , adsorption energies in the aqueous phase were found to be more favorable than those in the gaseous phase.
An efficient tool of mathematical prediction of physicochemical parameters such as adsorption properties is the (quantitative) structure–property relationship [(Q)SPR] approach [23, 34]. Several studies have been conducted that have utilized the QSPR approach to model nanocarbons and organics [24, 25, 26, 27]. For instance, Brasquet and Le Cloirec  determined the dependence of the adsorption of microorganics on activated carbon cloths on the structure of the microorganic using experimental and statistical techniques. The adsorption behavior of microorganics on activated charcoal cloths was compared to that of microorganics on granular activated carbon. The multiple linear correlation (MLR) correlation of microorganic structure with absorption was low, but artificial neural network (ANN) analysis yielded a good explanation for the adsorption data. Analysis of the main variables showed that the adsorption sites were located between the basic planes of the activated carbon, favoring the adsorption of flat molecules.
Xu et al.  modeled the toxicity of phenols using regression analysis and neural networks. The resulting nine-descriptor regression model displayed a high goodness of fit (R2) of 0.98 with a standard deviation of 0.147. Rofouei et al.  performed 3D-QSPR analysis of the dispersibility of SWCNTs in different organic solvents. The results suggested that hydrophobic interactions with small solvent molecules containing polar or bulky groups are restricted and reduce the dispersibility of the SWCNTs in the solvent. Another study  reported the development of a QSAR approach to analyzing the dispersion of SWNTs in different organic solvents. Three MLR models were constructed with R2 values ranging from 0.487 to 0.876 and errors ranging from 0.145 to 0.071. Three ANN models produced goodness of fit values ranging from 0.598 to 0.858 and errors ranging from 0.130 to 0.077. It was shown that steric effects, hydrogen-bonding ability and polarizability, molecular flexibility, and electrostatic interactions are important influences on the dispersibility of SWNTs in organic solvents.
The main operating cost of an adsorptive separation process derives from the need to clean or regenerate the adsorbent after use . Changing the conditions used during the cleaning process may increase or decrease its effectiveness. Thus, there is a need to optimize cleaning or regeneration procedures.
In the work reported in the present paper, we investigated the potential use of MWCNTs to adsorb chlorophenols in aqueous solutions. We analyzed the most important interactions between the selected MWCNTs, organic eluents, and chlorophenols using DFT and a QSAR methodology. The results obtained when six chlorophenols were recovered from six different solvents using five different MWCNTs were analyzed using structure–adsorption relationship analysis. To accurately reflect the features of the interactions between the eluents, chlorophenols, and MWCNTs, DFT and a mixture descriptor technique were utilized.
Materials and methods
Experimental data were taken from the literature . Briefly, water samples were separately spiked with six chlorophenols: 2-chlorophenol (2-Cl), 4-chlorophenol (4-Cl), 2,4-dichlorophenol (2,4-DCL), 2,6-dichlorophenol (2,6-DCL), 3,4-dichlorophenol (3,4-DCl), and 2,4,6-trichlorophenol (2,4,6-TCl), and were then sorbed on five types of MWCNTs: MWCNTs 8–15 nm in outer diameter (OD); MWCNTs >50 nm OD; helical MWCNTs 100–200 nm OD; COOH–MWCNTs <8 nm OD; and COOH–MWCNTs >50nm OD. Methanol, ethanol, acetone, dichloromethane, and combinations of them were tested as mobile phases to remove chlorophenols from MWCNT surfaces. Experimental data are provided in SI1 of the “Electronic supplementary material” (ESM).
The adsorption of six chlorophenols on pristine MWCNTs was investigated using DFT calculations. A DFT methodology was applied to provide mechanistic support for further SPR modeling . In order to reduce computation time, no diffusion or polarization functions were included in the basis set. Therefore, only general trends could be estimated. Another DFT-supported study of this type was recently reported .
The interval between the inner and outer tubes was comparatively small (3.35 Å), meaning that the inner space was inaccessible to organic molecules and solvent molecules . Thus, adsorption on the outer nanotube of the MWCNT was similar to that on the SWCNT. Therefore, we selected an open-ended zigzag (6,0) SWCNT saturated with hydrogen atoms. The length of the SWCNT was 13.5 Å and its diameter was 5.6 Å. The chlorophenols, the SWCNT, and the chlorophenol–SWCNT complexes were optimized at the M06-2X/6-311G level of theory using the implicit solvent model. Methanol was used for interference elution (see the experimental data shown in S1 of the ESM). The SWCNT and chlorophenols were fully relaxed. Full optimization and frequency calculations were carried out using the Gaussian 09 code .
The structures of the chlorophenols and eluents were built and optimized using HyperChem 5.0 . The DRAGON software  was applied to produce 1043 descriptors for each structure. These descriptors are referred to below as the “pure” descriptors.
SPR model development and validation
The percentage of the chlorophenol recovered from aqueous solution using the MWCNT was considered the endpoint of (Q)SPR modeling. Thus, the data set used in the present work consisted of 180 endpoints (i.e., values for the recovery of chlorophenol, %), which was presented as a three-dimensional matrix of 5 MWCNTs × 6 solvents × 6 chlorophenols. To simplify analysis, the initial data were presented as five two-dimensional matrices, in accordance with the number of MWCNTs studied. Tables S1–S5 in SI1 of the ESM contain those two-dimensional endpoint matrices.
Endpoints (recovery percentages) were transformed into ranked categories [38, 39] to standardize initial data. Both linear and nonlinear methods were utilized to develop SPR models. Linear SPR models were developed using a partial least squares (also known as “projections to latent structures,” PLS) approach with a genetic algorithm (PLS-GA). Traditionally, PLS has been utilized as a regression technique, but more recently it has also been used as a classification tool . PLS-GA was applied in PLS Toolbox , supported by MATLAB 2014 . Nonlinear models were built by a random forest (RF) approach . RF models were obtained using the R package randomForest. RF is an ensemble classifier that merges many decision-tree models into a consensus. The classification accuracy is the proportion of the samples that were correctly classified, or (1 − ME), where ME is the misclassification error. Validity and stability were evaluated using the ME for training (T), validation (V), and out-of-bag sets (O) . T/O and T/O/V validation schemas were applied to perform deeper analysis.
It is commonly assumed that a robust and reliable correlation is indicated by R2 ≥ 0.75 when using SPR methods . Reliable models also have RMSE ≤ 0.3 . Additionally, the domain applicability (DA) was assessed by ranking descriptor importance in descriptor space using variable importance values. The DA was calculated by developing a minimum-cost tree .
The initial data were split between the validation and test sets in the same manner for the PLS and RF techniques: every fifth compound was placed into the validation set  and the remaining compounds were considered members of the training set.
Results and discussion
Adsorption energies, distances, and HOMO and LUMO energies for chlorophenol derivatives on the SWCNT
Distance from oxygen to the sidewall (Å)
Distance from hydrogen to the sidewall (Å)
Equilibrium distance from –OH to the sidewall (Å)
The results of the DFT calculations demonstrated that the chlorophenols could be adsorbed on the carbon nanotube surface. They were adsorbed physically through the interaction of the aromatic ring with the rings of the SWCNT. Adsorption of the chlorophenol derivatives did not significantly change the structure of the SWCNT. The chlorophenols were adsorbed on the surface with adsorption energies ranging from −0.44 to −0.61 eV. A comparison of the equilibrium chlorophenol–SWCNT distances for the six chlorophenols studied here indicated that the distance between trichlorophenol and the SWCNT surface was the largest, most likely due to steric factors.
Possible correlations between the energies and chlorophenol desorption were investigated, and the Pearson correlation coefficient was found to be 0.937 for the relationship between chlorophenol recovery (in %, see SI1 in the ESM) and HOMO energy. Thus, we concluded that the chlorophenols were adsorbed onto the SWCNT sidewall, and that the HOMO energy is an indicator of the strength of the interaction of the chlorophenol with the nanotube.
SPR model development
To deduce the important features of chlorophenol adsorption on MWCNTs, a separate model was developed for each nanotube type. These PLS models were built using different combinations of pure and mixture descriptors (further details are presented in SI2 in the ESM).
Multicategorical RF performance estimates based on T/O and T/O/V dataset splits
Split 1 (T/O)
ME (training set)
Split 2 (T/O/V)
ME (training set)
ME (validation set)
The variation among trees was not significant, and the OOB estimate yielded properly constructed models with the ability to be applied to compounds other than those used to construct the model.
The random forest approach indicated that the removal of chlorophenols from MWCNTs can be described by various descriptors. Lists of important descriptors and the importance of each variable in each model (raw scores, in conventional units) are presented in SI2 of the ESM.
Split 1 (T/O)
Model 1 (MWNTs 8–15 nm OD) identified correlation amongst 20 descriptors, including topological indices, path count, 2D autocorrelations, edge adjacency indices, equality information indices, and constitutional indices. The pure phenol compounds contributed descriptors relating to topology and path count.
Model 2 (MWNTs >50 nm OD) identified nine descriptors. The pure phenol descriptors in model 2 were related to information and connectivity indices. Mixture descriptors included BCUT descriptors, information and connectivity indices, 2D autocorrelations, and connectivity indices.
Model 3 (helical MWNTs 100–200 nm OD) identified ten descriptors, including mixture descriptors and both pure phenol and eluent descriptors. Pure phenol descriptors based on information indices (IDDE) contributed significantly; other descriptors include 2D autocorrelations, path counts, and connectivity. For the mixture descriptors, BCUT, edge adjacency, topological indices, and information descriptors were chosen.
Eight descriptors (two relating to the phenol, one to the eluent, and five to the mixture) were selected for model 4 (COOH–MWNTs <8 nm OD). Descriptors of the pure phenol compounds related to BCUT. The main pure eluent descriptor was the structural information content index. Mixture descriptors that contributed to this model were structural indices, edge adjacency indices, topological indices, and molecular properties. Among the mixture descriptors, the octanol–water coefficient appeared to have a significant effect on phenol sorption.
Model 5 (COOH–MWNTs >50 nm OD) included 16 descriptors: 4 pure phenol descriptors and 12 mixture descriptors, including BCUT descriptors, edge adjacency indices, information indices, topological indices, constitutional indices, walk and path counts, and connectivity indices.
Split 2 (T/O/V)
Model 1 (MWNTs 8–15 nm OD) selected five descriptors: two BCUT descriptors, two 3D-MoRSE descriptors, and a WHIM descriptor. The main contributors were the highest eigenvalue of the Burden matrix weighted by Sanderson electronegativity and the 3D-MoRSE signal weighted by van der Waals volume. All of the chosen descriptors were mixture descriptors. It seems that sorption is dependent on the 3D structures of the phenol and eluent when they are mixed in a 1:1 ratio. BCUT descriptors reflect atomic charge, polarizability, and H-bonding ability. 3D-MoRSE descriptors are based on the idea of obtaining information from 3D atomic coordinates by performing the transformation used in electron diffraction studies to prepare theoretical scattering curves.
Model 2 (MWNTs >50 nm OD) selected 11 descriptors. The pure phenol WHIM descriptor was chosen, which measures the second component size directional WHIM index weighted by Sanderson electronegativity. The pure eluent GETAWAY descriptor chosen was the R maximal autocorrelation of lag 3 weighted by Sanderson electronegativity. Multiple mixture descriptors were chosen for model 2: geometrical, WHIM, topological, 3D-MoRSE, GETAWAY, and RDF descriptors. According to this model, desorption is dependent upon the 3D structure of the phenol and interactions within the mixture of compounds. The eluent affects sorption through the 2D structure and the electronegativity of the selected eluent.
Model 3 (helical MWNTs 100–200 nm OD) consisted of eight descriptors: three pure phenol descriptors relating to the 3D-MoRSE calculation and the WHIM descriptor that measures the D total accessibility index. Five mixture descriptors were also chosen, three of which were 3D-MoRSE descriptors, one was a 2D autocorrelation descriptor, and the other was a GETAWAY descriptor. The 3D structures of the phenol and the compounds in the mixture appeared to have a significant effect on sorption in this model.
Model 4 (COOH–MWNT <8 nm OD) consisted of eight descriptors: one 3D-MoRSE descriptor describing pure phenol, and seven mixture descriptors (of 3D-MoRSE and GETAWAY). Both of these types of descriptors capture important molecular 3D information on molecular size, shape, symmetry, and atom distributions with respect to invariant reference frames.
Model 5 (COOH–MWNT >50 nm OD) consisted of 13 descriptors: two pure phenol descriptors characterized by RDF and 3D-MoRSE, and 11 mixture descriptors relating to topological indices, WHIM, 2D autocorrelations, 3D-MoRSE, GETAWAY, and information indices.
As one can see from Table S1 of the ESM, recovery was higher with COOH-functionalized MWCNTs than with pristine nanotubes. High recovery values were observed for all chlorophenols when COOH-functionalized MWCNTs of <8 nm OD were employed. Recoveries were higher when MWCNTS of <8 nm OD were used than when using MWCNTs of >50 nm OD. These results indicate that small COOH-functionalized MWCNTs are efficient materials for the sorption and desorption of the tested organics.
The best solvent when using MWCNTs of 8–15 nm OD was a mixture of acetone and dichloromethane. For MWCNTs with larger ODs and helical MWCNTs, the best choice was acetone or an acetone/dichloromethane mixture. In most cases, mixtures of solvents were more efficient when COOH-functionalized MWCNTs (either <8 nm OD or >50 nm OD) were employed. Various attractive forces among the solute, solvent, and adsorbent are assumed to be responsible for the sorption–desorption process.
Acetone and dichloromethane are polar aprotic solvents. They can form hydrogen bonds. This feature is important for the solvation of chlorophenols, which are potential hydrogen donors. Both methanol and ethanol are polar protic solvents. They are less suitable solvents for the sorption/desorption of chlorophenols.
It appears that five types of interactions—hydrophobic interactions, π–π bonds, hydrogen bonds, covalent interactions, and electrostatic interactions—are responsible for the adsorption of chlorophenols on a carbon nanotube surface. Analysis of the results obtained using the DFT and SPR approaches indicates that increasing the chlorine content of the chlorophenol increases the binding activity, in agreement with Balamurugan’s findings . Chlorophenols contain both an –OH group (an electron-donating group) and chloride (an electron-withdrawing group), which both contribute to the overall binding ability of the molecule. By introducing an appropriate solvent, more electron-activating groups can be made available for bonding. The binding of chlorine or an -OH group to a phenol ring often occurs at the ortho or para position. This behavior is indicative of where binding occurs on the aromatic ring of a phenol.
Comparison of all the RF models highlighted the regular occurrence of several types of descriptors that were correlated with the experimental endpoints (SI2 in the ESM). The most popular descriptors were mixture descriptors related to electronegativity, topological and informational effects, and dipoles/polarizability. Dipole and polarizability descriptors reflect dispersion forces that interfere with the transition of solute molecules (chlorophenols) into the eluent. Topological and informational descriptors reflect features of phenol substitution. Analysis also demonstrated considerable influences of the electronegativity and polar substituents. As a rule, many polar solutes tend to show good solubility. These findings agree with the works of Lin et al. , Irving et al. , Tournas et al. , and Gianozzi et al. .
The experimental study yielded high recovery values for all of the investigated chlorophenols when COOH-functionalized MWCNTs with outer diameters of <8 nm were employed for sorption. These experimental results suggest that MWCNTs are an efficient material for sorption and desorption activities. The identification of components that significantly affect the sorption–desorption of phenols on/from MWCNTs should help to elucidate an inexpensive and rapid method of removing chlorophenols from water sources. Such a method should lead to improved water treatment, reducing the amount of chlorophenols from by-products, and reduce the human consumption of these contaminants and the long-term exposure of humans to high levels of them.
The results obtained from the DFT calculations performed in this work underline the most important physical features involved in the adsorption of chlorophenol derivatives on MWCNTs. A noncovalent interaction between the benzene ring and the nanotube is the dominant adsorption mechanism, whereas charge transfer from the functional groups has only a secondary effect. The calculated binding energies and equilibrium distances point to physical adsorption.
In this work, we utilized a novel SPR modeling methodology to build classification models for predicting various properties of mixture and regular descriptors that characterize the recovery of chlorophenols by different eluents. Random forest models were applied to identify components that influence desorption at the intermolecular level. However, the traditional linear models we derived did not adequately describe the intermolecular interactions that take place amongst phenols and eluents.
Five SPR models (one per type of MWCNT) were developed and validated, and they reliably described features of the intramolecular interactions. Based on an analysis of descriptor contributions, we found that descriptors relating to electronegativity, topological and informational effects, and dipoles/polarizability made significant contributions to the recovery in each model.
In the approach adopted here, we assumed that the chlorophenols and eluents interact as mixtures which can be characterized by mixture-weighted descriptors. This procedure provides a simple approach that allows the accurate characterization of such mixtures.
The authors thank the National Science Foundation for financial support (NSF EPSCoR # 362492-190200-01\NSFEPS-0903787 and NSF CREST grant HRD # 1547754).
Compliance with ethical standards
Conflict of interest
The authors declare that they have no conflict of interest.
- 4.Xing L, Liu H, Giesy JP, Zhang X, Yu H (2012) Probabilistic ecological risk assessment for three chlorophenols in surface waters of China. J Environ Sci 24(2):329–334. doi:10.1016/S1001-0742(11)60779-1
- 6.Selvam NCS, Narayanan S, Kennedy LJ, Vijaya JJ (2013) Pure and mg-doped self-assembled ZnO nanoparticles for the enhanced photocatalytic degradation of 4-chlorophenol. J Environ Sci 25(10):2157–2167. doi:10.1016/S1001-0742(12)60277-0
- 8.AfTSaD Registry (1999) Public health statement: chlorophenols. Public Health Service, U.S. Department of Health and Human Services, AtlantaGoogle Scholar
- 9.Scow K, Goyer M, Perwak J, Woodruff C, Saterson K, Payne E, Wood M (1982) An exposure and risk assessment for chlorinated phenols: 2-chlorophenol, 2,4-dichlorophenol, 2,4,6-trichlorophenol. Office of Water Regulations and Standards, Washington, DCGoogle Scholar
- 11.US EPA (2014) Priority pollutant list. United States Environmental Protection Agency, Washington, DCGoogle Scholar
- 17.Cantalini C, Valentini L, Armentano I, Lozzi L, Kenny JM, Santucci S (2003) Sensitivity to NO2 and cross-sensitivity analysis to NH3, ethanol and humidity of carbon nanotubes thin film prepared by PECVD. Sensors Actuators B 95:195–202. doi:10.1016/S0925-4005(03)00418-0
- 20.Balamurugan K, Subramanian V (2013) Adsorption of chlorobenzene onto (5,5) armchair single-walled carbon nanotube and graphene sheet: toxicity versus adsorption strength. J Phys Chem C 117(41):21217–21227. doi:10.1021/jp403646h
- 23.Sizochenko N, Leszczynski J (2016) Review of current and emerging approaches for quantitative nanostructure–activity relationship modeling: the case of inorganic nanoparticles. J Nanotoxicol Nanomed 1(1):1–16. doi:10.4018/JNN.2016010101
- 25.Xu L, Ball JW, Dixon SL, Jurs PC (1994) Quantitative structure–activity relationships for toxicity of phenols using regression analysis and computational neural networks. Environ Toxicol Chem 13(5):841–851. doi:10.1002/etc.5620130520
- 29.Gołębiowski M, Stepnowski P, Leszczynska D (2017) Application of carbon nanotubes as solid phase extraction sorbent for analysis of chlorophenols in water samples. Chem Pap. doi:10.1007/s11696-016-0098-z
- 30.Sizochenko N, Majumdar D, Roszak S, Leszczynski J (2016) Application of quantum mechanics and molecular mechanics in chemoinformatics. Handbook of computational chemistry. Springer, Dordrecht. doi:10.1007/978-94-007-6169-8_52-1
- 33.Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Scalmani G, Barone V, Mennucci B, Petersson GA, Nakatsuji H, Caricato M, Li X, Hratchian HP, Izmaylov AF, Bloino J, Zheng G, Sonnenberg JL, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Vreven T, Montgomery JA Jr, Peralta JE, Ogliaro F, Bearpark MJ, Heyd J, Brothers EN, Kudin KN, Staroverov VN, Kobayashi R, Normand J, Raghavachari K, Rendell AP, Burant JC, Iyengar SS, Tomasi J, Cossi M, Rega N, Millam NJ, Klene M, Knox JE, Cross JB, Bakken V, Adamo C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Martin RL, Morokuma K, Zakrzewski VG, Voth GA, Salvador P, Dannenberg JJ, Dapprich S, Daniels AD, Farkas Ö, Foresman JB, Ortiz JV, Cioslowski J, Fox DJ (2009) Gaussian 09. Gaussian, Inc., WallingfordGoogle Scholar
- 34.Tournas F, Charlier JC (2005) Ab initio study of benzene adsorption on carbon nanotubes. Phys Rev B 71(16):165421. doi:10.1103/PhysRevB.71.165421
- 35.Coleman WF, Arumainayagam CR (1998) Hyperchem 5 (by Hypercube, Inc.). J Chem Educ 75(4):416. doi:10.1021/ed075p416
- 36.Todeschini R, Consonni V, Mauri A, Pavan M (2004) Dragon 5.1. Milano Chemometrics and QSAR Research Group, MilanoGoogle Scholar
- 38.Brüggemann R, Carlsen L (2006) Partial order in environmental sciences and chemistry. Springer, BerlinGoogle Scholar
- 41.Eigenvector Research, Inc. (2014) PLS Toolbox 7.8.2. Eigenvector Research, Inc., WenatcheeGoogle Scholar
- 42.The MathWorks, Inc. (2014) MATLAB version 8.3. The MathWorks, Inc., NatickGoogle Scholar
- 44.Gramatica P (2007) Principles of QSAR models validation: internal and external. QSAR Comb Sci 26(5):694–701. doi:10.1002/qsar.200610151
- 49.Tournas F, Latil S, Heggie MI, Charlier JC (2005) Pi stacking interaction between carbon nanotubes and organic molecules. Phys Rev B 72(7):075431. doi: 10.1103/PhysRevB.72.075431