ABSTRACT
Figure 1.1 Covalent (a) and noncovalent (b) functionalization of carbon nanotubes.First problem arising in modeling the noncovalent interactions is usually the choice of an appropriate method of calculation. A correct description of the p-p interaction between carbon surfaces and planar organic molecules requires the use of methods capable to properly describing the effects of the electron correlation. The second-order many body perturbation theory (MP2) [30] is the lowest-order ab initio method that can handle the electron-correlation problem but currently it cannot be widely applied to larger molecular systems including carbon nanotubes
due to computer limitations. An alternative to the MP2 method is the density functional theory (DFT). We have analyzed the performance of a wide range of the density functional methods (including pure, hybrid, meta-hybrid, and dispersion-corrected methods) in predicting the structures and the interaction energies of complexes of the carbon nanotubes and graphene with neutral and charged molecules. The analysis has demonstrated that the binding energies calculated with the pure DFT methods (LDA or GGA) for p-p stacking configurations are underestimated, whereas the dispersion-corrected methods (DFT-D) overestimate them. At the same time, the new-generation meta-hybrid functionals (M05-MN12) have been found to produce very accurate interaction energies and geometries of the complexes as compared with the results obtained with the MP2 method. It is important to mention that the M05-MN12 methods are computationally much less expensive than the ab initio MP2 method.Another important issue that arises in computational studies of complexes involving carbon systems (nanotubes) is the selection of appropriate models for the carbon surfaces. Generally there are two different approaches. In the first the whole carbon nanotube with the appropriate chirality (with or without periodic boundary conditions) is used in the calculation and in the second only a part of the nanotube surface is used. Usually this part of the surface is cut from the whole nanotube and terminated with hydrogen atoms. The model created this way is usually a large bent aromatic molecule. Each of the two approaches has some advantages and limitations. The use of the whole nanotube allows for performing a full geometry optimization but it is limited to small-diameter nanotubes, as the number of atoms and, conversely, the computational resources needed in this case dramatically increase with the increase of the nanotube diameter. As a result, this approach has been only used to study small-diameter nanotubes. The second approach is free of this limitation and may be applied to any nanotube but the size of the fragment of the nanotube surface used in the calculation needs to be carefully selected to provide an appropriate representation of the system. As edges of the surface fragment are terminated with hydrogen atoms, this can alter some properties of the system. For example, in the calculation of the interaction energy of a complex involving a nanotube the size of the nanotube fragment used in the
calculation should be large enough to exclude a direct contact between the interacting molecule and the terminal hydrogens and with the peripheral carbon atoms of the fragment.An important role of the quantum-chemical calculations is to provide interaction parameters for the nanotube carbon atoms for the use in molecular dynamics (MD) simulations of the carbon systems. It has been shown that the accuracy of these parameter can be enhanced by placing a small negative charge (–0.01e) on each nanotube carbon. This significantly improves the agreement between the DFT and MD interaction energies for charged molecules interacting with single-wall carbon nanotubes (SWCNTs) [23]. The force-field parameters for the nanotube atoms, which are derived from the quantum-mechanical calculations, show some superiority over the standard MD parameters particularly in simulations of SWCNT hybrids with charged organic molecules. Thus these parameters can be recommended for MD calculations of nanotube systems. 1. Methods
In this section, we briefly discuss the ability of different computational approaches to correctly predict the structures and the interaction energies of noncovalent complexes involving carbon systems. 1..1 The Hartree-Fock MethodIt is known that the Hartree-Fock (HF) method does not account for the dispersion interaction [21] and it is unable to describe the stacked structures of molecules placed on the nanotube and graphene surfaces. Due to this deficiency, the HF investigations of the noncovalent interactions in complexes involving carbon nanotubes are very limited. Das et al. [10] studied complexes between nucleic acid bases (NAB) and an armchair (5,5) SWCNT and showed that the HF method is unable to reproduce the stacked structure of the NAB-nanotube complex. The HF geometry optimization of the complex converged to an unrealistic almost perpendicular structure shown in Fig. 1.2.
