COMPUTATIONAL STUDIES OF THE DERIVATIVES OF FULLERENES AND CARBON NANOTUBES

Abstract

Carbon exists in different allotropic forms such as graphite, diamond, fullerenes and carbon nanotubes. With the discovery of fullerenes and carbon nanotubes, a new branch of science called nanoscience was emerged. Fullerenes and carbon nanotubes are molecules which can encapsulate various species due to the vacant space available inside. Endohedral complexes of fullerenes and carbon nanotubes have taken wide attention of the scientific community during last few decades due to their wide applications in various fields. These complexes are mainly stabilized by the dispersive interactions between the guest and the host species. The endohedral complexes of fullerenes and carbon nanotubes can be diamagnetic or paramagnetic depending on the nature of the guest. Earlier studies on endohedral complexes of fullerenes and carbon nanotubes provided the details on the structure, stability and properties of some of the complexes in which paramagnetic atoms are trapped inside the cavity of fullerenes. One of the most remarkable findings of those studies is that in N@C60, the encapsulated nitrogen atom retained its atomic spin. However, information on spin-spin coupling, spin polarization and spin density transfer in endohedral fullerene dimers, endohedral heterofullerenes and endohedral heterofullerene dimers are lacking. Therefore, it is interesting to know how the spins of atomic nitrogen present inside adjacent cages of dimers interact and how the heteroatom of cage affects the interactions between guest species. An attempt is also made to understand the spin-spin coupling, spin polarization and spin density transfer in the complexes of carbon nanotubes and its BN analogue. The present thesis consists of seven chapters. In chapter 1, introduction, synthesis and applications of fullerenes and their derivatives are discussed. The structure, stability and properties of various endohedral complexes of fullerenes and heterofullerenes are reviewed. The host-guest interactions in the above complexes as well as the spin-spin coupling between their components are discussed. A brief review on the properties of various derivatives of carbon and boron nitride nanotubes is given. Chapter 2 briefly reviews the computational methods used in the present work. Various computational methods such as Hartree-Fock, post Hartree-Fock and density functional theoretical methods are briefly explained. It also overviews basis sets, time-dependent density functional methods and spin broken symmetry approach. The chapter also provides details of spin polarization parameter. ii In chapter 3, the results of the density functional theoretical calculations on the structure, stability and properties of nitrogen atom encapsulated fullerene derivatives obtained at different levels are discussed. For this purpose, N@C60, N@C59N and their respective dimers are considered which are important in the context of spin-spin interactions between the guest and the host as well as that between guest species. For the most stable spin states of each of the above complexes, spin density transfer and spin–spin coupling between different components are investigated. The study also focuses on spin polarization and spin degeneracy of the complexes. The analysis of spin density showed that the encapsulated nitrogen retained its atomic state in N@C60 and N@C59N. Depending on the multiplicity of N@C59N, the unpaired electrons of the encapsulated nitrogen are coupled with those of the cage antiferromagnetically or ferromagnetically. The study also showed that the complex (N@C60)2 can exist in two isoenergetic spin states, namely, 7[(N@C60)2] and 1[(N@C60)2]. In the former, the encapsulated nitrogens are ferromagnetically coupled, whereas they are coupled anti-ferromagnetically in the latter. A similar coupling between the guest species occurs in the nitrogen analogues 7[(N@C59N)2] and 1[(N@C59N)2] which indicates that the nitrogen atom on the surface does not assist any spin interactions between the components of the complexes. On encapsulating nitrogen atom inside fullerene derivatives, the energy gap between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) (ΔEHOMO-LUMO) of the latter did not change. It was also revealed that the encapsulation of nitrogen atom inside C60, C59N and their respective dimers is thermodynamically feasible. The thermodynamic feasibility of the formation of (N@C60)2 and (N@C59N)2 from their respective monomer units is also discussed. Considering the fact that boron atom is also reactive and paramagnetic, boron atom encapsulated complexes of C60, C59B, and C59N at B3LYP/6-311G* and B3LYP-GD2/6-311G* are investigated in chapter 4. In B@C60, the guest atom is located at the centre of host cage. The study showed that the complexes B@C59B and B@C59N are stable in their singlet and triplet states. The electronic properties such as electron affinity (VEA), ionization energy (VIE), and ΔEHOMO-LUMO of the complexes are calculated. On encapsulating boron, ΔEHOMO-LUMO of C60, C59B, and C59N is either decreased or increased depending upon the spin states of the resultant complexes. The transfer of spin density and spin–spin coupling between the guest and the host are examined. The study revealed that ferromagnetic core@shell spin coupling occurs between the host and the guest species of the complexes B@C59B and B@C59N in their triplet state without the transfer of spin density. The spin polarization in the complexes B@C60, B@C59B and B@C59N are also discussed. The thermodynamics of encapsulation of boron atom iii in C60, C59B and C59N is examined based on the values of change in Gibbs free energy and change in enthalpy. It suggested that the encapsulation of boron atom is thermodynamically feasible. In chapter 5, the dimer of endohedral fullerene derivatives (B@C59B)2, (B@C59N)2, (N@C59B)2, (B@C59N–N@C59B) and (B@C60)2 are investigated using dispersion corrected density functional theory. Several spin states of these complexes are considered and their stable spin states are reported. For 1[(B@C59B)2] and 1[(B@C59N–N@C59B)], the encapsulated atoms are located near the inner surface of the host cages, in contrast to other spin states where they are positioned at the centre of the cages. In complexes 1[(B@C59N)2], 3[(B@C59N)2], 7[(N@C59B)2], 1[(B@C60)2] and 3[(B@C60)2] the guest atoms are found to be at the centre of the host cages. The spin polarization and the transfer of spin density between the components of the complexes for different stable spin states are analyzed. Based on the spin states of the complexes, the spin–spin interaction is found to be either ferromagnetic or anti-ferromagnetic. Unlike other complexes, in 1[(B@C59B)2] and 1[(B@C59N–N@C59B)], the spin density is transferred from the guest to the host followed by anti-ferromagnetic coupling between the monomers. The complexes are found to be fully spin polarized, partially spin polarized or spin degenerate depending upon their spin states. The thermodynamic feasibility of formation of the complexes is also examined. The vertical electron affinity, vertical ionization energy and ΔEHOMO-LUMO as well as the dipole moment of the above systems are determined. The singlet state of the heterodimer (B@C59N–N@C59B) showed high polarity due to the slight rotation along the dihedral angle ϕNCCB. To know the effect of confinement due to different nanotubes, the nitrogen encapsulated complexes of carbon nanotube (CNT), boron nitride nanotubes (BNNT) and their respective dimers are investigated in chapter 6. The study showed that the complexes 4[N@CNT] and 4[N@BNNT] are stable due to the van der Waals interactions between the guest and the host species. In these complexes, the guest atoms are located at the center of the host nanotube. Similar to 4[N@C60], nitrogen atom retains its atomic spin inside CNT and BNNT. The complexes (N@CNT)2 and (N@BNNT)2 are stable in their isoenergetic singlet and septet states. In stable states of (N@CNT)2 and (N@BNNT)2, the guest atoms are shifted towards each other from the center of respective host nanotubes. The effect of the position of nitrogen atom on the stability is also discussed. The analysis of spin density for (N@CNT)2 revealed that the spins of guest nitrogen atoms are antiferromagnetically and ferromagnetically coupled in its singlet and septet states, respectively. Similar results are obtained for (N@BNNT)2. The study also indicated spin polarization in 4[N@CNT] and 4[N@BNNT]. The singlet states of iv (N@CNT)2 and (N@BNNT)2 are spin degenerate whereas their septet states are spin polarized. On encapsulating nitrogen atom, electronic properties such as VEA, VIE and ΔEHOMO-LUMO of the host nanotubes remained the same although VEA of BNNT and (BNNT)2 are significantly reduced. The effect of diameter of nanotubes on the spin-spin coupling between the encapsulated nitrogen atoms inside adjacent nanotubes is also examined. It is revealed that the cavity size of the nanotube does not affect the spin-spin coupling between nitrogen atoms present in adjacent CNTs. The spin polarization is also not much affected by decreasing the cavity size of CNTs.