Computational Study On The Nonclassical Small Fullerene

In the present paper, semi-empirical, Hartree-Fock, and density functional theory (DFT) calculations were performed on nonclassical small fullerenes Cn (n=26,30-50) to gain insight into the relationship between their structures and stability. This paper includes the following two parts:1. The complete set of 2333 isomers of C26 fullerene composed of square, pentagonal, hexagonal and heptagonal faces together with some non-cage structures is investigated at the semi-empirical, Hartree-Fock and density functional theory (DFT) levels. For the singlet states, a non-classical isomer C26-10-01 with a square embedded is predicted by the DFT method as the lowest energy isomer, followed by the sole classical isomer C26-00-01. Further explorations reveal that the electronic ground state of C26-10-01 is triplet state in C5 symmetry, while that of C26-00-01 corresponds to its quintet in D3h symmetry. Both the total energies and nucleus independent chemical shift values at DFT level favor the classical isomer. It is found that both C26-00-01 and C26-10-01 possess high vertical electron affinity. The addition of electron(s) to C26-10-01 increases its aromatic character and encapsulation of Li atom into this cage is highly exothermic, indicating that it may be captured in the form of derivatives. To clarify the relative stabilities at elevated temperatures, the entropy contributions are taken into account based on the Gibbs free energy at the B3LYP/6-311+G* level. C26-10-01 behaves thermodynamically more stable than the classical isomer over a wide range of temperatures related to fullerene formation. The IR spectra of these two lowest energy isomers are simulated to facilitate their experimental identification.2. To clarify the structures and stability of small fullerenes is crucial for understanding the growth mechanism of fullerenes and the stabilization mechanisms of their derivatives. A systematic survey is performed on small fullerenes from C30 to C50. The calculations demonstrate that most structures possess closed-shell electronic ground states, but a few cages exhibit triplet ground states. Generally, the classical isomers follow the pentagon adjacency penalty rule and possess the lowest energies. However, many square-containing structures behave competitively with their classical counterparts in chemical stability. Among them, C32-20-15 and C46-10-1 are predicted to be the lowest-energy structures in their peer isomeric set; C30-10-1 is essentially isoenergetic with its nearest classical rival. Meanwhile, many non-classical cages with a heptagon are energetically more favorable than their classical analogues with fewer pentagon-pentagon bonds. Further inspection reveals that non-classical structures incorporating one or two squares dominate the low-lying population of C30, C32, and C34, whereas the one-heptagon-containing cages become increasingly competitive relative to their classical analogues when the fullerene size increases. It is interesting that most non-classical structures with one or two squares exhibit unusually large HOMO-LUMO gaps, implying their unique kinetic stability. The nucleus independent chemical shift, the maximum and average pyramidization angle, and the sphericity parameter are also introduced to evaluate their stability. The relative thermodynamical stability is also evaluated in terms of the Gibbs function for C30, C32, and C46. The NMR and IR spectra of the 18 lowest-energy isomers are simulated and presented to facilitate future experimental identification.