| Classical fullerene can be defined as a closed-cage molecule containing only pentagonal and hexagonal rings. C60 was discovered by Kroto in 1985, and it was supposed to be of Ih symmetry. Interest in fullerenes was prompted by The discovery. In Chapter 1, on The bases of The topological structures of The Three big classes of icosahedral fullerenes: (1)Cn( Ih, n = 60h2; h = 1, 2, …), (2)Cn(Ih, n = 20h2; h = 1, 2, …) and (3) Cn(I, n = 20( h2 + hk + k2), h > k; h, k = 1, 2, …), we obtained Theoretically The (13)C NMR spectra of all The icosahedral (Ih and I) fullerenes. If (h –k)/3 for The Third type or h/3 for The second type is a non-integer, we are sure There are one set of 20 atoms lying on The Threefold axes, oTherwise, There are no atoms lying on Them. In Chapter 2, on analyzing The topological structures of The following tetrahedral ( Td , Th and T ) fullerenes: (1) Cn ( h , h; -i , i), Cn ( h ,0 ; -i ,2 i), Cn ( 2 h+ i , -h + i ; i , i), Cn ( h -i , h + 2i ; -i ,2 i )and Cn ( h , i ;0 , i) for Td symmetry; (2) Cn ( h , k ; k , h) , Cn ( h , k ; -h -k , k)and Cn ( h , k ; -h , h + k) for Th symmetry; (3) Cn ( h , k ; i , j) for T symmetry, we obtained The formulas for Their (13)C NMR spectrum line counts and relative intensities of each line of all The tetrahedral fullerenes Theoretically. For fullerene wiTh T symmetry, ( h -k) /3 and (i -j) /3 are boTh integers, There are no atoms lying on The Three fold axes; if one of Them is an integer, one set of four atoms lying on Them; or neiTher of Them is an integer, two sets of eight atoms lying on Them. The rule is also true for fullerene wiTh Th or Td symmetry. We also pointed out The relations between icosahedral fullerenes Cn ( h ,0 ; 0 , h), Cn ( h , h; -h ,2 h), and Cn ( h , k ; -k , h + k) and The tetrahedral fullerenes. In Chapter 3, similar to The discussions of Chapter 1, we obtained The infrared and Raman active modes for all The icosahedral (Ih and I) fullerenes Theoretically. In Chapter 4, similar to The discussions of Chapter 2, we obtained The infrared and Raman active modes for all The tetrahedral (Td , Th and T ) fullerenes Theoretically. In Chapter 5, The electronic structures of The tetrahedral (Td) fullerenes Cn with n ≤3600 were calculated in the Hückel approximation by means of group theory, and the frontier electronic energy levels were reported. Therefore their electronic spectra were discussed by use of the values of frontier energy levels. We found the highest occupied molecular orbitals are all open for the fullerenes Cn(h, h; –(3q + 1), 3q + 1), Cn(h, h; –(3q + 2), 3q + 2), Cn(3p + 1, 3q + 1; 0, 3q + 1), Cn(3p + 2, 3q + 2; 0, 3q + 2), Cn(3p + 1, 3q; 0, 3q), Cn(3p + 2, 3q; 0, 3q); all closed for the following fullerenes Cn(2h + i, –h + i; i, i), Cn(h, h; –3q, 3q), Cn(3p, 3q; 0, 3q); all pseudo-closed for the following fullerenes Cn(3p, 3q + 1; 0, 3q + 1), Cn(3p, 3q + 2; 0, 3q + 2); and pseudo-closed or open depending on p and q for the following fullerenes Cn(3p + 2, 3q + 1; 0, 3q + 1), Cn(3p + 1, 3q + 2; 0, 3q + 2). The work provides the theoretical evidence on the discovery of new fullerenes with I , Ih, T-d , Th or T symmetry. |
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