The geometry of small fullerene cages: C20 to C70

Abstract

The ground-state structures of small fullerenes below C70 were determined by tight-binding molecular-dynamics total energy optimization. An efficient simulated annealing scheme was used to generate closed, hollow, spheroidal cage structures for all even-numbered carbon clusters from C20 to C70. As a general trend, fullerenes prefer geometries which separate the pentagonal rings as far apart as possible. Except for C60, C70, and C50, most fullerenes have relatively low symmetries.

Theoretical and Quantitative Structural Relationship Study on Fullerenes Polarizabilities on the basis of Monopole-Dipole Interactions Theorem

“…26,27 The molecular structures were taken to be the predicted results by Zhang and co-workers with respect to the molecular dynamics energy optimization. 26,[28][29][30] The isotropic mean polarizabilities calculated for C 60 and C 70 are comparable to experimental data from solid film studies and quantum mechanical calculations. 26,[31][32][33][34][35][36][37][38][39][40][41][42][43] Polarizability tensors were calculated for conducting ellipsoidal shells which have the same moment of inertia tensor as the corresponding fullerenes by Shanker and Applequist.…”

“…[59][60][61] Therefore, it is interesting to investigate theoretically this effect from the viewpoint of AMDI (in Å 3 , Atom monopole-dipole interaction theory; α 1 to α 3 and α), Ellipsoid (in Å 3 , α 1 to α 3 and α) and semi-axes a,b,c of a thin ellipsoidal shell of uniform thickness (in Å, abc α 1 to α 3 ) for C 20 through C 300 . 26 Study on the comparison of the AMDI results with the conducting ellipsoid and monopole interaction treatments by Olson-Sundberg AMDI theory 27 , Zhang et al [28][29][30] , Shanker and Applequist studies. [26][27][28][29][30] , had given some insight into the behavior of the AMDI model.…”

“…26 Study on the comparison of the AMDI results with the conducting ellipsoid and monopole interaction treatments by Olson-Sundberg AMDI theory 27 , Zhang et al [28][29][30] , Shanker and Applequist studies. [26][27][28][29][30] , had given some insight into the behavior of the AMDI model. 26 The near parallel behavior of the three models is consistent with the major role of charge mobility in all three.…”

“…The results were extended for other empty fullerenes up to C 300 . 46,58 In this study, the relationship between the number of carbon atoms of fullerenes (C n ) index and polarizability of the fullerenes are presented on the basis of the Olson-Sundberg AMDI theory 27 , Zhang et al [28][29][30] , Shanker and Applequist studies. [26][27][28][29][30] Here, were extended the calculation of the parameters concern to atom monopole-dipole moment such as AMDI (in Å 3 , Atom monopoledipole interaction theory; α 1 to α 3 and α), Ellipsoid (in Å 3 , α 1 to α 3 and α) and semi-axes a,b,c of a thin ellipsoidal shell of uniform thickness (in Å, abc α 1 to α 3 ) for C 120 through C 300 , 6-15.…”

“…26 The results of the polarisability calculations were substantially smaller than the AMDI-polarizabilities for the smaller fullerenes, but the two calculations tend to converge for the larger molecules. [26][27][28][29][30][34][35][36][37][38][39][40][41][42][43][44] Graph theory has been found to be a useful tool in assessing the QSAR (Quantitative Structure Activity Relationship) and QSPR (Quantitative Structure Property Relationship). [45][46][47][48][49][50][51][52][53] Numerous studies in the above areas have also used what are called topological indices (TI).…”