Isomeric Higher and Smaller Fullerenes: A Profound Enthalpy/Entropy Interplay
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X. ZHAO, Z. SLANINA, AND E. OSAWA Laboratories of Computational Chemistry & Fullerene Science, Department of KnowledgeBased Information Engineering, Toyohashi University of Technology, Toyohashi 441-8580, Aichi, Japan ABSTRACT Computations of isomeric fullerenes are performed at semiempirical and ab initio quantum-chemical levels: C36 , C72 , C8 8 . C36 fullerenes and quasi-fullerenes are computed at the SAM1 level, and then at the B3LYP/6-31G* level. Altogether 598 cages are considered. The SAM1 method is also applied to C72 , i.e., the solitary isolated-pentagon-rule (IPR) structure and several non-IPR isomers. Finally, the complete set of thirty five topologically different IPR isomers of C8 8 is computed. In all the cases, energetics is combined with entropy contributions based on the harmonic-oscillator and rigid-rotator model. Considerable temperature effects on the relative stabilities in the systems are found. Relationships to available observed data are discussed throughout and a good agreement is found. INTRODUCTION Early results from the eighties for small carbon clusters like C4 or C6 have suggested [1,2] that the combined quantum-chemical and statistical-mechanical computations [3] could show some interesting temperature effects also for isomeric fullerenes. This feature was first demonstrated [4,5] on some C 50 and also C20 isomers. Later on, fullerene research
has indeed supplied [6] several sets of isomeric higher fullerenes. At present over twenty stable fullerenes C, have been identified with n varying from 60 to 96. Several such mixtures of fullerene isomers have been computed [7-14] (C76 till C94 ) and an agreement with observations found. Hence, the computations have demonstrated that the presumption of partial, inter-isomeric thermodynamic equilibrium is actually well working. In this report, the combined computational approach is applied to C 36 , C72 , and C88 . COMPUTATIONS The combined computational treatment starts from geometry optimizations. typically with some semiempirical method like [15] SAM1, or still prevailing AM1 and PM3 methods [16,17]. The computations reported here are carried out primarily with the AMPAC program package [18], and also with the MOPAC program [19]. The geometry optimizations are performed with no symmetry constraints in Cartesian coordinates and with analytically constructed potential-energy gradient. In the optimized geometries, the harmonic vibrational analysis is carried out by a numerical differentiation of the analytical potential-energy gradient. The semiempirical isomeric separation energies are further checked through some ab initio calculations. We have used the G94 program package [20] for the purpose. First, the 135 Mat. Res. Soc. Symp. Proc. Vol. 593 © 2000 Materials Research Society
Hartree-Fock (HF) SCF computation was performed with the standard 4-31G basis in the fixed optimized SAM1 geometries, HF/4-31G//SAM1. At the HF/4-31G computational level the stability of the SCF solution was checked (i.e., if it is really a local minimum in wavefunc
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