Molecular interactions, energy frequencies

These symmetry corrections, however, represent only a very first correction. In principle such properties as molecular weight, moment of inertia, and vibration frequency are just as accidental and nonintrinsic from the point of view of molecular interactions. Nevertheless, they can contribute significantly to free energy changes and should be corrected for if a molecular discussion of such changes is to be rigorous, or at least non-speculative. 

In order to minimize effects of nanotube edges in our molecular mechanics calculations we have chosen five unit cells (480 carbon atoms total) of (8,8) CNT. The calculated dependence of the interaction energy between the fullerene C20 and the (8,8) CNT on the fullerene displacement along the CNT axis is shown in Fig. 3. The calculated period of this dependence is a half of the translational period of the Kekule structure (Fig. 1). The small difference between two barriers in Fig. 3 is due to the edge effects. Correspondingly, the frequency of small oscillation of fullerene C20 along the CNT axis near the minimum of potential energy is v 60 GHz. 

As might be expected, the model leads to a great simplification over the calculations required for molecules with a continuous potential energy function, as it enables the analysis to be confined to binary collisions and permits the definition of a collision frequency. Because there is no molecular interaction between collisions, the velocity distributions of two colliding molecules may be assumed to be re-established by the time a second collision occurs between them. Thus a Maxwellian distribution around the local mass velocity may be postulated for the calculation of the mean frequency of collision and the average momentum and energy transported per collision in the nonuniform state of the liquid. 

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