The study of nanostructures’ vibrational properties is at the core of nanoscience research. They are known to represent a fingerprint of the system as well as to hint the underlying nature of chemical bonds. In this work, we focus on addressing how the vibrational density of states (VDOS) of the carbon fullerene family (C_n: n = 20 → 720 atoms) evolves from the molecular to the bulk material (graphene) behavior using density functional theory. We find that the fullerene’s VDOS smoothly converges to the graphene characteristic line-shape, with the only noticeable discrepancy in the frequency range of the out-of-plane optic (ZO) phonon band. From a comparison of both systems we obtain as main results that: (1) The pentagonal faces in the fullerenes impede the existence of the analog of the high frequency graphene’s ZO phonons, (2) which in the context of phonons could be interpreted as a compression (by 43%) of the ZO phonon band by decreasing its maximum allowed radial-optic vibration frequency. And 3) as a result, the deviation of fullerene’s VDOS relative to graphene may hold important thermodynamical implications, such as larger heat capacities compared to graphene at room-temperature. These results provide insights that can be extrapolated to other nanostructures containing pentagonal rings or pentagonal defects.

纳米结构振动特性的研究是纳米科学研究的核心。众所周知，它们代表了系统的指纹，并暗示了化学键的潜在性质。在这项工作中，我们专注于解决碳富勒烯家族 (C _n :  n = 20 → 720 个原子）使用密度泛函理论从分子演变为散装材料（石墨烯）行为。我们发现富勒烯的 VDOS 平滑地收敛到石墨烯的特征线形，在平面外光学 (ZO) 声子带的频率范围内唯一明显的差异。从两个系统的比较中，我们得到的主要结果是：（1）富勒烯中的五边形面阻碍了高频石墨烯的 ZO 声子类似物的存在，（2）在声子的背景下可以解释为通过降低 ZO 声子带的最大允许径向光学振动频率来压缩（43%）。3）因此，富勒烯的 VDOS 相对于石墨烯的偏差可能具有重要的热力学意义，例如与室温下的石墨烯相比具有更大的热容量。这些结果提供了可以外推到其他包含五边形环或五边形缺陷的纳米结构的见解。