Anomalous pressure dependence of Raman frequencies of carbon nanowires encapsulated in carbon nanotubes has been recently reported. Two hypotheses have been proposed to explain this phenomenon in linear carbon chains: softening of a carbon bond with pressure or charge transfer to the chain. However, carbon chains bend easily under stress, although stable structures under these conditions have yet to be discovered. In this study, we model linear and bent carbon nanowires under compression, including both stable and metastable structures. The structures, electronic properties, and vibrational frequencies are obtained through first-principles calculations within density functional theory. We find that polyyne, the dimerized linear ground-state structure of carbon chains at zero strain, is not stable under compression for an infinite carbon chain. Instead, the chain transforms into two possible configurations, a previously unknown three-dimensional helical shape or a two-dimensional sinusoidal shape. These structures can be modeled using an analytical atomistic force-constant model or with a continuum approach. In the continuum approach, an eigenvalue wave equation describes the energy and geometry of the chain. Moreover, this equation produces excited (metastable) structural states and can be applied to other one-dimensional systems. The wave equation formulation indicates that the much-pursued concept of Young's modulus in one-dimensional chains is ill-defined. Finally, the Raman anomaly under compression is not observed within the atomistic force-constant model contrary to assumptions in the literature. Instead, this anomaly can be understood using a model in which charge transfer between the nanotube and the nanowire occurs upon contact.
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