Recently, the novel system of linear carbon chains inside of double-walled carbon nanotubes has extended the length of $sp^1$ hybridized carbon chains from 44 to thousands of atoms [L. Shi et al., Nat. Mater. 15, 634 (2016)]. The optoelectronic properties of these ultra-long chains are poorly described by current theoretical models, which are based on short chain experimental data and assume a constant environment. As such, a physical understanding of the system in terms of charge transfer and van der Waals interactions is widely missing. We provide a reference for the intrinsic Raman frequency of polyynes in vacuo and explicitly describe the interactions between polyynes and carbon nanotubes. We find that van der Waals interactions strongly shift the Raman frequency, which has been neither expected nor addressed before. As a consequence of charge transfer from the tube to the chain, the Raman response of long chains is qualitatively different from the known phonon dispersion of polymers close to the $Gamma$-point. Based on these findings we show how to correctly interpret the Raman data, considering the nanotubes properties. This is essential for its use as an analytical tool to optimize the growth process for future applications.
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