  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 nanotube's properties. This
is essential for its use as an analytical tool to optimize the growth process
for future applications.
