  We integrated full core-hole density functional theory with Franck-Condon
calculations, considering Duschinsky rotation, to simulate
vibrationally-resolved C1s X-ray photoelectron spectra (XPS) of eight linear
alkanes, from methane to octane (C$_{n}$H$_{2n+2}$, $n$=1--8). Results align
excellently with experimental absolute binding energies and profiles. The
spectrum of ethane serves as a ``spectral seed'', with each longer alkane's
atom-specific spectrum displaying similar characteristics, albeit with shifts
and slight intensity adjustments. Detailed assignments clarify the distinct
spectra in short alkanes ($n$=1--4) and their stabilization in long alkanes
($n$=5--8). Carbons are classified as central or distal (C$_1$ and C$_2$), with
central carbons contributing nearly identically to the lowest-energy feature A,
while distal carbons contribute to the second lowest-energy feature B (both are
0-0 transitions). Increasing molecule size adds more central carbons, enhancing
feature A and weakening feature B. Our analysis identifies two dominant
Franck-Condon-active vibrations: C$^*$--H stretching ($\sim$3400-3500
cm$^{-1}$) and bending ($\sim$1400-1500 cm$^{-1}$) modes. Structural analysis
shows that core ionization minimally affects alkane geometry, less than in ring
compounds from previous studies. This work extends our protocol from rigid ring
compounds to flexible molecules, contributing to building a high-resolution
theoretical XPS library and enhancing the understanding of vibronic coupling.
