Raman Spectrum of carbon chains: How to identify the vibrational modes
When you perform a IR or Raman calculation, the primary step is the diagonalization of the mass-weighted Hessian:

$$
\begin{align}
H_{ij,ab}^{\mathrm{mw}} &amp;= \frac{1}{\sqrt{m_{i}m_{j}}} \frac{\partial^{2} E}{\partial a_{i} \partial b_{j}} \\
\mathbf{Hq} &amp;= \lambda \mathbf{q}
\end{align}
$$

where $H_{ij,ab}^{\mathrm{mw}}$ is a $3N\times3N$ Hermitian matrix, $i,j$ are indices running over the atoms, $m_{i}$ is the mass of atom $i$, and $a,b \in x,y,z$ (the $3N$ Cartesian molecular coordinates). The eigenvalue $\lambda_{i}$, multiplied by some conversion factors, is a frequency in the harmonic oscillator approximation, and the corresponding eigenvector $\vec{q}_{i}$ is the normal mode, the collective atomic displacements, for that frequency.

(A calculation of Raman intensities involves extra work, namely the calculation of $\frac{\partial^{3} E}{\partial \varepsilon_{\alpha} \partial \varepsilon_{\beta} \partial a_{i}}$, but the normal modes are identical.)

Aside from performing literature searches for normal mode frequency assignments on related systems, a good alternative is the visualization of these normal modes. Many outputs from frequency calculations can be opened in Avogadro:



Clicking on a frequency in the right-hand side pane (only IR intensities are displayed) can display both the displacement vectors and an animation of the displacement (see the lower right corner box). Avogadro is able to read this portion of the NWChem output file:


          -------------------------------------------------
          NORMAL MODE EIGENVECTORS IN CARTESIAN COORDINATES
          -------------------------------------------------
             (Projected Frequencies expressed in cm-1)
...
                    7           8           9          10          11          12

 P.Frequency      252.66      366.45      606.76      773.89      790.45      808.06

           1     0.06344     0.00000    -0.02127     0.00000     0.00000     0.00096
           2    -0.10753     0.00000    -0.09540     0.00000     0.00000    -0.00247
           3     0.00000    -0.03639     0.00000    -0.01614     0.01014     0.00000
           4    -0.08820     0.00000    -0.09326     0.00000     0.00000     0.00127
           5     0.02291     0.00000    -0.01064     0.00000     0.00000    -0.00238
           6     0.00000     0.00615     0.00000     0.14073    -0.07465     0.00000
           7    -0.13091     0.00000     0.17533     0.00000     0.00000     0.05512
           8     0.01443     0.00000     0.09744     0.00000     0.00000     0.01777
           9     0.00000     0.19419     0.00000    -0.08894     0.11256     0.00000
          10     0.11294     0.00000    -0.04324     0.00000     0.00000    -0.12834
          11     0.07728     0.00000     0.04956     0.00000     0.00000    -0.02839
          12     0.00000    -0.10132     0.00000    -0.04711    -0.12489     0.00000
          13     0.29675     0.00000    -0.23722     0.00000     0.00000     0.83429
          14     0.12532     0.00000     0.00136     0.00000     0.00000     0.22209
          15     0.00000    -0.33078     0.00000     0.53191     0.69392     0.00000
          16     0.24449     0.00000     0.20104     0.00000     0.00000     0.01418
          17    -0.04794     0.00000    -0.02443     0.00000     0.00000     0.00175
          18     0.00000    -0.37449     0.00000    -0.49495     0.26769     0.00000
          19     0.03319     0.00000    -0.05962     0.00000     0.00000    -0.00066
          20    -0.29762     0.00000    -0.33571     0.00000     0.00000    -0.01410
          21     0.00000     0.25757     0.00000     0.27323    -0.15332     0.00000
          22    -0.06568     0.00000    -0.11340     0.00000     0.00000    -0.00250
          23     0.13575     0.00000    -0.12891     0.00000     0.00000    -0.02550
          24     0.00000    -0.29795     0.00000    -0.17367     0.10673     0.00000
...


So, to find the C-C stretching mode (or any vibration of interest), clicking through the list in Avogadro is more convenient than eyeballing the displacements in the output file. With the advent of accurate computational methods, the assignment of peaks in experimental spectra is usually aided by calculations identical to these. It's even possible to plot the computed spectra with some artificial broadening: