# Raman Spectrum of carbon chains: How to identify the vibrational modes

So I am using NWChem to calculate the raman spectra of C2H2 and C4H4. For example for the first I obtained the following frequencies:

#  freq [ 1/cm]  S [Ang**4/amu]
------------------------------------------------------------
1   644.63        0.0087
2   679.18        0.0076
3   792.83        0.0001
4  2146.53        8.0917
5  3506.05        0.0007
6  3645.57       37.8189


and for example, when comparing with the expected results from http://www.chem.purdue.edu/gchelp/vibs/c2h2.html , I could say that my mode number four corresponds to C-C stretching. So now, when I perform the same calculation for C4H4, I get the following:

#  freq [ 1/cm]  S [Ang**4/amu]
------------------------------------------------------------
1   216.77        2.3873
2   305.29        0.7775
3   548.05        0.8095
4   643.94        1.7042
5   677.47        0.5218
6   700.29        6.8906
7   893.88        0.1890
8   928.98        0.5379
9  1033.68        0.1554
10  1134.09        1.5802
11  1357.84       16.9774
12  1504.93       31.2415
13  1715.33       17.1094
14  2269.08       38.4659
15  3293.55       19.5975
16  3313.05       78.1132
17  3449.94       44.9757
18  3578.50       24.6781


My question is this, how could I identify the vibrational mode corresponding to C-C stretching now? And if I performed the same calculation for C6H6, how could I identify the C-C vibrational mode? Is there a way of identifying what each mode corresponds to? not only in calculation but also in experiments?

thank you

## 1 Answer

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}} &= \frac{1}{\sqrt{m_{i}m_{j}}} \frac{\partial^{2} E}{\partial a_{i} \partial b_{j}} \\ \mathbf{Hq} &= \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:

• I am looking at avogadro.cc/wiki/Spectra , along with some other pages related to avogadro, and there seems to be no way of reading nwchem's output from a raman task. How did you do it? – user2804865 Apr 23 '16 at 4:22
• 1. I used a NWChem IR job, because I couldn't get a Raman job to run for some reason. 2. On the page you've linked, when it says what software is supported, only the latest development versions support Raman intensities, and only for GAMESS. The point I was trying to make is that the NWChem frequencies and normal modes will still be read, which is what you want. If you're interested in Raman intensities, you'll have to match them in the output file directly. – pentavalentcarbon Apr 23 '16 at 14:00
• What o you mean by match them to the output files? How exactly? – user2804865 Apr 23 '16 at 14:22
• If you're interested in Raman spectra, find the frequency/mode you want to identify in Avogadro, then look at the NWChem output file, find that frequency, and read the Raman intensity. – pentavalentcarbon Apr 23 '16 at 14:24
• The problem I am having is with getting the information from nwchem to avogadro. Could you provide a bit more detail on how to get the IR frequencies from nwchem and visualize them on avogadro, please? – user2804865 Apr 23 '16 at 14:28