Supplementary Material
Nanostructural organization in carbon disulfide/ionic liquid mixtures:
molecular dynamics simulations and optical Kerr effect spectroscopy
Peng Yang, Gregory A. Voth, Dong Xiao, Larry G. Hines Jr.,
Richard A. Bartsch, and Edward L. Quitevis
Effect of the Gaussian Window Function on Reduced Spectral Densities
Because of the low signal strengths at long delays, noise is present in the long-time tail of
the OHD-RIKES signal of ionic liquids, where the signal at 10 ps is 3 orders of magnitude
weaker than the signal at zero delay (see Figure 8 in article). Moreover, because the RSD is
obtained by applying the Fourier-transform-deconvolution procedure to the reduced
response, noise present in the long-time tail of the signal will be present in the lowfrequency part (0-200 cm-1) of the spectrum. This noise however can be eliminated by
applying a window function to the data prior to performing the Fourier-transformdeconvolution procedure.1 Following Giraud et al.,2 the reduced response is multiplied by a
Gaussian window function w(t) = exp[-(t-t0)2/22], where    /2 2 ,  = 4 ps, and t0 is the
zero delay time. This window gives a spectral resolution of ≈ 9 cm-1.

Figure S1 compares the RSDs obtained with and without a window function for the 25
mol % CS2/[C5mim][NTf2] mixture. For this mixture, application of a window function
reduces the noise without affecting the line shape of the RSD for this mixture. Because of
the strength of the signal in the long-time tail of the OHD-RIKES signal, the noise in the RSD
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without the window function is low. The 10 mol % mixture provides a more stringent test
of the window function because the signal in the long-time tail of the signal for this mixture
is much weaker and therefore noisier that than that of the 25 mol % mixture. Figure S2
shows the RSD obtained with and without the window function for the 10 mol % mixture.
The noise in the RSD without the window function is clearly much greater for the 10 mol %
mixture than for the 25 mol % mixture. Application of the window function therefore has a
much more dramatic effect on the noise in the case of the 10 mol % mixture than in the
case of the 25 mol % mixture.
The RSD with the window function is qualitatively similar to the RSD without the
window function. Without the window function, <> = 64.6 cm-1 and  = 96.3 cm-1,
whereas, with the window function, <> = 66.7 cm-1 and  = 104.3 cm-1. For noisy RSDs,
such as the one shown in Figure S2, application of the window function shifts the RSD to
higher frequencies by ≈ 2 cm-1 and broadens the RSD by ≈ 8 cm-1. This suggests that in the
case of the lower mole fraction mixtures, the true RSDs are probably slightly narrower and
lower in frequency than the ones shown in Figure 10 of the paper for which a window
function was used to reduce the noise. Moreover, the dependence of the width of the CS2
contribution to the RSD on the mole fraction of CS2 is probably stronger than indicated in
Figure 12 and Table 3 of the paper.
2
Figure S1. Reduced spectral density for 25 mol % CS2
mixture without a window function (blue curve) and
with a window function (red curve).
Figure S2. Reduced spectral density for 10 mol % CS2
mixture without a window function (blue curve) and
with a window function (red curve).
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Table S1. CS2/IL RSD Multicomponent Fit Parameters from Additivity Modela,b
Fit
Parameters
CS2 Mol %
0%
10%
15%
20%
25%
100%
CS2 Contribution to RSD
ABL
0
0.00135
0.00722
0.00763
0.03804
0.084
a
0
1.92987
1.95921
1.9975
1.39838
1.14
BL / cm-1
0
11.87637
5.75006
5.67356
8.68992
19.4
AG
0
0.5463
0.87359
0.93838
1.10082
0.21
G / cm-1
0
8.43449
14.08137
15.05522
15.99756
50.2
 / cm-1
0
27.03208
28.02414
27.4261
29.87864
20.3
IL Contribution to RSD
ABL
0.08534
0.06157
0.04032
0.0335
0.01589
0
a
1.18897
1.18897
1.18897
1.18897
1.18897
0
16.75199
16.75199
16.75199
16.75199
16.75199
0
0.14538
0.10488
0.06868
0.05707
0.02707
0
G1 / cm-1
58.09096
58.09096
58.09096
58.09096
58.09096
0
1 / cm-1
12.79986
12.79986
12.79986
12.79986
12.79986
0
0.82212
0.59309
0.38838
0.32274
0.15309
0
85.58099
85.58099
85.58099
85.58099
85.58099
0
30
30
30
30
30
0
0.163
0.11502
0.07532
0.06259
0.02969
0
122.90556
123.21116
123.21116
123.21116
123.21116
0
5
6.22282
6.22282
6.22282
6.22282
0
0.08826
0.06367
0.04169
0.03465
0.01644
0
174.58273
171.27683
170.49804
165.2259
174.58273
0
4 / cm-1
9.09037
7.02851
8.84144
15
9.09037
0
AG5
0.07826
0.05646
0.03697
0.03072
0.01457
0
150
126.30495
125.39341
162.60736
200
0
20
40
40
40
2.16033
0
BL / cm-1
AG1
AG2
G2 / cm-1
2 / cm-1
AG3
G3 / cm-1
3 / cm-1
AG4
G4 / cm-1
G5 / cm-1
5 / cm-1
a, BL – Bucaro-Litovitz line shape function parameters (see eq 5 in paper). bAG,, G,  – Antisymmetrized
Gaussian line shape function parameters (see eq 6 in paper). cAdditivity Model (see eq 8 in paper).
aABL,
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References
1
W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in
Fortran 77, Second ed. (Cambridge University Press, New York, 1992).
2
G. Giraud, J. Karolin, and K. Wynne, Biophys. J. 85, 1903 (2003).
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