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Supplementary material
Vibrational Dynamics of Azide-Derivatized Amino Acids Studied by Nonlinear
Infrared Spectroscopy
Masaki Okuda,1 Kaoru Ohta,2 and Keisuke Tominaga1,2
1Graduate
School of Science, Kobe University, Rokkodai-cho 1-1, Nada. Kobe
657-8501 Japan
2Moleuclar
Photoscience Research Center, Kobe University, Rokkodai-cho 1-1,
Nada. Kobe 657-8501 Japan
e-mail: tominaga@kobe-u.ac.jp
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We performed simulations of the linear absorption spectra and its 2D-IR spectra of the
N3 anti-symmetric stretching band of N3-Ala and N3-Pro which contains two
components (N3,low and N3,high bands) with the procedure developed by Fenn and Fayer
[1]. We calculated the linear absorption spectra and its 2D-IR spectra as follows:
I tot,linear ( )  a1I1,linear ( )  (1  a1 ) I 2,linear ( )  S1,linear ( )  S2,linear ( )
(1)
Stot, 2 DIR (1 , 3 ;T )  f1 (1 )S1, 2 DIR (1 , 3 ;T )  (1  f1 (1 )) S2, 2 DIR (1 , 3 ;T )
(2)
where Ii,linear() and Si,2D-IR( ) are the ith component of the linear absorption
spectrum and 2D-IR spectrum, respectively, and a1 is a weighting factor for component
1. The term f1(1) in eq. (2) is calculated as follows:
f1 (1 ) 
S1,linear (1 )
S1,linear (1 )  S1,linear (2 )
(3)
where Si,linear(1) is the linear absorption spectrum of the ith component defined in eq.
(1). In these simulations, we set the parameter a1 of the peak intensity of N3,low band A2
for N3-Ala and A1 for N3-Pro given in Table 2. Because the spectral signatures due to the
chemical exchange process between two transitions are not seen clearly in the
off-diagonal regions of 2D-IR spectra in our experimental time window (see Fig. 7), we
neglect it in the simulations. We assumed that the vibrational energy relaxation time and
rotational relaxation time of N3 anti-symmetric stretching mode do not significantly
depend on the observed wavenumber in the IR pump-probe measurements, and we used
the experimentally obtained time constants T12 and TR given in Table 3 as those of
N3,low and N3,high band. Moreover, we assumed that the functional forms of the
correlation function C(T) of N3,low and N3,high bands can be expressed as follows:
C (T )   (T ) / T2  21 exp  T /  C   22
(3)
We used the parameters given in Table 4 as the parameters in FFTCF of N3,low band. We
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varied the parameters of N3,high band to reproduce the line shape of N3,high band. To
look at the dependence of the simulated results on the parameters of N3,high band, we
performed simulations using different sets of parameters of N3,high band. The
parameters of N3,high band used in the simulations are given in Table S1. Figure S1
shows the linear absorption spectra of the N3 anti-symmetric stretching band of N3-Ala
and N3-Pro simulated for each set of parameters of N3,high band. As shown in Fig. S1,
the measured IR spectra of N3-Ala and N3-Pro are well reproduced by a sum of N3,low
and N3,high bands. Figures S2 and S3 display the 2D-IR spectra simulated at T = 0.2 ps
and 1 ps of N3-Ala and N3-Pro, respectively. Figure S4 shows CLSs of N3-Ala and
N3-Pro calculated from the 2D-IR spectra of N3,low, N3,high and whole bands. As shown
in Fig. S4, the values of CLSs for whole band are similar to those for N3,low band, and
we observed weak dependence of the simulated CLSs on the parameters for FFTCF of
N3,high band. To see the relative contributions of the 2D-IR spectra of N3,high band to
that of the whole band, we took the slices of the 2D-IR spectra of N3,low, N3,high and
whole bands at two different 1 frequencies. Figure S5 and S6 display the slices of the
2D-IR spectra at T = 0.2 ps and 1 ps at frequencies indicated by the dotted black lines in
Fig. S2 and S3. As described in Fig. S5 and S6, it is found that the traces of the 2D-IR
spectrum of N3,low band have stronger intensity than those of N3,high band, and is
similar to those of whole band. These results indicate that the 2D-IR spectrum of the
whole band is mainly characterized by that of N3,low band. Therefore, in spite of the
presence of second transitions, we concluded that the experimentally obtained CLS of
N3-Ala and N3-Pro still represents FFTCF for stronger transition.
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Figure captions
Figure S1.
Linear absorption spectra of (left) N3-Ala and (right) N3-Pro in H2O
simulated with (a) parameters 1, (b) parameters 2, and (c) parameters 3 in FFTCF given
in Table S1. Red line indicates the experimental data. Green and pink lines are the
simulated absorption spectra of N3,low and N3,high bands, respectively, and blue line
corresponds to the sum of the two bands.
Figure S2.
Simulated 2D-IR spectra of N3-Ala in H2O with (a) parameters 1, (b)
parameters 2, and (c) parameters 3 in FFTCF given in Table S1 at T = 0.2 ps (left) and 1
ps (right). Green lines represent the center lines of the 2D-IR spectra. Dotted black lines
indicate the frequencies where slices of the 2D-IR spectrum are taken.
Figure S3.
Same as Figure S2 except for N3-Pro in H2O.
Figure S4.
CLS (solid line with close circles) of (left) N3-Ala and (right) N3-Pro
at each population time simulated with (a) parameters 1, (b) parameters 2, and (c)
parameters 3 in FFTCF given in Table S1. Red close circles and blue squares indicate
CLS for N3,low and N3,high bands, respectively, and green triangles represent CLS for
whole band.
Figure S5.
Slices of the 2D-IR spectra of N3-Ala in H2O at T = 0.2 ps and 1 ps
simulated with (a, d) parameters 1, (b, e) parameters 2, and (c, f) parameters 3 in FFTCF
given in Table S1 at the (left) lower and (right) higher frequencies indicated by the
dotted black lines in Fig. S2. Red and blue lines indicate the component of N3,low and
N3,high band, respectively, and green line is the sum of the two components.
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Figure S6.
Same as Figure S5 except for N3-Pro in H2O.
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Figure S1.
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Figure S2.
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Figure S3.
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Figure S4.
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Figure S5
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Figure S6.
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Table S1. Parameters in the FFTCF of N3,high band used for the simulation of linear
absorption spectra and 2D-IR spectra of N3-Ala and N3-Pro in H2O.
Solute
Parameters
2* / ps
1 / ps-1
C / ps
2 / ps-1

/ cm-1 
Ala
Pro
Parameters 1
0.7
4.2
1.5
3.6
79.5
Parameters 2
0.7
3.0
0.75
3.9
78.9
Parameters 3
0.7
3.0
0.325
4.7
78.9
Parameters 1
1.2
3.1
1.0
1.5
47.7
Parameters 2
1.2
2.8
0.5
2.1
47.8
Parameters 3
1.2
2.8
0.25
2.4
47.8
We assumed the form of FFTCF as follows :
T 0   (T ) / T2  21 exp  T /  C   22 .
: full width at the half maximum of the calculated N3,high band.
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