SUPPORTING INFORMATION
Communication: Probing non-equilibrium vibrational relaxation
pathways of highly excited CN stretching modes following ultrafast
back-electron transfer
Michael S. Lynch, Karla M. Slenkamp, and Munira Khalil
Department of Chemistry, University of Washington, Seattle, WA. 98195, United States
Contents
SI. Materials and methods .......................................................................................................... 1
SII. Coherent oscillations along 2 ............................................................................................... 2
SIII. Data analysis and kinetic schemes ...................................................................................... 3
REFERENCES .............................................................................................................................. 6
FIG. S1 ........................................................................................................................................... 1
FIG. S2 ........................................................................................................................................... 3
FIG. S3 ........................................................................................................................................... 4
TAB. S1 .......................................................................................................................................... 6
SI.
Materials and methods
The model complex Na4[(NC)5FeII–CN–PtIV(NH3)4–NC–FeII(CN)5] (i.e., FeIIPtIVFeII) was
synthesized according to literature procedures and subsequently purified.1 Sample purity was
verified with FTIR and UV/vis spectroscopy (see Figure S1). Samples were prepared in D2O to
a concentration of ~8 mM.
FIG. S1. Steady-state spectra of FeIIPtIVFeII in D2O at room temperature with experimental
visible and IR spectra overlaid. (a) UV/vis (–) and 400 nm pump spectra (---). (b) FTIR (–) and
IR pulse spectra (---).
Complete experimental details and data analysis methods have been published
elsewhere.2 In brief, the experiments are performed with the output of a commercial Spectra
Physics Spitfire Pro 35F-XP regenerative amplifier operating at 1 kHz (800 nm, 35 fs, 3 W). The
visible pump pulse (vis = 400 nm) is generated by frequency doubling a portion of the 800 nm
beam in a 0.1 mm thick -barium borate (-BBO) crystal. An acousto-optic programmable
dispersive filter (Fastlite, Dazzler UV-250–400) temporally compresses the spectrally broad
(fwhm = 8 nm = 500 cm–1; see Fig. S1a) pump pulse to a final temporal width of ~35 fs. The
- S1 -
visible pulse energy at the sample was 1 J. The mid-IR pulses are generated via frequency
conversion of the 800 nm pulses with an optical parametric amplifier (OPA), whereby ~1 W of
the amplified 800 nm beam is directed into a dual-pass OPA (Newport, OPA-800C) to generate
near-IR signal and idler pulses. Near-IR pulses are spatially and temporally overlapped in a 0.5
mm thick AgGaS2 crystal for difference frequency mixing to generate tunable mid-IR pulses.
For this experiment, the 80 fs mid-IR pulses were centered at MIR = 2030 cm–1 with a
bandwidth of fwhm = 270 cm–1 (see Fig. S1b). The temporal width of the IR pulse at the
sample is optimized by placing 3 mm of uncoated CaF2 into the beam path to compensate for
group velocity dispersion mismatch.3 IR pulse energies at the sample were 0.5 J.
Data generated with this apparatus is a matrix including variables vis, 2, and 3 (1 = 0
for an IR DPP pump–probe measurement). We measured five values of vis (120, 300, 500, 700,
and 5000 fs), 2 was scanned from 0–13 ps in unequal time steps, and 3 ranged from 1870 cm–1
to 2130 cm–1 with ~4 cm–1 spectral resolution. Kinetics along vis were not fit since previous
vis–IR pump–probe work in our group characterized dynamics occurring along this time
variable.4
SII.
Coherent oscillations along 2
Transient DPP traces as a function of 2 in the bridge region are shown in Figure S2 at five
values of vis, including a ground state (GS) trace that has been scaled. Power spectra shown in
Figure 2 of the Communication were generated as follows: (i) normalize trace, (ii) fit data from
2 = 0–2 ps to a biexponential (no offset) and subtract the fit from the data, (iii) interpolate the
data (linear interpolation) to the smallest time step of 50 fs and delete the first two points ( 2 = 0,
50 fs) to avoid erroneous frequencies from the subtraction, (iv) multiply the data by the Nuttal
- S2 -
apodization filter function, and (v) take the magnitude-squared of the FFT of the resulting trace
to afford the Fourier power spectrum.
FIG. S2. Transient DPP signals in the bridge mode region (3 = 2114 cm–1), which oscillate as a
function of 2. The GS spectrum has been scaled by a factor of –4, whereas the transient spectra
follow the 10 OD scale shown with the arrow. The trace at vis = 5.0 ps shows that the
oscillations are within the noise.
SIII.
Data analysis and kinetic schemes
Kinetic traces shown in each panel of Figure 3 of the Communication were simultaneously fit to
one of two schemes depending on the value of vis. The schemes illustrated in Fig. S3 only differ
in the first step of vibrational relaxation. We note that many other target models were created
and fit to the data but were not as successful as the two Schemes shown in Fig. S3.
- S3 -
FIG. S3. Two schemes used to fit the nonequilibrium vibrational relaxation dynamics for vis =
120 and 300 fs (Scheme 1a) and vis = 500, 700, and 5000 fs (Scheme 1b). Here we define the
time constant ti = 1/ki, where k is the first order rate of the process. In some cases multiple
arrows are given for one time constant to point out that many pathways are possible; however,
data was fit by following one pathway in the above schemes.
A total of four time traces (corresponding to 4 unique IR frequencies) from the raw data
matrix were simultaneously fit from 2 = 0.1–13 ps. Data between 2 = 0–0.1 ps was excluded to
ensure the resulting kinetic parameters were not due to cross-phase modulation and/or solvent
response. Each set of four kinetic traces at a particular vis was either fit to Scheme 1a or 1b with
corresponding equations given by
f1a  2 ; 3   A1 3  ExpErf  B, t0 , t1 , 2 
 A2 3   ExpErf  B, t0 , t2 , 2   ExpErf  B, t0 , t1 , 2 
 A3 3   ExpErf  B, t0 , t3 , 2   ExpErf  B, t0 , t2 , 2 
(S1)
 A4 3   ExpErf  B, t0 , t4 , 2   ExpErf  B, t0 , t2 , 2  ,
f1b  2 ; 3   A1 3  ExpErf  B, t0 , t1 , 2 
 A2 3  ExpErf  B, t0 , t2 , 2 
 A3 3   ExpErf  B, t0 , t3 , 2   ExpErf  B, t0 , t2 , 2 
 A4 3   ExpErf  B, t0 , t4 , 2   ExpErf  B, t0 , t2 , 2  ,
- S4 -
(S2)
where

B
ExpErf  B, t0 , ti , 2   exp 
 4 ln  2   t
i

2
  t 
  2 0

ti 



  t
 
1
B
2
0

  1

erf
 2 ln  2  
2
 B
4
ln
2

t
  i  


(S3)
Here, erf is an error function. Note that eq S3 is the result of the convolution of an exponential
decay with a Gaussian to account for the instrument response function (IRF). In the above
equations, Ai is the IR-frequency dependent amplitude of the ith exponential decay, B is the fullwidth at half-maximum (fwhm) of the Gaussian IRF (B = tIRF = 114 fs), t0 is time zero (t0 = 0),
and ti (= 1/ki) is the time-constant of the ith exponential decay.
The amplitude terms Ai() are fit locally whereas the time constants were fit globally.
Thus, four time constants (t1–4) are obtained from the global fit. We note that t4 corresponds to
the vibrational relaxation time constant commonly written as T1. Complete fittings results are
given in Table S1.
- S5 -
TABLE S1. Fitting parameters for the fits shown in Figure 3 following the labeling in the
schemes. Error bars are reported at the 95% confidence level.
t1 a
t2
t3
t4
A1 b (nbridge > 6)
A2
A3
A4
A1 (ntrans = 2–3)
A2
A3
A4
A1 (n = 0)
A2
A3
A4
A1 (nbridge = 1)
A2
A3
A4
a
vis = 120 fs
vis = 300 fs
vis = 500 fs
vis = 700 fs
vis = 5000 fs
0.25 0.02
0.38 0.08
1.2 0.1
17 3
0.18 0.03
0.42 0.06
1.3 0.1
17 4
0.19 0.02
0.68 0.07
1.38 0.08
13 2
0.17 0.04
0.69 0.09
1.3 0.1
15 5
0.2 0.1
0.5 0.2
0.9 0.2
16 6
–0.8 0.3
--------0.6 0.4
--0.20 0.03
–0.4 0.2
--–0.2 0.1
–0.12 0.02
----0.5 0.3
0.30 0.05
–0.8 0.4
--------0.6 0.3
--0.18 0.03
–0.4 0.2
–0.3 0.1
–0.16 0.08
–0.13 0.02
----0.5 0.2
0.22 0.03
–0.6 0.3
--–0.3 0.2
--0.3 0.1
0.31 0.06
0.2 0.1
0.14 0.02
–0.4 0.2
–0.19 0.08
–0.3 0.1
–0.12 0.02
----0.5 0.2
0.16 0.04
–0.5 0.3
--–0.5 0.3
----0.5 0.2
--0.13 0.05
–0.3 0.2
–0.26 0.09
–0.3 0.2
–0.15 0.03
----0.4 0.2
0.16 0.03
--------------0.08 0.07
----–0.4 0.3
–0.16 0.06
------0.26 0.04
Time constants in ps. The first two time traces (left of vertical double bar) were fit with
scheme 1a, whereas scheme 1b was used to fit the traces to the right of the double bar.
b
Amplitudes are normalized such that

i
Ai  vis , 3   1 . Dashed lines (---) indicate a
statistically insignificant contribution to the fit. In some cases (e.g., nbridge > 6, vis = 5000 fs),
the fit is within the noise of the data implying that within the 95% confidence interval the
signal is zero.
REFERENCES
(1)
(2)
(3)
(4)
Wu, Y.; Cohran, C.; Bocarsly, A. Inorg. Chim. Acta 1994, 226, 251-258.
M. S. Lynch, K. M. Slenkamp, M. Cheng and M. Khalil, J. Phys. Chem. A, Just Accepted
Manuscript (2012). DOI: 10.1021/jp303701b.
Demirdöven, N.; Khalil, M.; Golonzka, O.; Tokmakoff, A. Opt. Lett. 2002, 27, 433-435.
Lynch, M. S.; Van Kuiken, B. E.; Daifuku, S. L.; Khalil, M. J. Phys. Chem. Lett. 2011, 2,
2252-2257.
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