Isomerization and intermolecular solute-solvent interactions of ethyl isocyanate: Ultrafast infrared vibrational echoes and linear vibrational spectroscopy

Article abstract of DOI:10.1063/1.1527926

The dynamics of ethyl isocyanate (EIC) in the solvent, 2-methylpentane (2MP), are investigated by examining the temperature dependences of the isocyanate (N=C=O) antisymmetric stretching mode's absorption spectrum and ultrafast infrared vibrational echo decay. By combining the spectral data and the vibrational echo data, an interesting picture of the EIC dynamics emerges. As such, electronic structure calculations of the isolated molecule show that trans and gauche forms should be stable, while the cis conformation is a saddle point on the potential surface.

Full text of DOI:10.1063/1.1527926

Isomerization and intermolecular solute–solvent interactions of ethyl isocyanate:
Ultrafast infrared vibrational echoes and linear vibrational spectroscopy
Nancy E. Levinger, Paul H. Davis, Pradipta Kumar Behera, D. J. Myers, Christopher Stromberg, and M. D. Fayer
Citation: The Journal of Chemical Physics 118, 1312 (2003); doi: 10.1063/1.1527926
View online: http://dx.doi.org/10.1063/1.1527926
View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/118/3?ver=pdfcov
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 118, NUMBER 3
15 JANUARY 2003
Isomerization and intermolecular solute–solvent interactions
of ethyl isocyanate: Ultrafast infrared vibrational echoes and linear
vibrational spectroscopy
Nancy E. Levinger,a) Paul H. Davis,b) Pradipta Kumar Behera,c) D. J. Myers,d)
Christopher Stromberg, and M. D. Fayere)
Department of Chemistry, Stanford University, Stanford, California 94305
͑Received 19 August 2002; accepted 17 October 2002͒
Thermally induced gauche–trans isomerization and direct solute–solvent interactions of the solute,
ethyl isocyanate ͑EIC͒, in the solvent, 2-methylpentane ͑2MP͒, are investigated using ultrafast
infrared vibrational echo experiments and linear vibrational absorption spectroscopy of the
isocyanate ͑NϭCϭO͒ antisymmetric stretching mode ͑2278 cmϪ1͒. Both the EIC vibrational echo
measured pure vibrational dephasing and the absorption spectra show complex behavior as a
function of temperature from room temperature to 8 K. The EIC data are compared to absorption
experiments on the same mode of isocyanic acid ͑HNCO͒, which cannot undergo isomerization. To
describe the observations, a model is presented that involves both intramolecular dynamics and
intermolecular dynamical interactions. At room temperature, gauche–trans isomerization is very
fast, and the isomerization dynamics contribution to the vibrational echo decay and the absorption
line shape is small because it is motionally narrowed. The dominant contribution to both the
vibrational echo decay and the absorption spectrum is from direct dynamical interactions of the
solute with the solvent. As the temperature is lowered, the direct contribution to vibrational
dephasing decreases rapidly, but the contribution from isomerization increases because the extent of
motional narrowing diminishes. The combined effect is a very gradual decrease of the rate of pure
dephasing as the temperature is initially lowered from room temperature. At very low temperature,
below the 2MP glass transition, isomerization cannot occur. The absorption spectrum displays two
peaks, interpreted as the distinct gauche and trans absorption bands. Even at 8 K, the pure dephasing
is surprisingly fast. The direct solvent-induced dephasing is negligible. The dephasing is caused by
motions of the ethyl group without isomerization occuring. At intermediate temperatures (150 K
ϾTϾ100 K), isomerization takes place, but its contribution to the pure dephasing is not motionally
narrowed. The absorption spectral shapes are complex. Dephasing arising from direct interaction
with the solvent is small. Both isomerization and fluctuations on the gauche–trans surface
contribute to the absorption line shape. The model that is used to describe the results involves a
NMR type exchange calculation with additional contributions from the direct solvent interactions
that are obtained from the temperature-dependent HNCO IR spectra. From the temperature
dependence of the isomerization ‘‘jump’’ rate, the barrier height for the isomerization is found to be
ϳ400 cmϪ1. © 2003 American Institute of Physics. ͓DOI: 10.1063/1.1527926͔
I. INTRODUCTION
For example, in a glassy solvent, the variety of essentially
static local solvent environments will give rise to inhomoge-
neous broadening of the spectrum.1 Dynamics that may oc-
cur can be totally masked by inhomogeneous broadening.
Even in a liquid at room temperature, a variety of processes,
such as the vibrational lifetime and pure dephasing, can con-
tribute to line broadening.2
In this paper, dynamics of ethyl isocyanate ͑EIC͒ in the
solvent, 2-methylpentane ͑2MP͒, are investigated by ex-
amining the temperature dependences of the isocyanate
͑NϭCϭO͒ antisymmetric stretching mode’s absorption spec-
trum ͑centered near 2280 cmϪ1͒ and ultrafast infrared vibra-
tional echo decay. By combining the spectral data and the
vibrational echo data, an interesting, but complex, picture of
the EIC dynamics emerges. The ethyl group can sample a
range of conformations. Electronic structure calculations of
the isolated molecule3 show that trans and gauche forms
A vibrational absorption spectrum of a solute mode in a
solvent reflects all of the dynamics of processes that are
coupled to the mode. The line shape and linewidth of the
spectrum are sensitive to both intramolecular and intermo-
lecular interactions. However, it is difficult to separate the
various influences on a mode through an absorption spec-
trum alone. Processes on all time scales affect the spectrum.
a͒
Permanent address: Department of Chemistry, Colorado State University,
Fort Collins, Colorado 80523.
b͒
Current address: Department of Chemistry & Biochemistry, University of
California at San Diego, La Jolla, California 92093-0303.
Permanent address: Department of Chemistry, Sambalpur University, Jyoti
c͒
Vihar, Sambalpur, PIN—768019, India.
d͒
Permanent address: Alexza Molecular Delivery Corporation, Palo Alto,
California 94303.
Corresponding author. Electronic mail: fayer@stanford.edu
e͒
0021-9606/2003/118(3)/1312/15/$20.00
1312
© 2003 American Institute of Physics
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J. Chem. Phys., Vol. 118, No. 3, 15 January 2003
Solute-solvent interactions of ethyl isocyanate
1313
should be stable, while the cis conformation is a saddle point
on the potential surface. While the calculated potential sur-
face must be considered an approximation for the molecule
in a liquid, it shows that the trans configuration is only
somewhat higher in energy than the gauche, and the barrier
is relatively low. The two conformations are also calculated
to give somewhat different vibrational frequencies for the
isocyanate antisymmetric stretch.3,4
Because of the low barrier and small energy difference
between the isomers, rapid switching of conformations
would be expected at room temperature. For fast enough
exchange, the two vibrational transitions associated with the
trans and gauche conformations will be motionally narrowed
into a single line.5–7 In fact, at room temperature a single line
is observed, while at low temperature the line separates into
two overlapping peaks. Comparisons to the spectrum of iso-
cyanic acid, H–NϭCϭO ͑HNCO͒, which cannot undergo
trans–gauche isomerization, and detailed vibrational echo
experiments show that there are several contributions to the
line shape that vary in importance with temperature. The line
pure dephasing is not motionally narrowed. A direct interac-
tion with the solvent impacts the dephasing to some extent,
and the dephasing and the absorption line shape have contri-
butions from both isomerization and fluctuations on the
gauche–trans surface.
The combination of experiments and the model calcula-
tions provide a very complete description of the processes
under observation. The model calculations are quantitative,
but because of assumptions used to untangle the data, there
may be some systematic error in the analysis. Therefore,
temperature-dependent isomerization jump times that emerge
from the data fitting may have some error. Nonetheless, the
experiments demonstrate that by using a combination of vi-
brational echo experiments and conventional vibrational
spectroscopy it is possible to observe isomerization, a very
basic chemical structural change on the electronic ground
state potential surface that is induced thermally. Furthermore,
the data analysis yields a estimate of the barrier for isomer-
ization of 400Ϯ50 cmϪ1
.
*
shape and the vibrational pure dephasing time, T2 , are in-
II. EXPERIMENTAL METHODS
A. Sample preparation
fluenced by intermolecular and intramolecular processes.
The intermolecular processes involve the direct interaction of
the isocyanate asymmetric stretch with solvent dynamics.
The intramolecular dynamics are isomerization at high tem-
peratures and motions on the isomerization potential surface
that do not result in isomerization at low temperatures.
At high temperature, the solvent dynamics are the domi-
nant contribution to the spectrum and the pure dephasing.
The major contribution of the intermolecular dynamics is
demonstrated by the broad Lorentzian line width of HNCO,
which lacks contributions from intramolecular ethyl dynam-
ics. At room temperature, the HNCO linewidth is almost
identical to that of EIC. As the temperature is lowered, the
HNCO linewidth narrows very rapidly; in contrast, the EIC
Ethyl isocyanate ͑EIC, Aldrich, 98% purity͒ was pur-
chased from Aldrich and distilled prior to use. After distilla-
tion the EIC was stored at low temperature to minimize deg-
radation of the molecule via hydrolysis. 2-methylpentane
͑2MP, Aldrich, 99ϩ% purity͒ was used as received and
stored over molecular sieves after opening to prevent the
uptake of water. Samples were prepared in a low humidity
environment to minimize hydrolysis.
Isocyanic acid ͑HNCO͒ was synthesized by a dropwise
addition of a saturated aqueous solution of potassium cyan-
ate ͑KOCN, Aldrich, 96% purity͒ to concentrated phosphoric
acid ͑Baker, 85% by weight in water͒, according to the
method of Ashby and Werner.8 The resultant HNCO gas was
passed through a trap cooled by a dry ice/acetone bath to
remove volatiles before being bubbled through 2MP. FTIR
spectra confirmed the presence of HNCO in 2MP solution.
Unfortunately, because the NϭCϭO antisymmetric stretch
of HNCO in 2MP occurs at the same wavelength as the
antisymmetric stretch of CO2 , we were precluded from per-
forming laser-based experiments on this molecule due to at-
mospheric absorption of the laser beam.
Custom optical cuvettes consisting of a copper body
with CaF2 windows secured by copper flanges were used for
both the steady-state and time-resolved experiments. Vari-
able thickness Teflon spacers placed between the CaF2 win-
dows determined the pathlength of the cells. For all experi-
ments reported in this paper, the pathlength used was 400
␮m. A 100 ␮m diameter stainless steel pinhole was also
placed between the cuvette windows to assist in the spatial
overlap of the laser beams in the sample. Initially, a decom-
position product appeared in some of the EIC samples sev-
eral days after injection into the copper sample cells. On the
basis of the possible chemical reactions that the EIC can
undergo9 and the position of the peak in the IR spectrum
corresponding to the decomposition product, we believe that
the decomposition product was CO2 dissolved in the 2MP.
*
T2 measured with vibrational echoes and the EIC spectro-
scopic linewidth change very slowly. A model is presented
that treats the isomerization in terms of a NMR-type ex-
change formalism combined with the other contributions to
the line shape and the pure dephasing. The analysis using the
model demonstrates that as the temperature is lowered, the
direct contribution to vibrational dephasing decreases rap-
idly, but the contribution from isomerization increases be-
cause the extent of motional narrowing lessens. The tradeoff
between the decreasing direct solvent contribution and the
increasing isomerization contribution makes both the pure
dephasing and the EIC line shape change relatively slowly
with temperature down to ϳ120 K.
As the temperature is decreased, isomerization slows and
then ceases. The single peak observed in the high-
temperature absorption spectrum develops two distinct spec-
tral features attributable to the trans and gauche configura-
tions of EIC. Surprisingly, even at the lowest temperature
probed, 8 K, the dephasing is still fast. At low temperatures,
direct solvent-induced dephasing is negligible. Instead, the
dephasing arises from fluctuations of the ethyl group without
isomerization occuring. At intermediate temperatures
(150 KϾTϾ100 K), the absorption spectral shapes are com-
plex. Isomerization takes place, but its contribution to the
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1314
J. Chem. Phys., Vol. 118, No. 3, 15 January 2003
Levinger et al.
To prevent this decomposition from occurring, sample cells
were carefully cleaned and dried in an oven prior to use.
For measurements of steady-state spectra, a closed-cycle
He refrigerator cooled the samples, while for the time-
resolved studies the samples were cooled in a constant-flow
cryostat using either liquid nitrogen or liquid helium. The
temperature of the samples was monitored via a silicon diode
temperature sensor ͑Lakeshore Cryotronics Model DT-470-
SD-11; accuracy of better than Ϯ0.5 K, 100–305 K, better
than Ϯ0.25 K, 2–100 K͒ mounted to the exterior of the
cuvette window with thermally conducting low-temperature
epoxy. Temperature regulation ͑temperature stability Ϯ0.02
K or better͒ was accomplished using a second silicon diode
temperature sensor linked to a feedback temperature control-
ler.
FIG. 1. Representative vibrational echo data of the NϭCϭO antisymmetric
stretching mode of ethyl isocyanate in 2-methylpentane at 22 K. The solid
line through the points is a fit to a single exponential decay convolved with
a Gaussian instrument response function obtained from the autocorrelation
of the infrared pulses.
B. Spectroscopy
Steady-state IR spectra with 0.25 cmϪ1 resolution were
collected using a FTIR ͑Mattson͒. All spectra reported rep-
resent an average of 64 individual scans.
The laser system used for the time-resolved studies has
been described in detail previously.10 Here we describe cer-
tain modifications of the basic system unique to these stud-
ies. Briefly, the output of a home-built mode-locked Ti:Sap-
phire oscillator was temporally stretched in a curved mirror/
grating stretcher. The band width was limited to 25 cmϪ1 by
introducing a slit into the stretcher. The light was then am-
plified in a regenerative amplifier and recompressed using a
single grating compressor. The output pulse was ϳ1 mJ, cen-
tered at 800 nm, with a pulse duration of ϳ750 fs.
were very nearly Gaussian in shape. The spectrum of the
pulses was also close to Gaussian. The pulses were always
within a factor of 1.4 or less of the transform limit ͑i.e., 1.4
times the Gaussian time–bandwidth product of 0.44͒. Exten-
sive tests for power dependence were performed, and the
beams were attenuated to eliminate saturation, heating, and
other power-dependent effects.
The amplified Ti:Sapphire pulses were then used to cre-
ate tunable IR light in a multistage OPA. Because the pulses
were relatively long, the white light continuum used to seed
the OPA was generated in a 6 mm long Nd:YAG crystal.11
The continuum seed was mixed in an 8 mm Type I BBO
crystal with part of the 800 nm light from the regenerative
amplifier to produce signal and idler beams at 1.35 and 1.95
␮m, respectively. The idler beam was then bandwidth limited
using a grating ͑600 grooves/mm͒ and used to seed a second
BBO crystal ͑8 mm long, Type II͒. The amplified signal and
idler were then difference mixed in a 2 mm long Type II
AgGaS2 crystal to produce tunable mid-IR light. For the ex-
periments reported here, the resulting 5 ␮J pulses were cen-
tered at 2278 cmϪ1 with a bandwidth ͑FWHM͒ of ϳ25
III. RESULTS
A. Vibrational echo experiments
Figure 1 displays vibrational echo data ͑circles͒ taken on
the antisymmetric NϭCϭO stretching mode of EIC in 2MP
at 22 K. The solid line through the points is a fit to a single
exponential decay convolved with a Gaussian instrument re-
sponse function obtained from the autocorrelation of the in-
frared pulses. As discussed below, at this and other low tem-
peratures, the vibrational echo decays are in the
inhomogeneous limit, that is, the inhomogeneous linewidth
is large compared to the dynamic linewidth.12,13 Therefore,
the dephasing time, T2 , can be obtained directly from the
vibrational echo decay, and T2 is four times the vibrational
echo decay time, T2ϭ4␶
cmϪ1
.
12,13
.
At 22 K, T2ϭ6.6 ps,
echo
The mid IR pulses were split into strong ͑90%͒ and weak
͑10%͒ beams that traversed different paths before crossing in
the sample. The weak beam was chopped at 500 Hz and
directed along a variable pathlength delay line. The probe
beam polarization could be controlled by a ZnSe Brewster-
plate polarizer in its path. A small amount of the mid-IR light
was split off and used for shot-to-shot normalization. Signal
and reference beams impinged on liquid nitrogen cooled
MCT detectors whose outputs were processed by gated inte-
grators, divided by an analog processor, and input to a
lock-in amplifier. The output of the lock-in was read into a
computer using an A/D board.
which corresponds to a dynamic linewidth (1/␲T2) of 1.6
cmϪ1
.
Within experimental error, the vibrational echo decays
are exponential at all temperatures, but they are not all in the
inhomogeneous broadening limit. Figure 2͑A͒ displays the
vibrational echo decay times as a function of temperature.
Figure 2͑B͒ displays the vibrational lifetimes as a function of
temperature measured with infrared pump–probe experi-
ments. For an exponential decay of the vibrational echo sig-
nal characterized by the dynamic dephasing time, T2 , there
are three contributions:
1
1
1
1
The IR pulse duration was measured by autocorrelation
in a 1 mm-long Type I AgGaS2 crystal. The ϳ750 fs pulses
ϭ
ϩ
ϩ
.
͑1͒
*
T2
T2
2T1 3Tor
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J. Chem. Phys., Vol. 118, No. 3, 15 January 2003
Solute-solvent interactions of ethyl isocyanate
1315
matches the vibrational echo-determined linewidth within
experimental error.
Between the low-temperature ͑inhomogeneous line͒ and
high-temperature ͑homogeneous line͒ limits, the system falls
in an intermediate regime. The vibrational echo decay data at
intermediate temperatures can be analyzed by fitting it to the
appropriate decay function. In principle, eight double-sided
Feynman diagrams contribute to the analysis of the data.12
Three of these are rephasing diagrams that give rise to the
vibrational echo decay after ␶ϭ0. However, the laser band-
width ͑25 cmϪ1͒ is sufficient to span the 0–1 transition but is
small compared to vibrational anharmonicity.4 Therefore, the
rephasing diagram that involves the 1–2 transition does not
contribute to the vibrational echo decay. This is confirmed by
the absence of anharmonic beats on the vibrational echo
decay.15–17 The other five diagrams contribute at negative
times and only around ␶ϭ0. They determine the shape of the
rising edge of the signal. To simplify the calculations, the
rising edge of the data is described in terms of an instrument
response function, that is, the Gaussian pulse shape con-
volved with the square of the pulse shape. This reflects the
fact that there is a single interaction of the radiation field
with the system during the first pulse but two interactions
with the second pulse. Then for exponential vibrational echo
decays, the signal for a delta function pulse is12
ϱ
2
S ␶͒ϭ
͑
dt exp Ϫ⌬2 tϪ␶͒ exp Ϫ2 tϩ␶͒/T
,
͑2͒
͓
͑
͔
͓
͑
͔
͵
2
0
where ⌬ is the inhomogeneous linewidth in rad/s. Equation
͑2͒ is then convolved with the instrument response function.
As discussed in detail below, the absorption spectrum at
very low temperatures consists of two lines: one correspond-
ing to the gauche conformation of the ethyl group and one
corresponding to the trans conformation. These can be ap-
proximated well as the sum of two overlapping Gaussian
lines at the lowest temperatures. At high temperature, a rapid
interchange of the conformations produces an absorption
spectrum that is a single line. To account for the two transi-
tions, Eq. ͑2͒ can be extended to give
FIG. 2. ͑A͒ Vibrational echo decay time constants, T2 , and ͑B͒ vibrational
lifetimes measured with infrared pump–probe experiments, T1 , of the
NϭCϭO antisymmetric stretching mode of ethyl isocyanate in
2-methylpentane as a function of temperature.
*
T2 is the pure dephasing time; T1 is the vibrational lifetime;
and Tor is the orientational relaxation time. Using the
Debye–Stokes–Einstein equation,14 Tor was estimated to be
ϳ7.5 ps at room temperature. This contribution to T2 is neg-
ligible at room temperature, and because of the rapid in-
crease in viscosity as the temperature is decreased, Tor makes
ϱ
S ␶͒ϭa2
dt exp Ϫ⌬2 tϪ␶͒ exp Ϫ tϩ␶͒/T
a negligible contribution at all temperatures. Therefore, it is
2
͑
͓
͑
1
͔
͓
͑
͔
͵
2
1
1
2
0
not considered further. T1 is very small compared to 1T2 at
the highest temperatures, but it makes a small contribution at
the lower temperatures ͑see Fig. 2͒. Therefore, Eq. ͑1͒ is
used below to remove the lifetime contribution from the ex-
perimentally determined dephasing times to obtain the
ϱ
ϩa2
dt exp Ϫ⌬2 tϪ␶͒ exp Ϫ tϩ␶͒/T
͓ ͑ ͔ ͓ ͑ ͔
2
2
2
͵
2
0
ϱ
*
*
temperature-dependent pure dephasing times, T2 . T2 is re-
lated to the fluctuations in the vibrational transition energy,
which is of interest here.
ϩa a
dt 2 cos„␻ tϪ␶͒…
͑
͵
1
2
0
ϫexp Ϫ ⌬2ϩ⌬2͒ tϪ␶͒2/2 exp Ϫ tϩ␶͒/T
,
͔
2
͑3͒
͓
͑
͑
2
͔
͓
͑
1
At the lowest temperatures, the inhomogeneous width is
significantly greater than the dynamic linewidth, 1/␲T2 .
Thus, the vibrational echo decay is in the inhomogeneous
limit, and T2 can be obtained directly from the vibrational
echo decay time. At the highest temperature probed, the sys-
tem is in the homogeneous limit. In this limit, T2 is 2␶
where ⌬1 and ⌬2 are the inhomogeneous widths of the indi-
vidual lines and ␻ is the splitting between them. Amplitudes
a1 and a2 are obtained from a fit of the steady-state spectrum
to a sum of two Gaussians. Equation ͑3͒ is then convolved
with the instrument response function.
12
.
echo
This is confirmed by a comparison of the EIC antisymmetric
stretching mode absorption spectrum linewidth with the dy-
namic linewidth, 1/␲T2 . The absorption line shape is
Lorentzian at high temperatures, and the absorption width
Figure 3 displays fits to Eq. ͑3͒ for several datasets at
intermediate temperatures, where the system is neither in the
inhomogeneous nor homogeneous broadening limits. The
*
quality of the fits is good. The pure dephasing times T2 are
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1316
J. Chem. Phys., Vol. 118, No. 3, 15 January 2003
Levinger et al.
*
FIG. 4. Pure dephasing times, T2 , as a function of temperature for the
NϭCϭO antisymmetric stretching mode of ethyl isocyanate in
2-methylpentane.
low temperature.1 By 8 K, one might expect T2ϭϳ2T1 .
However, in this system, pure dephasing is the dominant
contribution to the dynamic dephasing, even at 8 K, where
the solvent is a glass far below Tg .
B. Linear absorption spectroscopy
An understanding of the temperature-dependent dynam-
ics of EIC can be obtained by combining results from the
vibrational echo experiments with temperature-dependent
linear absorption measurements of the antisymmetric
NϭCϭO stretch of both EIC and isocyanic acid ͑HNCO͒.
Like the vibrational echoes, the linear spectroscopy of the
EIC NϭCϭO antisymmetric stretching mode does not dis-
play a simple temperature dependence. Representative
steady-state IR absorption spectra of EIC in 2MP are shown
in Fig. 5 for four different temperatures, from room tempera-
ture to below the 2MP glass transition temperature (Tg
ϭ80 K). First consider the 298 K spectrum. The strong ab-
sorption peak near 2278 cmϪ1 has been attributed to the
18
NϭCϭO antisymmetric stretching vibration, ␯
.
Several
AS
other features at lower energy are visible in the spectrum:
one located at ϳ2260 cmϪ1 and one at ϳ2220 cmϪ1. A nor-
mal mode analysis of EIC using MACSPARTAN and a search
of the literature reveals that these are not fundamental vibra-
tional modes of the molecule; we attribute them to various
FIG. 3. Fits of vibrational echo decays at three temperatures to Eq. ͑3͒
convolved with a Gaussian instrument response function ͑see the text͒.
combination bands of lower-frequency modes, possibly ␯
7
ϩ␯ or ␯10ϩ␯11 , as reported by Durig et al.19 These same
12
shown in Fig. 4. The data display a number of interesting
features. First, from room temperature down to ϳ120 K, the
change in the pure dephasing time with temperature is very
mild. Then, at ϳ120 K, the temperature dependence appears
to change slope rather suddenly. From 120 to 8 K, the lowest
peaks appear in the spectra at all temperatures, and are es-
sentially temperature independent. In the 298 K spectrum,
the 2260 cmϪ1 peak appears as a shoulder on the side of the
main peak. In the 61 K spectrum, the 2260 cmϪ1 peak ap-
pears distinct from the shoulder at ϳ2274 cmϪ1. These com-
bination band peaks play no role in the line shape analysis
that follows. ͑In the vibrational echo experiments, the band-
width of the laser was narrow enough to avoid overlap with
them.͒ However, the peak at 2260 cmϪ1 makes it necessary
to compare calculated absorption curve shapes on the blue
side ͑high-energy side͒ of the line and only partway down
the red side of the line.
*
temperature studied, the increase in T2 with decreasing tem-
perature is much steeper than at high temperature. Both the
high temperature and low temperature portions of the data
appear approximately linear, but with very different slopes.
*
Also, at the lowest temperatures, T2 is relatively fast. In
other vibrational echo experiments, the total dynamic
dephasing (T2) is dominated by the vibrational lifetime at
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J. Chem. Phys., Vol. 118, No. 3, 15 January 2003
Solute-solvent interactions of ethyl isocyanate
1317
FIG. 5. Representative steady-state IR absorption spectra of the NϭCϭO antisymmetric stretching mode of ethyl isocyanate in 2-methylpentane with
decreasing temperature: ͑a͒ room temperature ͑298 K͒, ͑b͒ 175 K, ͑c͒ 120 K, and ͑d͒ 61 K. The lines at ϳ2260 and 2220 cmϪ1 are combination bands that
do not play a role in the analysis. By 120 K it can be seen that the main peak is separating into two lines. At 61 K, the main band is composed of two
absorption lines: the trans conformation ͑2273.5 cmϪ1͒ and the gauche conformation ͑2282.5 cmϪ1͒. At high temperatures, a rapid exchange between the
conformations has collapsed the gauche and trans peaks into a single band.
At room temperature ͑298 K͒ the NϭCϭO feature ap-
pears as a single peak at ϳ2278 cmϪ1, and the line shape fits
very well to a Lorentzian function. As the temperature is
HNCO in 2MP spectrum at four temperatures. The HNCO
IR spectra differ drastically from those of EIC. At room tem-
perature, the HNCO spectrum has a Lorentzian line shape,
with a width almost identical to that of the room temperature
EIC spectrum. Comparing the EIC and HNCO spectra only
at room temperature could lead to the erroneous conclusion
that the ethyl group is unimportant because it seems to make
little difference at room temperature. However, unlike the
spectrum of EIC, the HNCO spectrum narrows dramatically
with decreasing temperature while maintaining its Lorentz-
ian shape. By 140 K, the HNCO spectrum is ϳ1.5 cmϪ1
FWHM. As the temperature is lowered farther, the shape is
no longer a Lorentzian. From 140 to ϳ110 K, the HNCO can
be modeled well with the convolution of a Lorentzian with a
Gaussian ͑i.e., a Voigt profile͒, making it possible to extract
the Lorentzian component. Below ϳ110 K, the spectrum is
temperature independent, presumably because it is domi-
nated by inhomogeneous broadening. At low temperatures,
below Tg , the HNCO spectrum is a single, very narrow line.
In contrast, the EIC spectrum is much broader in the glass
lowered, the NϭCϭO ␯ feature first broadens and then
AS
splits into two spectral features: a main peak at ϳ2283 cmϪ1
and a shoulder near ϳ2274 cmϪ1. The line becomes decid-
edly non-Lorentzian in shape. The onset of the separation
into two lines can be seen in the 120 K spectrum near the
peak; it is the very distinct shoulder in the 61 K spectrum.
Below the 2MP Tg , the NϭCϭO ␯ band stops changing
AS
as the temperature decreases, maintaining both its position
and shape. In fact, all of the spectra below 86 K are so
similar that they can be overlaid without a scaling factor.
The spectrum of EIC has contributions that involve di-
rect interactions with the solvent and contributions that de-
pend on the ethyl group. The contribution from the ethyl
group can be seen clearly by comparing the EIC and the
HNCO temperature-dependent spectra. The only difference
between these two molecules is the replacement of the ethyl
group on EIC with an H on HNCO. Figure 6 shows the
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1318
J. Chem. Phys., Vol. 118, No. 3, 15 January 2003
Levinger et al.
FIG. 6. Representative steady-state IR absorption spectra of the NϭCϭO antisymmetric stretching mode of isocyanic acid in 2-methylpentane with decreasing
temperature: ͑a͒ room temperature ͑298 K͒, ͑b͒ 175 K, ͑c͒ 120 K, and ͑d͒ 61 K. At all temperatures, a single line is observed that narrows rapidly with
decreasing temperature.
and is composed of two lines, as is evident by the shoulder
that is clearly visible in all of the low-temperature spectra
͑see the 61 K spectrum in Fig. 5͒.
Thus, while the room temperature spectra of HNCO and
EIC are very similar, their behaviors diverge significantly as
the temperature is lowered. These differences demonstrate
that the presence of the ethyl group in the EIC molecule
greatly affects the temperature-dependent behavior of both
ecule ͑with the gauche conformation ϳ118 cmϪ1 lower in
energy than the trans conformation͒, the cis configuration is
predicted to be a local maximum ͑i.e., a saddle point between
the two gauche conformations͒ in the isomerization poten-
tial, and thus should not be observed.3 The ab initio calcula-
tions need to be considered as qualitative input in the present
context since they do not include the solvent. The solvent
will contribute both enthalpy and entropy to the free energy
surface. In addition, the calculation, while comprehensive,
was not at a high level by today’s standards. Therefore, the
actual numbers obtained from the calculations cannot be uti-
lized, but the qualitative picture of two isomers not widely
separated in energy is undoubtedly correct.
the linewidth and line shape of the NϭCϭO ␯ transition
AS
of EIC in 2MP.
The splitting of the NϭCϭO ␯ peak at low tempera-
AS
ture suggests the existence of two isomers of EIC. The ori-
entation of the ethyl tail with respect to the NϭCϭO group
changes the NϭCϭO ␯ frequency, leading to two distinct
AS
spectral features observed at low temperature. Indeed, ab ini-
tio calculations of the vibrational spectrum of isolated EIC
IV. QUALITATIVE CONSIDERATION
OF THE VIBRATIONAL ECHO
AND SPECTROSCOPIC RESULTS
predict that the NϭCϭO ␯ vibrational frequency is ϳ7
AS
cmϪ1 higher in energy when the ethyl group is trans to the
NϭCϭO moiety than when it is gauche.3,4,20 While both the
trans and gauche conformations are predicted to be local
minima in the potential energy surface for the isolated mol-
A. The high-temperature regime
The vibrational echo pure dephasing results ͑Fig. 4͒ dis-
play a very weak temperature dependence at high tempera-
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J. Chem. Phys., Vol. 118, No. 3, 15 January 2003
Solute-solvent interactions of ethyl isocyanate
1319
tures with a much steeper temperature dependence at low
temperatures. The EIC spectrum displays a weak but com-
plex temperature dependence, changing from a single
Lorentzian line at room temperature to two Gaussian lines at
low temperature. In contrast, the HNCO spectrum is a single
Lorentzian line at room temperature that narrows rapidly as
the temperature is decreased, but it remains a single line.
These results suggest that the time-dependent and time-
independent contributions to the EIC results can be divided
into two types: intermolecular and intramolecular interac-
tions with the NϭCϭO chromophore. The intermolecular
interactions involve the direct interaction of the NϭCϭO
with the solvent. The intramolecular interactions occur
through the interaction of the NϭCϭO with the ethyl group.
The direct interactions of the NϭCϭO with the solvent
should be essentially the same for EIC and HNCO. The fact
that the room temperature absorption spectra of EIC and
HNCO are virtually identical indicates that direct solvent
interactions dominate both the spectrum and the vibrational
echo decay of EIC at room temperature.
FIG. 7. A comparison of dephasing times, T2 , for the NϭCϭO antisym-
metric stretching mode in ethyl isocyanate ͑᭝͒ and HNCO ͑᭺͒ in
2-methylpentane as a function of temperature. Using these data, the contri-
bution to the EIC dephasing time from isomerization, Ti2 , ͑᭿͒ is obtained.
As the temperature is first decreased, Ti2 becomes shorter because the extent
of motional narrowing is reduced. The line through the squares is an aid to
the eye.
The EIC spectrum clearly consists of two peaks at low
temperature. The spectrum is separating into two peaks at
intermediate temperatures ͑see Fig. 5, 120 K spectrum͒, but
the spectrum is a single Lorentzian peak at room tempera-
ture. The temperature dependence of the EIC spectrum indi-
cates that there is rapid exchange between the trans and
gauche isomers at high temperatures. As in NMR, the rapid
exchange between the two conformations will collapse the
two peaks into a single motionally narrowed peak.5–7 The
EIC spectrum and the HNCO spectrum are almost identical
at room temperature. Therefore, both spectra must be domi-
nated by the direct intermolecular dynamic interactions with
the solvent because HNCO does not have isomerization as a
possible broadening mechanism. From these facts, we con-
clude that at room temperature, the intramolecular isomeriza-
tion contribution to both the EIC vibrational echo decay and
the absorption spectrum is small. The isomerization contri-
bution will be small if the exchange time is very fast, pro-
ducing a very narrow motionally narrowed ‘‘intramolecular
line.’’
separated from the intermolecular contribution by using the
HNCO vibrational line shape data. The HNCO linewidths
͑⌫͒ were converted to dephasing times using
⌫ϭ1/␲T2 .
͑4͒
These dephasing times can be subtracted from the vibrational
echo measured dephasing times to give the intramolecular
isomerization contribution to the EIC vibrational echo data.
At room temperature, the HNCO line is slightly wider than
the EIC line, presumably because HNCO has a somewhat
stronger coupling to the solvent. The detailed calculations
presented below indicate that the intramolecular motionally
narrowed isomerization contribution to the EIC is ϳ5% at
room temperature. Therefore, we use the temperature depen-
dence of the HNCO data but scale all of the points with a
single factor so that the HNCO width is 0.95 of the EIC
width at room temperature prior to subtraction.
The very weak temperature dependence of the pure
The dephasing data and the results of subtraction are
shown in Fig. 7. The triangles are the temperature-dependent
EIC dephasing times obtained from vibrational echo mea-
surements. The circles are the HNCO dephasing times ob-
tained from the linewidths. The HNCO dephasing times in-
crease rapidly with decreasing temperature mirroring the
rapid narrowing of the absorption line that is evident in Fig.
6. The black squares result from subtraction of the scaled
HNCO data from the EIC data. The squares are the intramo-
lecular contribution to the EIC dephasing. The line through
the squares is an aid to the eye. As shown in Fig. 7, as the
temperature is decreased, the intramolecular dephasing time
first becomes shorter ͑the line width becomes broader͒ before
increasing at lower temperatures. The increase in the in-
tramolecular contribution to the linewidth as T is decreased
is caused by the reduction in the isomer exchange motional
narrowing. The isomer exchange will rigorously produce a
single line as long as ⌬ϫ␶ Ͻ1, where ⌬ is the line splitting
and ␶ is the exchange time between the two conformations.
*
dephasing, T2 ͑see Fig. 4͒ above ϳ120 K reflects a tradeoff
between the intramolecular and intermolecular temperature
dependences. Assuming that the intermolecular temperature
dependence is the same for the NϭCϭO chromophore in
EIC and HNCO, the intermolecular contribution to the EIC
vibrational echo decay decreases rapidly with falling tem-
perature. However, as the temperature is lowered, the rate of
isomerization will slow. As the exchange rate slows, the ex-
tent of motional narrowing will decrease, causing the line to
broaden and the intramolecular contribution to the EIC vi-
brational echo decay to increase. The opposite temperature
dependences of the intermolecular and intramolecular contri-
butions to the dephasing produce the observed weak tem-
perature dependence of the vibrational echo decay above
ϳ120 K.
At the higher temperatures, the EIC vibrational echo
data reflect a combination of the intramolecular and intermo-
lecular dynamics. The intramolecular contribution can be
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1320
J. Chem. Phys., Vol. 118, No. 3, 15 January 2003
Levinger et al.
By ϳ150 K, the isomerization is no longer rapid enough to
collapse the two isomer absorption lines into a single line. In
Fig. 5, the 175 K spectrum is a single line, while the 120 K
spectrum clearly shows evidence of the two underlying trans
and gauche absorption lines.
B. The low-temperature regime
As shown in Fig. 7, by ϳ110 K, the direct intermolecu-
lar solvent contribution to the dephasing ͑circles͒ is very
small. In addition, as will be shown in detail below, the con-
tribution from isomerization is almost negligible. By Tg ͑80
K͒, isomerization has ceased. However, the dephasing time
in the low-temperature regime, as measured by the vibra-
tional echo, is very fast compared to HNCO and other sys-
tems that have been studied.1 Therefore, it is reasonable to
assume that both the dynamics and the extent of inhomoge-
neous broadening in the low-temperature regime are caused
by the EIC ethyl group.
To understand these data, we first, consider the inhomo-
geneous broadening at low temperatures. In EIC, the low-
temperature band is composed of two lines: one for the
gauche and one for the trans conformation ͑see Fig. 5, 61 K
spectrum͒. These lines are each ϳ8 cmϪ1 wide. In contrast,
the HNCO line in the low-temperature glass is ϳ1.5 cmϪ1
wide ͑see Fig. 6, 61 K spectrum͒. The HNCO width arises
from the intermolecular interactions of the NϭCϭO chro-
mophore with the disordered glassy solvent. Because the
NϭCϭO chromophore of EIC will have the same intermo-
lecular interactions with the solvent, the cause of the exten-
sive inhomogeneous broadening must be due to small varia-
tions in the conformations of the ethyl chain. This is
represented schematically in Fig. 8. The upper part of the
figure shows a schematic of the isomerization potential
surface.3 At low temperatures, Ͻ110 K, in the extremely
viscous liquid and in the glass, the gauche and trans surfaces
are not smooth. Variations in the local solvent structure can
result in variations in the configuration of the ethyl chain.
These variations give rise to differences in the NϭCϭO
transition frequency. In the low-temperature glass, the barri-
ers between the local minima are too high to surmount. Even
in the liquid near Tg , the time scale for structural evolution
is so long that the NϭCϭO absorption line still has a sig-
nificant inhomogeneous contribution.
FIG. 8. Upper portion: schematic representation of the isomerization poten-
tial surface. Middle portion: expanded view of the ethyl isocyanate isomer-
ization potential surface. Small variations in the ethyl group configuration
give rise to differences in the NϭCϭO transition frequency. For T
рϳ225 K, these variations contribute to inhomogeneous broadening.
Lower portion: at low temperature, each local variation ͑shown above͒ can
itself have structure. Minima are so shallow that the system can be activated
over the barriers or, with phonon assistance, tunnel through the barriers.
Transitions among these shallow minima produce fluctuations in the
NϭCϭO transition frequency and rapid low-temperature dephasing.
At low temperature, each minimum of the inhomoge-
neous structure can itself have structure ͑the lowest portion
of Fig. 8͒. However, these minima are so shallow that the
system can be activated over the barriers or, with phonon
assistance, tunnel through the barriers. Transitions among
these shallow minima produce fluctuations in the NϭCϭO
transition frequency and rapid low-temperature dephasing.
Both the low-temperature inhomogeneous broadening and
the dynamic dephasing result from the interactions of the
ethyl group with the NϭCϭO chromophore. In contrast,
HNCO has neither substantial inhomogeneous broadening
nor significant dynamic dephasing at low temperatures.
Figure 8 can be used to visualize the temperature depen-
dence of the intramolecular components of the vibrational
echo data and the absorption spectrum. At the lowest tem-
peratures, from 8 K to ϳ60, the transition is substantially
inhomogeneously broadened. The dephasing dynamics in-
volve motions that primarily remain in the local minima that
give rise to the inhomogeneous broadening ͑the middle part
of Fig. 8͒. As the temperature is raised further, transitions
among these local minima can occur. At higher temperatures
͑Ͼϳ100 K͒, the amplitudes of the ethyl motions in the trans
and gauche potential minima become sufficiently large that
some isomerization can occur. Up to ϳ150 K, the isomeriza-
tion is slow enough that there are still two distinct lines.
However, the exchange between trans and gauche configu-
rations causes significant dephasing, broadening the lines
and shifting them toward each other ͑see Fig. 5, 120 K spec-
trum͒. In this temperature range ͑ϳ100–150 K͒, both motion
in the trans and gauche minima and isomerization contribute
to the dephasing. By 175 K, the isomerization is so fast that
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J. Chem. Phys., Vol. 118, No. 3, 15 January 2003
Solute-solvent interactions of ethyl isocyanate
1321
the two lines have undergone exchange collapse into a single
line, and motions within the individual minima are no longer
important. As the temperature is raised from 175 K to room
temperature, the intramolecular isomerization contribution to
the dephasing and absorption spectrum is reduced by mo-
tional narrowing ͑see Fig. 7, squares͒. In addition to the in-
tramolecular contributions to dephasing and the absorption
line shape, the intermolecular direct interaction with the sol-
vent dynamics plays a significant role at higher temperatures
͑see Fig. 7, circles͒. The increase in the dephasing caused by
the intermolecular dynamics at high temperature offsets the
decrease in dephasing caused by motional narrowing be-
tween 175 and 298 K. The result is the very weak tempera-
ture dependence of the vibrational echo pure dephasing at the
higher temperatures ͑see Fig. 4͒.
spectrum, the numerical results, for example, the isomeriza-
tion times at each temperature, could have some systematic
error.
The time scales probed in vibrational spectroscopy are
much faster than those studied in NMR. While the concept of
motional narrowing exists in vibrational spectroscopy,7,21 the
short time scale for vibrational dephasing, caused in part by
influences other than isomerization, makes it difficult to
separate the exchange contribution to the dephasing from the
direct intermolecular solvent-induced dephasing.7,21 Contri-
butions from solvent-induced dephasing and inhomogeneous
broadening cannot be neglected. However, the basic concepts
of the effect of interconversion between two spectrally dis-
tinguishable molecular configurations, such as trans and
gauche isomers of EIC, still hold. Thus, we employ NMR
exchange formalism in the data analysis.5,6 The additional
contributions of solvent-induced dephasing and inhomoge-
neous broadening are included through convolution, as dis-
cussed below.
V. A MODEL FOR THE COMBINED SPECTROSCOPIC
AND VIBRATIONAL ECHO DATA
In this section, the ideas presented qualitatively in Sec.
IV are modeled theoretically. The model captures the essen-
tial features of the problem using a relatively simple ap-
proach. While the method shows a remarkable ability to
combine the various aspects of the problem and thereby re-
produce the temperature dependence of the EIC absorption
In NMR, the spectral line shape is obtained from the
imaginary portion of the expression for the magnetization.5,6
F(␻) is the spectral line shape in the limit that the line shape
is dominated by exchange between two different molecular
forms, A and B:
2
PABPBA ␻ Ϫ␻ ͒
͑
A
B
F ␻͒ϰ
͑
,
2
͑5͒
2
2
P
ABϩPBA͒„PBA ␻Ϫ␻ ͒ϩP ␻Ϫ␻ ͒… ϩ ␻Ϫ␻ ͒ ␻Ϫ␻ ͒
͑
͑
͑
AB
͑
͑
A
B
A
B
where PAB is the probability of making a transition from
state A to state B in the time interval ␦t, and PBA is the
probability of making a transition from state B to state A in
the time interval ␦t. ␻A is the frequency of A in the absence
with the solvent and the intramolecular isomerization. These
dynamics govern the observed line shape from 298 to ϳ200
K. In addition, as the temperature is lowered, inhomoge-
neous broadening contributes to the line shape. The follow-
ing procedure is used to fit the spectra in this temperature
regime. All of the direct solvent-induced dephasing times
obtained from the HNCO spectra are multiplied by a single
constant so that at 298 K the HNCO spectroscopic width is
95% of the EIC width ͑see the discussion in Sec. IV A͒. The
resulting widths, 1/␲Td2 , are used as the direct solvent con-
tributions to the EIC linewidths. Assigning a 5% contribution
to the isomerization portion of the dephasing at room tem-
perature produces the best overall agreement with the tem-
perature dependence of the data. Varying this value by Ϯ2%
yields only a small difference. However, outside of this
range, the temperature-dependent fits degrade substantially.
The isomerization contribution to T2 , Ti2 , is obtained from
of exchange, and ␻ is the frequency of B in the absence of
B
exchange. fa and fb are the fractions of molecules in con-
figurations A and B, respectively, and are given by
PAB
PBA
fAϭ
,
fBϭ
.
͑6͒
P
ABϩPAB
P
ABϩPBA
Taking state A to be lower in energy than state B, then the
rate for the upward transition, PAB , is the probability of the
downward transition, PBA , scaled by a Boltzmann factor,
T
B
P
ABϭPBAeϪ⌬E/␬
.
͑7͒
As mentioned above, the exchange formula, Eq. ͑5͒, can-
not be considered in the absence of other broadening mecha-
nisms. Thus we combine Eq. ͑5͒ with the other aspects of the
problem to calculate the temperature-dependent absorption
spectrum. For temperatures at which the absorption data
were measured but vibrational echo data were not measured,
the vibrational echo values are obtained by interpolation be-
tween the available points. The calculation of the EIC ab-
sorption spectrum falls into three temperature regimes: high,
intermediate, and low.
1
T2i
1
1
T2d
ϭ
Ϫ
.
͑8͒
T2
The exchange line shape equation, Eq. ͑5͒, is then used to
produce a calculated line at each temperature to match the
value of Ti2 . At each temperature, the exchange line shape is
convolved with a Gaussian, to account for inhomogeneous
broadening, and subsequently convolved with a Lorentzian,
1/␲Td2 , to account for the direct solvent contribution.
In the high-temperature regime, the absorption line
shape is dominated by the direct intermolecular interaction
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1322
J. Chem. Phys., Vol. 118, No. 3, 15 January 2003
Levinger et al.
TABLE I. Parameters used in the fits of the linear IR spectra. ␶j—jump
time, the inverse of jump rate used in the exchange calculation; ⌬E—energy
difference between gauche and trans lines. The gauche configuration is
lower in energy; widths—the columns labeled w are full width half-max;
wG—width of Gaussian inhomogeneous contribution to the absorption lines;
w
L,d—width of Lorentzian contribution to the absorption lines from the
direct interaction with the solvent; wL,m—width of Lorentzian contribution
to the absorption lines from motions of the ethyl group that do not lead to
isomerization.
Temperature
␶
͑ps͒
⌬E
wG
wL,d
wL,m
j
(cmϪ1
)
(cmϪ1
)
(cmϪ1
)
(cmϪ1
)
͑K͒
298a
275a
250
225
200
175
150
140
130
125
120
115
110
101
93
2.2
4.8
7.4
7.5
10
10
20
20
25
28
45
70
90
ϱ
Ͻ20
Ͻ20
Ͻ20
Ͻ20
15
15
15
15
15
20
20
20
20
30
42
54
¯
¯
¯
6
8
8
8
8
8
8
8
8
8
8
8
8
14.9
11.8
8.9
6.4
4.5
2.9
1.9
1.5
1.1
1.2
0.9
0.8
0.7
0.7
0.2
¯
¯
¯
¯
¯
¯
1.7
1.8
1.8
2.4
2.5
3.4
3.4
3.2
ϱ
ϱ
86
There are three fitting parameters in this procedure: the
jump time (PAB) and the energy difference between the po-
tential minima of the trans and gauche isomers in the ex-
change model, ⌬E ͓see Eq. ͑7͒ and see Fig. 8͔, and the
inhomogeneous width (wG). The separation between the
lines in the absence of exchange was determined from low-
temperature spectra. The splitting is 9 cmϪ1. This value is
used at all temperatures. In the high-temperature regime, the
jump time, PBA , and ⌬E are determined from Ti2 . wG was
adjusted to give the best fit to the spectrum at each tempera-
ture, and was found to be temperature independent below
225 K within experimental error ͑see Table I͒.
Figure 9 shows the line shape data and the calculated
curves for the high-temperature regime ͑298–200 K͒. As can
be seen in the figure, the agreement between the data and the
calculated curves is excellent. The parameters used to fit the
data in the three temperature regimes are displayed in Table
I. At 298 K, the line shape is rigorously in the motional
narrowing limit. The motional narrowing limit occurs when
⌬ϫ␶jϽ1, where ⌬ is the separation of the two lines in the
FIG. 9. Representative ethyl isocyanate antisymmetric stretch steady-state
IR absorption spectra and calculated spectral line shapes in the high-
temperature regime. The calculations include the effects of isomerization
͓Eq. ͑5͔͒, direct dynamic solvent interactions obtained using the HNCO
data, and inhomogeneous broadening. The agreement between the calcula-
tions and the data is excellent except on the red side, where the combination
band at ϳ2260 cmϪ1 overlaps the antisymmetric stretch spectrum.
absence of exchange and ␶ is the jump time. At 298 K,
j
⌬ϫ␶jϭ0.59. The system is homogeneously broadened; the
inhomogeneous contribution to the line shape is zero. By 200
K, ⌬ϫ␶jϭ2.7, and the system is moving away from the
motionally narrowed regime in which the two lines are com-
pletely collapsed into a single line. However, the experimen-
tally observed absorption line still appears to be a single line,
and its shape remains basically Lorentzian. By 225 K, the
extent of inhomogeneous broadening has increased to 8
cmϪ1 ͑see Table I͒. This value of the inhomogeneous broad-
ening is essentially the same for all lower temperatures. The
value of ⌬E in the high-temperature regime was found to be
Ͻ20 cmϪ1 ͑see Table I͒. Larger values of ⌬E could not
reproduce the temperature trends in the curves in the high-
temperature regime. However, any value Ͻ20 cmϪ1 yields
the same fit in the high-temperature regime.
In the low-temperature regime ͑р101 K͒, the calculation
of the absorption line shapes is straightforward. At low tem-
peratures, isomerization makes a negligible contribution to
the dephasing. In the glass, isomerization does not occur, but
even in the very viscous liquid just above Tg , extrapolation
of the jump times from higher temperatures shows that
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J. Chem. Phys., Vol. 118, No. 3, 15 January 2003
Solute-solvent interactions of ethyl isocyanate
1323
isomerization can be neglected as a contribution to the line
shape. In addition, the contribution from the direct solvent-
induced dephasing is very small. For the temperatures 101
and 93 K, extrapolation of the direct contribution curve ͑Fig.
7, circles͒ is used to estimate the direct contribution. Below
93 K, it is taken to be zero. Therefore, the main contributions
to the line shape are the dynamic dephasing associated with
motions of the ethyl group around the bottom of the gauche
and trans well that do not lead to isomerization ͑see the
discussion in Sec. IV B and Fig. 8͒. The relative heights of
the two lines that comprise the total line shape do not change
with temperature near and below Tg . In the liquid, some-
what above Tg , the jump time is very long, but it can still
bring the gauche and trans isomers into thermal equilibrium.
As the temperature approaches Tg , the time scale to achieve
thermal equilibrium between the two isomers becomes
longer than the time spent at each temperature as the tem-
perature is lowered. Below ϳ93 K, the ratio of the ampli-
tudes of the two peaks is locked in and no longer reflects the
true Boltzmann factor.
At the low temperatures, two lines separated by ϳ9
cmϪ1 comprise the spectra. Because the jump times between
the trans and gauche configurations are very long or infinite,
the exchange model can be replaced by a pair of Lorentzian
line shapes, which account for the dynamic broadening pro-
cesses other than isomerization. The dynamic broadening is
convolved with a Gaussian to account for the inhomoge-
neous broadening ͑Voigt profile͒. The spectra fit well to the
sum of two Voigt line shapes, as shown in Fig. 10. The
Lorentzian component is determined by the vibrational echo
decay, that is, 1/␲T2 . The widths and relative amplitudes of
the two Gaussians are obtained by fitting. As at the higher
temperatures, the Gaussian widths, wG , are all 8 cmϪ1. The
parameters used to reproduce the absorption spectra are
listed in Table I. Note that the ⌬E value is larger at low
temperature than at high temperature. This fact will be dis-
cussed in the context of the analysis of the intermediate tem-
perature regime, which is the most complex. Between 86 and
61 K, the only change in the line shapes is a reduction in the
Lorentzian contribution. The Lorentzian contribution is ob-
tained directly from the vibrational echo measurements using
the data in Fig. 2͑a͒. At 86 K, the Lorentzian contribution is
2.9 cmϪ1, which is small compared to the inhomogeneous
width of 8 cmϪ1. Below 61 K, the line shapes are determined
solely by inhomogeneous broadening; they are identical. Be-
tween 86 and 61 K, the Lorentzian contribution is so small
that its affect on the line shapes is almost negligible.
FIG. 10. Representative ethyl isocyanate antisymmetric stretch steady-state
IR absorption spectra and calculated spectral line shapes in the low-
temperature regime. The calculations include the effects of motions of the
ethyl group that do not lead to isomerization and inhomogeneous broaden-
ing. At low temperatures, the contributions from isomerization and solvent
dynamics are negligible. The agreement between the calculations and the
data is excellent except on the red side, where the combination band at
ϳ2260 cmϪ1 overlaps the antisymmetric stretch spectrum.
In the high-temperature regime motions of the ethyl
group lead to isomerization, which contributes to the absorp-
tion line shape as 1/␲Ti2 . In the low-temperature regime,
motions of the ethyl group do not result in isomerization and
contribute to the absorption line shape as 1/␲Tm2 . In the
intermediate-temperature regime, the absorption line shape
has contributions from both types of motions. Furthermore,
in the intermediate-temperature regime, isomerization does
not lead to complete collapse of the two absorption lines into
a single line. Isomerization ͓Eq. ͑5͔͒ produces a complex-
shaped spectrum that contributes to the overall line shape. In
addition, in the intermediate-temperature region, the direct
solvent dephasing is non-negligible.
As can be seen in Fig. 5, the 120 K spectrum shows the
beginning of the separation of the spectrum into two peaks.
The isomerization contribution to the line shape determines
this aspect of the line shape. All other factors contribute
equally to the two lines, and do not determine the separation
of the lines. Figure 11͑a͒ illustrates the initial steps used in
calculating the line shape at intermediate temperatures. Pa-
rameters are selected for the exchange calculation, that is, the
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1324
J. Chem. Phys., Vol. 118, No. 3, 15 January 2003
Levinger et al.
wing of the line is obscured by combination bands ͑see
Sec. III B͒.
The calculation of the spectrum in Fig. 11͑a͒ does not fit
the data well because the ethyl group motions other than
isomerization have not been included. The total dynamic
dephasing is measured by the vibrational echo decay. The
vibrational echo data can be used to determine the additional
contribution, 1/␲Tm2 , to the absorption line shape. In the
intermediate temperature range, for example 120 K, the ex-
change contribution to the spectrum can be reasonably ap-
proximated as the sum of two displaced Lorentzians. The
Lorentzian linewidth, 1/␲Ti2 , is used to determine T2i . The
direct solvent contribution, Td2 , is also known ͑Table I—
wL,d). Then Tm2 is determined from the vibrational echo data
using
1
T2m
1
1
1
ϭ
Ϫ
Ϫ
.
͑9͒
Ti2 Td2
T2
Therefore, Tm2 is not an independent adjustable parameter.
The Tm2 contribution to the line shape is included by convolv-
ing a Lorentzian with width 1/␲Tm2 with the line shape as in
Fig. 11͑a͒. The values of wL,d ͑full width at half-max of the
Lorentzian direct solvent contribution͒ used for the interme-
diate temperature calculations are listed in Table I. The pro-
cedure yields very good agreement with the data, but the
agreement can be improved by then making a small adjust-
ment in Ti2 , recalculating Tm2 , and then calculating the final
line shape. The result of this procedure is shown in Fig. 11͑b͒
for the 120 K spectrum. The calculated spectrum now agrees
with the measured spectrum exceedingly well. The calcu-
lated spectrum in Fig. 11͑b͒ fits the region around the peak of
the spectrum and in the wings of the spectrum.
While the procedure is approximate, it is clear that it is
adequate to give a very reasonable description of the absorp-
tion line shape. The overall method, combining the vibra-
tional echo decay data with the linear absorption spectra of
EIC and HNCO permits the EIC spectrum to be separated
into a direct solvent contribution, an isomerization contribu-
tion, an ethyl group motion ͑no isomerization͒ contribution,
and an inhomogeneous contribution. Figure 12 shows the
results of this fitting procedure for several of the spectra
taken at intermediate temperatures. The figure shows that the
agreement between the absorption spectrum data and the cal-
culations is nearly perfect. In these computations, only pa-
rameters associated with the exchange part of the calculation
are adjustable, and these are very tightly constrained by the
shape of the spectrum around its maximum.
One aspect of the parameters in Table I that may be
unexpected is that the value of ⌬E changes with tempera-
ture. In the high-temperature regime, only a limit on ⌬E
could be determined. However, at intermediate temperature
and low temperature, once two peaks can be discerned, the
shape of the calculated spectrum is quite sensitive to ⌬E.
From room temperature through 130 K, a value of ⌬E
ϭ15 cmϪ1 works consistently. From 125–110 K, the value
has increased to 20 cmϪ1. Below 110 K, ⌬E increases sig-
nificantly until it is locked in at 86 K. This could be an
artifact of the approximate approach used in the calculations.
FIG. 11. Steady-state IR spectrum of the NϭCϭO antisymmetric stretching
mode in ethyl isocyanate in 2-methyl pentane at 120 and two stages of
calculation of the spectrum for the intermediate temperature regime. ͑a͒
Exchange model fit ͓Eq. ͑5͒; see the text͔ including direct solvent and inho-
mogeneous broadening contributions. The agreement is not good around the
peak of the spectrum and in the high-energy wing. ͑b͒ The effect of the
motions of the ethyl group that do not lead to isomerization is included in
the calculation. The agreement between the data and the calculation is ex-
cellent except on the low-energy side, where the combination band at 2260
cmϪ1 overlaps the spectrum.
jump time and ⌬E. The resulting exchange line shape is
convolved with the Lorentzian direct contribution ͑Fig.
7—circles; Table I—wL,d) and then convolved with the in-
homogeneous Gaussian profile. While, the inhomogeneous
width is treated as an adjustable parameter, the result is al-
ways 8 cmϪ1. The parameters in the exchange calculation are
varied until the region around the peak of the spectrum is fit
as well as possible. As can be seen in Fig. 11͑a͒, this proce-
dure is able to produce a rough approximation of the spec-
trum. However, it misses around the peak, and it does not
reproduce the broad wings of the line, as can be seen in the
wavelength range from 2290 to 2310 cmϪ1. The low-energy
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J. Chem. Phys., Vol. 118, No. 3, 15 January 2003
Solute-solvent interactions of ethyl isocyanate
1325
FIG. 13. An Arrhenius plot of the isomerization times, ␶ ͑inverse of the
j
isomerization rate͒. While there is significant scatter in the points, they are
reasonably well represented by a line over four factors of e. The slope yields
the gauche–trans isomerization barrier of 400Ϯ50 cmϪ1
.
VI. ISOMERIZATION RATES AND THE
ISOMERIZATION BARRIER HEIGHT
The analysis presented above explains the nature of the
temperature-dependent dynamics, the absorption line shapes,
and the vibrational echo data. One of the main features of the
experiment is its observation of very fast isomerization oc-
curing on the ground state potential surface. The EIC
gauche–trans isomerization is not laser induced as in, for
example, the cis–trans stilbene isomerization, which occurs
following electronic excitation.22,23 As has been pointed out,
it is difficult to obtain thermal isomerization rates from the
analysis of temperature-dependent vibrational spectra alone
because of the other contributions, dynamic and static, to the
line shape.7,21 By combining vibrational echo experiments
with linear spectroscopic measurements, we have been able
to separate the various contributions to the vibrational
dephasing and line shapes. The results yield the temperature-
dependent gauche–trans isomerization times, ␶j , ͑inverse of
the isomerization rates͒ listed in Table I.
Figure 13 shows an Arrhenius plot of the ␶j , that is, a
plot of ln(␶j) versus 1/T. While there is considerable scatter,
the plot shows that the points can be reasonably taken to fall
on a line. The line through the points yields an estimate of
the activation energy ͑barrier height͒ for the isomerization of
400Ϯ50 cmϪ1. The isomerization occurs when the EIC me-
thylene rotates around the nitrogen–methylene carbon bond.
The simplest picture of the bonding in EIC would assign an
sp2 hybrid to the N, with the NϭCϭO linear and the meth-
ylene carbon, making a 120° angle with the linear NϭCϭO.
Quantum chemistry calculations show that the NϭCϭO is
almost linear, but the methylene carbon–NϭCϭO angle is
138°.3 In ethane, the rotation of a methyl group around the
C–C bond is hindered by the steric interaction of the three
hydrogens on one methyl with the three hydrogens on the
FIG. 12. Representative ethyl isocyanate antisymmetric stretch steady-state
IR absorption spectra and calculated spectral line shapes in the intermediate
temperature regime. The calculations include the effects of isomerization
͓Eq. ͑5͔͒, motions of the ethyl group that do not lead to isomerization, direct
dynamic solvent interactions, and inhomogeneous broadening. The agree-
ment between the calculations and the data is excellent except on the red
side, where the combination band at ϳ2260 cmϪ1 overlaps the antisymmet-
ric stretch spectrum.
Another explanation is that the potential surface depends
on both intramolecular and intermolecular coordinates. As
the temperature is lowered, the properties of the solvent
change, for example, the density of the solvent increases.
Therefore, it is possible that the difference in energy of
the gauche and trans configurations is actually temperature
dependent.
other methyl. The barrier to rotation is 1030 cmϪ1 24
.
The rotation of EIC methylene around the N–C bond
should have less steric hindrance than that of ethane. Ex-
amples of molecules with less steric hindrance are acetalde-
hyde and methanol, which have a barrier to rotation of 425
and 390 cmϪ1, respectively.24 These qualitative consider-
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1326
J. Chem. Phys., Vol. 118, No. 3, 15 January 2003
Levinger et al.
ations suggest that the value of the barrier height obtained
for the EIC gauche–trans isomerization is reasonable.
Finally, the information obtained on the gauche–trans
isomerization dynamics of ethyl isocyanate could not be at-
tained from absorption spectroscopy alone. It is necessary
to take the contributions to the line shape apart to under-
stand how the various aspects coalesce to produce the
temperature-dependent absorption spectra. The analysis was
made possible by combining linear absorption spectroscopy
with ultrafast infrared vibrational echo and pump–probe ex-
periments.
VII. CONCLUDING REMARKS
The temperature-dependent dynamics of the antisym-
metric stretching mode of ethyl isocyanate are complex. At
high temperatures, gauche–trans isomerization is very rapid
͑ϳ2 ps͒ and direct dynamical interactions of the solvent with
the isocyanate are substantial. The isomerization is so fast
that the individual gauche and trans absorption lines are mo-
tionally narrowed into a single line. As the temperature is
reduced, the rate of isomerization and the extent of the direct
solvent interactions decrease. However, these two processes
have opposite effects on the dynamic dephasing and the line
shape. The reduced rate of isomerization takes the system
away from the motionally narrowed limit. At sufficiently low
temperature, the absorption spectrum changes from a single
peak into two peaks. The contributions from isomerization
and direct dynamical solvent interactions become negligible,
but the dynamic dephasing, measured with the vibrational
echoes, is still fast because of motions of the ethyl group that
do not result in isomerization.
The theoretical method used to combine the various ex-
perimental observables into calculations of the temperature-
dependent vibrational line shapes ͑Figs. 9–12͒ does an ex-
cellent job. However, this method is approximate. It
separates the contributions to the line shape into parts. The
contribution from isomerization was included using a NMR-
type exchange calculation. The other contributions, direct
solvent interactions, motions of the ethyl group that do not
produce isomerization, and inhomogeneous broadening,
were included through convolutions. While the agreement
with the data is excellent, there is the question of whether a
theoretical method that did not treat each aspect as indepen-
dent would produce different results, particular the
temperature-dependent isomerization rates. The theoretical
problem is extremely difficult and unsolved. It involves cal-
culating the influence on dephasing of isomerization when
the transition energies are fluctuating because of direct sol-
vent dynamical interactions and motions of the ethyl group
that do not result in isomerization. Here we treated the
isomerization as jumping between two time-independent
states. A more detailed approach would recognize that the
gauche and trans states are each time evolving and that the
isomerization occurs between these time-evolving states.
From the temperature-dependent isomerization rates, the
barrier for gauche–trans isomerization was obtained. The
experiments yield a barrier height of 400Ϯ50 cmϪ1. It is a
challenging theoretical problem to calculate this barrier
height for ethyl isocyanate in the presence of the solvent
2-methylpentane.
ACKNOWLEDGMENTS
The authors are grateful to Professor T. J. Wandless and
Professor J. Brauman for many helpful conversations. This
work was supported by the National Science Foundation
͑DMR-0088942͒ and the National Institutes of Health
͑1RO1-GM61137͒. N.E.L. gratefully acknowledges support
for a sabbatical leave from the NSF POWRE program
͑CHE-0074913͒.
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