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C. Dynamics of Doorway Vibrations

C. Dynamics of Doorway Vibrations

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574



Iwaki et al.



Figure 16 IR-Raman data for the lowest frequency doorway vibrations of three

liquids after C–H stretch pumping at ¾3000 cm 1 . The build-up reflects the complicated vibrational cooling (VC) processes of each liquid. The higher frequency

doorway vibrations have longer lifetimes. (From Ref. 96.)



vibration occupation number would jump from its thermal equilibrium value

of n D 0.38 to a value n D 0.38 ð 0.02 ð 4 D 0.46. That would represent

a jump in doorway vibration occupation number of ¾20% in the first few

picoseconds. What is actually observed in Fig. 10 is a jump of only a

few percent, which can be used to show the doorway vibration lifetime is

considerably less than 5 ps. After the ¾5 ps jump, doorway vibration excitation builds up with a complicated functional form, which reflects heat

build-up in the bath due to subsequent processes of C–H bend and C–C

stretch relaxation.

In the NM data (48) in Fig. 16, energy builds up in the 480 cm 1 NO2

rock in two stages, as described in Section IV.B. The subsequent decay of

NO2 rock excitation seen in Fig. 16 indicates this doorway vibration has a

much longer lifetime than in ACN. The lifetime is about 50 ps.



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Ultrafast IR-Raman Spectroscopy



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In the benzene data (49) in Fig. 16, the 606 cm 1 ring deformation

mode has a two-part rise. The first part mirrors the ¾10 ps decay of the

C–H stretch. The second part mirrors the ¾40 ps decay of intermediate

energy vibrations such as the ring breathing mode at 992 cm 1 . The decay

lifetime is difficult to determine accurately because it is so slow, but is

estimated at 100 š20 ps.

As these examples show, the rather complicated behavior of the

doorway vibrations in each liquid opens a window directly into the complicated VC process following C–H stretch pumping. The doorway vibration

data by itself is not sufficient to unravel the entirety of the VC process, but

when combined with IR-Raman data from a few other vibrations, most of

the puzzle can be solved (49). It is interesting to note that by comparing

ACN, NM, and benzene, the doorway vibration lifetime increases with

increasing frequency, which is qualitatively what would be expected for the

predicted (82) energy-gap law. Of course things are not really that simple,

since the comparison involves changing both the vibrational frequency and

the bath. Ideally one should calculate the fluctuating forces on each doorway

vibration in its own bath and in comparing different liquids consider both

the change in vibrational frequency and the change in Debye frequency ωD .

D. Monitoring the Bath



In these studies we attempt to develop a consistent picture of VER in a

given system by watching energy move among a polyatomic molecule’s

intramolecular vibrations. It would help a great deal to know at all times

how much of the system’s energy had been dissipated to the bath. A technique we have developed to monitor the build-up of bath excitation involves

spiking the liquid with carbon tetrachloride CCl4 . CCl4 is a nonpolar,

noncomplexing liquid, which is miscible with most other liquids. CCl4 has

three lower frequency vibrations with large Raman cross sections, as shown

in Fig. 17, a Raman spectrum of a mixture of benzene and CCl4 . CCl4 has

little effect on the vibrations of benzene (49) or most other liquids. The

primary effects of CCl4 are to slightly modify the phonon density of states

(54), usually by shifting the density of states a bit to lower energy.

Intermolecular energy transfer from a vibrationally excited molecule

such as benzene to CCl4 could occur by two mechanisms termed “direct”

and “indirect,” as diagrammed in Fig. 18. In a liquid mixture, the phonons

are collective excitations of the mixture. But the coupling between

intramolecular vibrations on adjacent molecules is ordinarily quite weak.

Direct intermolecular transfer is important primarily in the long-lived

vibrations of cryogenic liquids (7,84). In polyatomic liquid mixtures, VER



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Iwaki et al.



Figure 17 Raman spectrum of liquid benzene with CCl. The CCl4 has little effect

on the benzene vibrational spectrum or the benzene VER rates. Monitoring the CCl4

vibrational transitions while pumping benzene vibrations provides an indication of

the energy build up in the bath. (From Ref. 49.)



occurs on the picosecond time scale, so there is rarely enough time for

direct transfer to occur. Direct transfer in polyatomic liquid mixtures has

been observed in a few cases, most notably pyrrole to benzene (38) and

alcohol to nitromethane (42). In both systems, there is a relatively strong

noncovalent interaction between the two components, which would not be

the case with CCl4 mixtures.

Indirect transfer occurs by a two-part mechanism, as shown in Fig. 18.

First a vibrational excitation decays by generating phonons. The phonons

then produce vibrational excitation on other molecules by multiphonon

up-pumping. Indirect transfer will not occur unless the density of vibrational excitations is large enough to produce a real increase in the bath

temperature.

Our experiments with mixtures of CCl4 and other liquids indicate it

does not matter much which of the three CCl4 vibrations shown in Fig. 17

are monitored, because all three pump up at about the same rate. Some

CCl4 data are shown in Fig. 19, where the transient CCl4 population buildup results from C–H pumping of methanol, benzene, or NM. In methanol

and benzene, all three CCl4 transitions could be observed, and they all



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Figure 18 Direct and indirect intermolecular vibrational energy transfer in a polyatomic liquid mixture consisting of molecules A and B. In polyatomics, direct

transfer does not often compete efficiently with VER. Indirect transfer from A to B

occurs when A undergoes VER, which produces phonons, which pump vibrations

on B. Indirect transfer is efficient only when the density of excited vibrations is

large enough to significantly increase the phonon population.



behaved similarly. In NM, the 479 cm 1 CCl4 transition is obscured by the

480 cm 1 NM doorway vibration, so the 315 cm 1 CCl4 transition was

monitored. This CCl4 technique proved problematic with ACN since all

three useful CCl4 transitions were obscured by ACN transitions similar

frequencies.

The data in Fig. 19 show that the build-up of bath excitation, as

measured by CCl4 , is complete in about 20 ps in methanol, in about 60 ps

in benzene, and in about 150 ps in NM. By comparing Fig. 19 to Fig. 16,

we can compare the behavior of the doorway vibrations in benzene and

NM to the behavior of CCl4 vibrations at about the same frequency in

solution with benzene or NM. The doorway vibration and the CCl4 data

in a particular solution both attain a stable plateau value at about the same

time, which indicates the time when VC has ceased and all vibrational levels

have come to equilibrium at the new temperature. The doorway vibration



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Figure 19 Build-up of bath excitation, monitored via CCl4 vibrations, in

methanol, benzene, and nitromethane after C–H stretch excitation.



and CCl4 transients differ substantially at short times. At short times, the

fast decay of the C–H stretch in benzene and NM generates vibrational

population in the doorway vibrations but does not generate much bath

excitation. The CCl4 data for these systems shows that the initial C–H

stretch decay is primarily an intramolecular energy redistribution process

and that it is the subsequent decay of daughter processes that generates

most of the bath excitation.

E. Fermi Resonance and Overtones



A sizable literature exists describing how C–H stretch decay in polyatomic

liquids usually takes a few ps (34) and occurs by exciting daughter C–H



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Ultrafast IR-Raman Spectroscopy



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bending vibrations (22,33,34). Since C–H bends have about one-half the

energy of the stretch, two quite different C–H stretch decay processes are

possible, depending on whether the daughter excitation is the nearly isoenergetic D 2 first overtone of the bend or the D 1 bending fundamental.

A common occurrence in molecules with methyl groups is degeneracy

between the fundamental C–H stretch and the first overtone of the C–H

bend, that is, Fermi resonance.

Broadly speaking, there are two ways of picturing C–H stretch decay

with Fermi resonance (Fig. 20a,b). One possibility (Fig. 20a) is that the



Figure 20 Fermi resonance and overtone pumping in acetonitrile (ACN). (a) The

laser might pump a pure C–H stretch, which decays into the degenerate first overtone of the C–H bend. (b) The laser might pump a coupled bend-stretch state,

which decays into lower energy levels. (c) t D 0 spectrum in the C–H stretching

region of ACN after 3000 cm 1 pumping. The two C–H bending fundamentals are

at 1372 and 1440 cm 1 . The new peak at ¾1500 cm 1 is due to the C–H bending

overtone transition D 2 ! 1, which is shifted out of the region between the two

fundamentals by pumping the higher energy tail of the bend overtone. (d) The bend

overtone decays along with the C–H stretch, indicating that scheme (b) is correct.

(From Ref. 96.)



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