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E. Fermi Resonance and Overtones

E. Fermi Resonance and Overtones

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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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laser prepares a nearly pure C–H stretch, whose decay populates the nearly

isoenergetic C–H bend overtone. Overtone decay would subsequently

populate lower energy vibrations such as the C–H bend fundamentals.

Another is that the pulse pumps a coupled C–H stretch and C–H bend

overtone state (Fig. 20b), which goes on to decay by populating lower

energy vibrations. In the former case, the bend overtone would build up

as the C–H stretch decayed. In the latter case, C–H stretch and bend

excitations would decay together.

The problem in investigating these two mechanisms is spectroscopically distinguishing the C–H bend overtone D 2 from the fundamental

D 1 . The Raman cross section of the two-quantum D 2 ! 0 transition

is orders of magnitude smaller than one-quantum transitions. The overtone

is more easily detected via its D 2 ! 1 transition. Unfortunately that

transition is likely to be near the fundamental D 1 ! 0 transition. With

the relatively low spectral resolution of ultrafast laser systems, it is often

impossible to distinguish the two transitions. In that case, overtone excitation appears as excitation of the fundamental with twice the amplitude

(44), since the Raman cross section for the D 2 ! 1 transition is twice

as large as the cross section for the D 1 ! 0 transition.

In the specific example of ACN (46) (point group C3v ), there is one

C–H stretch and one C–H bend of a1 -symmetry and a pair of doubly degenerate stretches and bends of e-symmetry (84). In Fig. 5, the ACN Raman

spectrum in the C–H bending region can be seen. The spectrum consists

of a sharper a1 -symmetry bend 1372 cm 1 and a broader e-symmetry bend

at 1440 cm 1 . The e-symmetry bend is broadened by Fermi resonance

because the e-bend overtones 2 ð ¾1440 cm 1 are degenerate with the

e-stretches ¾3000 cm 1 . The a1 -bend and stretch have no Fermi resonance because the bend overtone 2 ð ¾1372 cm 1 is not degenerate with

the stretch 2943 cm 1 . In the gas phase, the anharmonicity of the e-bend

is ¾25 cm 1 [85]. For an e-bend D 1 ! 0 transition at 1440 cm 1 , the

D 2 ! 1 transition would be at ¾1415 cm 1 , in the region between the

a1 - and e-bend fundamentals, and it would be very difficult to see.

It would help if the e-bend overtone could be frequency-shifted away

from the fundamentals. That would be possible if the e-bend were inhomogeneously broadened (see Section IV.G.). Then we could pump the

C–H stretch around 3000 cm 1 and excite only bend overtones in the

¾1500 cm 1 region, away from the region between the two fundamentals.

Figure 20c,d shows the results of pumping ACN at 3000 cm 1 . At t D 0, a

new peak is observed in the C–H bend spectrum near 1500 cm 1 , whose

spectral width is about the same as the apparatus-limited bandwidth. This



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peak cannot be an SFG artifact. It is attributed to bend overtone transitions

of a subset of ACN molecules with bending vibrations at the higher end

of the spectral range. The overtone transition (Fig. 20c) is observed only

while C–H stretch excitations are present (near t D 0), and the overtone

decays along with the C–H stretch. These results are consistent with the

picture of a mixed C–H stretch and bend overtone state, which decays into

bend fundamentals, as indicated in Fig. 20b.

F. Multiple Vibrational Excitations



It is interesting to study molecules where two or more vibrational excitations are simultaneously present. Since excited vibrations interact via cubic,

quartic, or even higher order anharmonic coupling, a complicated nonlinear

interaction can be expected, which cannot be understood solely by studying

molecules with only a single vibrational excitation. This nonlinear interaction will play a role in the exothermic reaction dynamics of polyatomic

molecules, since unless the reaction proceeds solely along a simple onedimensional reaction coordinate, nascent product molecules will be created

with several vibrational excitations. By using the pump pulse to excite a

combination band (47), a pair of interacting vibrational excitations can be

produced on the same molecule.

In the IR absorption spectrum of ACN (Fig. 5) there is a small

relatively sharp transition at ¾3150 cm 1 . This transition has previously

been assigned as a combination of C–C stretch 918 cm 1 and

C N 2253 cm 1 stretch (84). Since the combination transition overlaps

the higher energy tail of the C–H stretch fundamental, pumping at this

frequency is expected to produce vibrationally excited molecules where

all three vibrations interact. The excitations may be viewed as weakly

interacting independent vibrations (47). The weak interaction is assured

since the anharmonicity is relatively small (<0.3% of the vibrational

frequency). Any coherent vibrational states produced by the pump pulse

will lose coherence very rapidly, since the dephasing time constant (T2 ³

0.5 ps) (51) is much faster than the VER lifetime.

Some results are shown (47) in Fig. 21. The left-hand column of

Fig. 21 is a reminder of how VER occurs in ACN with only the C–H stretch

fundamental ¾3000 cm 1 pumped. The C–H stretch decays in ¾5 ps,

and only ¾2% of this energy populates the 2153 cm 1 C N stretch, which

has an 80 ps lifetime. The 918 cm 1 C–C stretch rises in ¾30 ps because

it is populated by the pathway C–H stretch ! C–H bend ! C–C stretch.

Subsequent C–C stretch decay occurs with an ¾45 ps time constant. With

combination band pumping (right-hand column of Fig. 21), the C–H stretch



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Figure 21 Anti-Stokes transients for acetonitrile (ACN) with C–H stretch

pumping (left) and with combination band (C N C C–C stretch) pumping (right).

With combination band pumping, population builds up instantaneously in the C N

stretch and C–C stretch, the decay of the C N stretch is about 10 times faster,

and a population oscillation is seen in the C–C stretch. (From Ref. 47.)



decay is unchanged. A much larger build-up is seen in the C N stretch,

whose lifetime dramatically drops from 80 to 5 ps. The C–C stretch shows

a population oscillation. Its population rises instantaneously, decays a bit

over 5 ps, rises again over ¾30 ps, and then decays with an ¾45 ps time

constant.

Since the combination band anharmonicity <10 cm 1 (84) is less

than our spectral resolution (¾60 cm 1 in this measurement), excitation of

the combination C–C stretch and C N stretch is seen as excitation of both

fundamentals (44). Pumping the combination band causes an instantaneous

jump in the populations of the C–H stretch, C–C stretch, and C N stretch.

The directly pumped C N stretch excitation rises to a level about 20 times

greater than when it is indirectly populated with C–H stretch pumping. A

C N stretch and a C–C stretch on the same molecule can annihilate each

other via cubic anharmonic coupling to create C–H stretch excitations (47).



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This is an up-conversion process (57). The C N stretch and C–C stretch

excitations are in fast equilibrium with C–H stretch excitations, but the

C–H stretch decays with a 5 ps time constant. That explains the C N

stretch decay in 5 ps. The population oscillation in the C–C stretch data

occurs as follows. First we see C–C stretch excitation pumped by the

laser. This is actually a sign of combination band excitation (C N C C–C

stretch). Then the C–C stretch starts to be annihilated by the ¾5 ps upconversion and C–H stretch decay process. C–H stretch decay produces

C–H bending excitations, which subsequently repopulate the C–C stretch,

causing the second rise in the C–C stretch transient (47).

These results illustrate some of the very interesting phenomena that

can be observed with combination band pumping. The pump pulses create

a large population at 2253 and 917 cm 1 , which would ordinarily require

intense ultrashort pulses at 4.43 and 10.9 µm — hard to do with today’s

technology. With combination band pumping, the lifetime of the C N

stretch was reduced from its normal value of 80 ps to about 5 ps because

C N stretches were annihilated by C–C stretches on the same molecule.

The C–C stretch population was caused to undergo an oscillation. These

new phenomena suggest some of the complicated behavior that might result

when a chemical reaction releases enough chemical energy to excite several

different vibrations on the same molecule.

G. Spectral Evolution in Associated Liquids



When a vibrational transition is inhomogeneously broadened, optical lineshape studies provide no dynamical information (78). A variety of nonlinear

and coherent techniques, collectively called line-narrowing techniques, have

been developed to study the dynamics underneath an inhomogeneously

broadened transition (78). These include hole burning, fluorescence linenarrowing, photon and vibrational echoes, etc. The IR-Raman experiment

sees the excited vibrational population during the probe pulse, so it is

closely analogous to the fluorescence line-narrowing (FLN) technique with

time resolution (85). In time-resolved FLN, a narrow-band laser is used

to excite a selected isochromatic packet of an inhomogeneously broadened transition. Fluorescent emission from the excited isochromat is time

resolved and spectrally dispersed. The emission is at first narrower than the

inhomogeneous width, but it may broaden or otherwise evolve with time

due to the system’s dynamics (85).

Neat liquid methanol is an associated liquid characterized by an

extended hydrogen bonding network (86,87). Much of the width of the

broad O–H stretching transition is due to a distribution of hydrogen-bonded



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environments. There is a direct inverse correlation between the strength of

the hydrogen bond and the O–H stretching frequency: the lowest frequency

O–H stretch is associated with the strongest hydrogen bond and vice

versa (86,87). Pumping the O–H stretch of associated alcohol oligomers

is known to result in a vibrational predissociation process which breaks

the hydrogen bond (88–91), so the transition from D 1 ! 0 is accompanied by hydrogen bond cleavage. Vibrational predissociation in associated

alcohols reduces the vibrational lifetime from tens or more picoseconds to

¾1 ps (88–92).

Figure 22 shows some data on methanol pumped in the O–H

stretching region by a 35 cm 1 wide pulse at 3400 cm 1 . When the pump

and probe pulses are time coincident, a coherent artifact is observed at an

anti-Stokes shift of 3400 cm 1 . By about 2 ps this artifact has vanished



Figure 22 O–H stretching region of neat methanol with 3400 cm 1 pumping.

The peak at 3400 cm 1 is a coherent artifact. After the artifact has disappeared, the

spectrum of O–H stretching excitations decays and the peak of the OH stretching

spectrum shifts to higher energy. Methanol molecules with higher frequency O–H

stretching transitions and weaker hydrogen bonding decay more slowly. (From

L. K. Iwaki et al., unpublished.)



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