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B. Pseudo-vibrational Cascade in Nitromethane

B. Pseudo-vibrational Cascade in Nitromethane

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Ultrafast IR-Raman Spectroscopy



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vibrational excitation continously moving to lower energy, it appeared as

if a vibrational cascade occurred after C–H stretch excitation.

With the Ti:sapphire system, it became possible to see all relevant

VER processes in NM 48. Some representative data are shown in Fig. 14,

where the pumped 3000 cm 1 C–H stretch decays with a 2.6 ps time

constant. C–H stretch excitation is also associated with excitation in the first

overtone of the antisymmetrical C–H bend and the antisymmetrical NO2

stretch. As the C–H stretch decays, energy builds up with a 2.6 ps time

constant in the symmetrical C–H bending and NO2 stretching vibrations at

¾1400 cm 1 , as shown in Fig. 14a. These daughter vibrations decay with

a 15 ps time constant. Looking to lower energy vibrations such as the C–H



Figure 14 IR-Raman data from neat nitromethane (NM), (a) C–H stretch pumped

by the laser decays with 2.6 ps time constant. C–H bending and NO2 stretching

vibrations at ¾1500 cm 1 build up in 2.6 ps and decay in 15 ps. (b) All the lower

frequency vibrations Ä918 cm 1 have a two-part build-up (2.6 and 15 ps) and

decay time constants in the 30–50 ps time range. (From Ref. 96.)



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rock 1100 cm 1 , the C–N stretch 918 cm 1 , and NO2 symmetrical bend

and rock (657 and 480 cm 1 ; omitted for clarity), as seen in Fig. 14b, there

is a two-stage build-up. The first stage occurs with the 2.6 ps decay of the

C–H stretch and the second with the 15 ps decay of the C–H bend and NO2

stretch. These lower energy vibrations subsequently decay with lifetimes in

the 30–50 ps range. A 2.6 ps rise is seen in every vibration of NM other

than the pumped C–H stretch (48).

A level diagram for NM (48) in Fig. 15 provides an overview of

VER and VC in this system. VC occurs in three stages. First the C–H

stretch decay, a fast IVR process, populates every other vibration. Then

the intermediate vibrations decay in 15 ps by populating all lower energy

vibrations. Finally, the longest-lived lower energy vibrations decay into



Figure 15 Energy level diagram showing the three stages of vibrational energy

relaxation of nitromethane (NM) after C–H stretch excitation. The C–H stretch

fundamental and the first overtones of antisymmetrical C–H bend and NO2 stretch

are pumped. In stage 1, this energy is redistributed among all other vibrations with

a 2.6 ps time constant. The population increase in the lowest vibration NO2 is

twice as great as in the others. In stage 2, the intermediate energy vibrations decay

by exciting the lower energy vibrations with a 15 ps time constant. In stage 3, the

lower energy vibrations, which build up in the first two stages, decay in ¾100 ps

by exciting the bath. (From Ref. 48.)



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phonons. It was easy to mistake this complicated VC process for a vibrational cascade because in NM, the vibrational lifetimes increase as the

vibrational frequency decreases. Thus, after C–H stretch excitation, the

highest energy vibrations vanish first, the intermediate vibrations vanish

next, and the lowest energy vibrations vanish last. But neither of the first

two processes, which cause the two-stage build-up in the lower vibrations,

would occur in a true vibrational cascade.

C. Dynamics of Doorway Vibrations



Doorway vibration decay is particularly interesting because it is the one

situation where polyatomic molecule VER looks just like diatomic molecule

VER. The doorway vibrations of polyatomic molecules decay by exactly

the same multiphonon mechanism as the VER of a diatomic molecule.

Diatomic molecules have been extensively studied (7). One prediction for

diatomic molecules is an exponential energy-gap law (2). As the vibrational

frequency is increased, with everything else held constant, the number of

emitted phonons increases (the order of the multiphonon process increases)

and the VER rate should decrease exponentially with increasing vibrational

frequency.

Representative data for the doorway vibrations of ACN (C–C N

bend; 379 cm 1 ), NM (NO2 rock; 480 cm 1 ), and benzene (ring deformation; 606 cm 1 ) are shown in Fig. 16. It would be preferable to pump the

doorway vibration directly, but suitably powerful ultrashort pulse sources

are not yet available in the needed range (here 16–26 µm). We have been

able to understand the behavior of doorway vibrations by watching energy

run in and out of these vibrations after C–H stretch pumping; however,

this indirect method of excitation complicates the problem somewhat.

The doorway vibration data in Fig. 16 at a glance shows how fast

VC occurs in each molecule. The end of the doorway vibration population

build-up denotes the end of the VC process. Fig. 16 shows that in ACN,

VC takes ¾250 ps. In NM VC takes ¾100 ps, and in benzene VC takes

¾150 ps.

The VER lifetime of the doorway vibration in ACN is quite short.

It was estimated to be <5 ps (46). This estimate was obtained by molecular thermometry. As discussed above, the occupation number of C–H

stretching excitations produced by the laser is 0.02. Since about one half

of the C–H stretch excitation energy ¾1500 cm 1 is transferred to the

doorway vibration at 379 cm 1 , about 4 quanta of doorway excitations

will be produced in the first ¾5 ps due to C–H stretch decay. If the

doorway vibration were long-lived (i.e., if T1 > 5 ps), then the doorway



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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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B. Pseudo-vibrational Cascade in Nitromethane

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