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Dynamic Rotational Spectroscopy
FTMW-Detected IR Spectroscopy
Broadband FTMW Spectrometer

Dynamic Rotational Spectroscopy (DRS)

We have named the technique we use to study highly vibrationally excited molecules “dynamic rotational spectroscopy” (DRS) because of its analogy to dynamic NMR experiments. These methods combine laser spectroscopy with state-of-the-art rotational spectroscopic techniques. In dynamic NMR, the exchange, or isomerization, rate is reflected in the overall lineshape of the spectrum. Dynamic NMR studies as a function of temperature reveal well-known coalescence phenomenon as the exchange rate competes with the frequency separation of the transitions of interest. Similarly, lineshape analysis of the DRS spectrum can extract the isomerization rates of isolated gas phase molecules. This analysis provides a clear picture of the timescale for energy flow into and out of the reaction coordinate (at least for isomerization reactions). The advantage of the DRS technique is that the timescales probed are significantly shorter than those extracted from dynamic NMR experiments. Furthermore, the rotational techniques we are developing for DRS allow the development of true 2-D rotational spectroscopic techniques analogous to the powerful 2-D NMR methods already commonplace in many laboratories around the world.
It is well documented that when gas-phase molecules are excited to high-energy regions of the potential surface, interesting dynamical effects such as intramolecular vibrational energy redistribution (IVR), isomerization, and unimolecular dissociation become prevalent. Under these conditions, the concept of a well-defined molecular geometry breaks down. As nuclei begin to move on the time scale of molecular rotation, the moments of inertia become time-dependant quantities. As a consequence, the rotational spectrum is no longer precisely defined as it is in pure rotational spectroscopy, but covers a frequency range that is determined by the nuclear motion.

 

Figure 1

Figure 1 compares the ground state J=2>1 rotational transitions for the cis and skew isomer of pent-1-en-4-yne, a molecule we have recently studied, with the vibrationally excited spectrum at 3330 cm-1, prepared by infrared excitation of the acetylenic C-H stretch. Pentenyne consists of two conformational isomers (cis and skew), both of which are observed in a free-jet expansion. These isomers can undergo isomerization following excitation of the acetylenic C-H stretch fundamental. Figure 1 clearly shows how the nuclear dynamics affect the appearance of the rotational spectrum. When the nuclear excursions induced by IVR compete with the time-scale of overall rotation, the moments-of-inertia become time-dependant quantities. In the case of pentenyne, where excitation above the barrier to isomerization occurs, the spectrum represents an “average” rotational constant that reflects the nuclear dynamics related to the isomerization process. The lower spectrum was taken after exciting the cis isomer with the IR laser, while the upper spectrum was measured after exciting the skew isomer with the IR laser. It is clear that the spectrum exhibits the same overall lineshape independent of the starting geometry.

 

Figure 2
The underlying dynamical information that we are interested in observing is embedded in the overall lineshape of the rotational spectrum. If the molecular dynamics are slow on the time scale of molecular rotation then the resulting spectrum will reflect the frequency distribution of the coupled normal-mode vibrational states. When the nuclear dynamics begin to compete with the time scale of overall rotation, the rotational spectrum will reflect the vibrational dependence of the rotational constants. If the dynamics become fast enough, the rotational spectrum will undergo motional (IVR) and exchange narrowing (isomerization) phenomena analogous to those found in NMR spectroscopy. Figure 2 explicitly shows these principles for the molecule pentenyne. The red traces represent the analytical lineshape calculated by a three-state Bloch model modified for chemical exchange. When the isomerization is slow compared to the frequency separation of the conformers (upper trace), two distinct peaks are observed which correspond to the cis and skew structures of the molecule. As the isomerization rate increases (middle traces), the rotational spectrum undergoes the coalescence phenomenon analogous to dynamic NMR measurements. As the isomerization rate increases further, the rotational spectrum undergoes motional narrowing (bottom trace). An important feature of the DRS technique is that fast dynamical processes lead to narrow spectra. The trace labelled 20 ps compares the “best-fit” analytic lineshape to the experimentally measured spectrum, corresponding to an isomerization lifetime of 20 psec. Such data demonstrates the time-scales that can be probed by the DRS technique. It should be noted that the RRKM prediction for this isomerization lifetime is 0.5 psec, substantially less than the measured value.