Overtone line-widths

Local-Mode Excitation In local-mode sampling an individual local mode such as a CH bond in benzene is excited.This type of trajectory calculation has been performed to determine the population of a local-mode state v) versus time, from which the absorption linewidth of the overtone state may be determined.Good agreement has been found with both experimental and quantum-mechanically calculated overtone line-widths for benzene and linear alkanes. 

Ro-vibrational transitions in molecules provide an enormous number of narrow absorption lines in the infrared region. By using overtones of these transitions a large number of visible and near visible absorption lines could be provided. However, the weakness of these lines require very sensitive spectroscopic techniques. An example is the NICE OHMS technique [58, 67] where a gas sample of C2HD contained in a high finesse cavity absorbs at the (+ 3Vj) overtone at a 1064 nm. In beat experiments between this system and a iodine-stabilized YAG-laser, stabilities of below lO in 800 s have been observed. Especially interesting, is the demonstration of how this technique could be combined with the selective cold-atom technique to obtain line widths as narrow as 20 kHz. 

The spectra in figure 4.16 show that a single atom substitution may have an enormous effect on the intramolecular dynamics, since there is a remarkable difference in the rotationally resolved spectra of the fundamental and first overtone of these two molecules. The line width of the silicon-substituted compound is significantly narrower than that of tert-butylacetylene in both the fundamental and first overtone. There is also a striking different behavior of the two molecules in going from fundamental to overtone excitation. Tert-butylacetylene shows a decreased IVR lifetime in the overtone, dropping by almost a factor of 2. In contrast, the silicon substituted compound shows exactly the opposite behavior since the lifetime in the fundamental is decreased by almost a factor of 2 compared to the overtone. 

Figure 7.25 Calculated and measured dissociation rates for the HOOH reaction. The open triangle is the upper limit of the rate inferred from a line widths measurement at the fifth overtone transition. The solid triangle is from a time resolved measurement (Scherer and Zewail, 1987). The solid lines are SACM calculated k(E, j) curves for various values of J. Taken with permission from Brouwer et al. (1987).

When Eq. (289) is substituted in Eq. (285), one finds a Lorentzian line shape where the half-width at half-maximum (HWHM) is t"1. Thus by assuming an exponential decay, as in Eq. (289), t can be obtained directly from either Eq. (282) or Eq. (290). However, (2(0)2(0) may be nonexponential, as opposed to exponential as assumed in Oxtoby s work, and, as shown later, may give rise to an overall subquadratic overtone dependence of the rate. 

Scanning the frequency of the dissociation laser and collecting the total OH fluorescence, while the state-selection and probe frequencies are kept fixed on specific transitions, produces a PHOFEX spectrum an example is displayed in the right-hand panel of Fig. 10. The lines correspond to specific resonance states with rotational quantum number J and projection quantum number if = 2 in vibrational state (6,0,0). If the individual lines are broader than the resolution of the laser system, one can determine the width from fitting the spectrum and thus determine the state-specific dissociation rate. If the true linewidth caused by dissociation is smaller than the resolution of the laser system, the rates can be extracted from time-resolved measurements. All three laser frequencies are fixed, and the OH probe laser used to detect a particular state of OH is delayed with respect to the dissociation laser. In this way one can monitor the appearance of the OH products as function of the delay time, in the same way as described above for N02- In contrast to NO2, however, the rate is a state-specific rate rather than an average rate, because of the high selectivity of the overtone... 

The sensitivity of this technique is demonstrated by Fig. 1.9, which shows an overtone absorption line of the water molecule H2O, recorded with an unmodulated laser and with this modulation technique. The signal-to-noise ratio of the absorption measured with phase modulation is about 2 orders of magnitude higher than without modulation. The sensitivity reaches a maximum if the modulation frequency is chosen to be equal to the width of the absorption line. 

To determine the rate constant e), the spectral width Av of particular lines of the overtone excitation spectrum of the H2O2 was measured. The lifetime of the excited molecule x was determined by the uncertainty x = 1/Av. The microscopic rate constant was determined from the relation x = l/ (e). In principle, this method for determination of k(E) should be used with care because not only dissociation but also non-uniform broadening can contribute to the measured spectral width Av. However, in this example, the measured lifetime is x = 3.5 ps and, hence, k e) = 2.9-10 s agrees with the calculation using the statistical theory. 

In the unstable region, the symmetric-stretch overtones are broadened bands (i.e. a cluster of lines) with the width given by... 

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