A 3D Version of the Model and Its Application to Triatomic Molecules

In this section we apply the model presented in Section 3 to the XS of triatomic molecules such as O3, 2/ CO2. In line with Heller [5], Schinke, on pages 115-116 of his book [6], proposed a 2D version of the simple reflection model but without the curvature and quantum effects taken into account in Sections 2 and 3. For triatomic molecules the quantities corresponding to Vq/P and V / or r (see Formula (12)) defined in Section 2 and corresponding to t (see Formula (27)) defined 

Alternatively, Formulae (12 ), (27 ) or (29) can be used numerically to fit the ct(E)/E of triatomic molecules, even if the interpretation of the fitted parameters is not yet possible. The results presented below show that the numerical improvement obtained by using Formulae (12), (27) or (29) (all have 4 parameters and are able to describe the asymmetry of a a E)/E) is comparable with the improvement observed for CI2 (the Chi /DoF is reduced by typically up two orders of magnitude see Section 4). Here, it is essential to note that the reflection models are only able to describe the envelope of the XS, (corresponding to very short time evolution (f 10 fs (femtosecond)) of the wavepacket after the photon absorption) and not the vibronic structures which are specific to each molecule and correspond to some vibrational (and or vibronic) oscillations at a time scale of several hiuidred femtoseconds. 

This explains why, below, for each XS, the first step of the analysis is to smooth the XS in order to blur all the vibronic structures. The second step is to divide each smoothed XS by E in order to characterize the asymmetry of the a E)/E. 

As mentioned above, the interpretation of the asymmetry of a a E)/E for a triatomic molecule is much more difficult than for a diatomic molecule. However, the asymmetry is a relevant phenomenological parameter which characterizes the XS in addition to the centre, the width and the amplitude. The isotopic (isotopologue) dependence of these four parameters is of special interest when dealing with the photodissociation processes [9,15]. In fact, this aspect was our initial motivation when starting this study and will be treated in the future. Below, we characterize the XS asymmetry of three important molecules O3, SO2 and CO2. 

FIGURE 6.3 Fit of the ozone XS (cr(E)/ ) of Bogumil (2003) (Ref. [25]). The upper part shows the smoothed r( )/ and a fitted Gaussian (dashed). When fitted with Formula (29) the experimental and fitted curves overlap and cannot be discriminated, in the lower part, the difference between the exp. and fitted curves is shown. Note that this difference is, at most, 0.3% of the maximum amplitude while the max difference with the Gaussian (dashed curve of the upper part) reach 7%. The superimposed oscillating structure is due to the vibronic structure of the Exp. Abs. XS which has not been completely smoothed. 

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