Spectrum of vibrationally excited

The V (OCO) ion has a structured electronic photodissociation spectrum, which allows us to measure its vibrational spectrum using vibrationally mediated photodissociation (VMP). This technique requires that the absorption spectrum (or, in our case, the photodissociation spectrum) of vibrationally excited molecules differ from that of vibrationally unexcited molecules. The photodissociation spectrum of V (OCO) has an extended progression in the V OCO stretch, indicating that the ground and excited electronic states have different equilibrium V "—OCO bond lengths. Thus, the OCO antisymmetric stretch frequency Vj should be different in the two states, and the... 

The microwave spectrum of vibrationally excited COFj has been obtained [1435] the rotational constants and inertial defects obtained were used to resolve the ambiguity in the absoiute assignment of its r 3 and r 3 bending modes vide infra). 

Mollaaghababa, R. Gottlieb, C.A. Vrtilek, J.M. Thaddeus, P. Millimeter-wave spectrum of vibrationally excited cyclopropenylidene, C-C3H2. J- Chem. Phys. 1993, 99, 890-896. 

Figure 13. Photodissociation spectrum of V (OCO), with assignments. Insets and their assignments show the photodissociation spectrum of molecules excited with one quanmm of OCO antisymmetric stretch, v" at 2390.9 cm . These intensities have been multiplied by a factor of 2. The shifts show that Vj (excited state) lies 24 cm below v ( (ground state), and that there is a small amount of vibrational cross-anharmonicity. The box shows a hot band at 15,591 cm that is shifted by 210 cm from the origin peak and is assigned to the V" -OCO stretch in the ground state.

In particular, Shapiro and others calculated state-to-state photodissociation cross sections from vibrationally excited states of HCN and DCN [58], N2O [59], and O3 [60]. Eor instance, the detailed product-vibrational state distributions and absorption spectra of HCN(DCN) were compared [58]. These results were obtained employing a half-collision approximation, where the photodissociation could be depicted as consisting of two steps, that is, absorption of the photon and the dissociation, as well as an exact numerical integration of the coupled equations. In particular, it was predicted that large isotope effects can be obtained in certain regions of the spectrum by photodissociation of vibrationally excited molecules. 

Figure 2.6 CHjNHj vibrational spectra (a) H action spectrum obtained via 243.135 nm dissociation of vibrationally excited molecules and (b) ionization-loss stimulated Raman spectroscopy exhibiting the depletion of parent molecule ionization signal due to vibrational preexcitation. Reproduced with permission from Ref. [86]. Copyright (2009) AlP Publishing LLC.

In this section we will consider the case of a multi-level electronic system in interaction with a bosonic bath [288,289], We will use unitary transformation techniques to deal with the problem, but will only focus on the low-bias transport, so that strong non-equilibrium effects can be disregarded. Our interest is to explore how the qualitative low-energy properties of the electronic system are modified by the interaction with the bosonic bath. We will see that the existence of a continuum of vibrational excitations (up to some cut-off frequency) dramatically changes the analytic properties of the electronic Green function and may lead in some limiting cases to a qualitative modification of the low-energy electronic spectrum. As a result, the I-V characteristics at low bias may display metallic behavior (finite current) even if the isolated electronic system does exhibit a band gap. The model to be discussed below... 

This ultrasimple classical theory is, of course, too crude for practical applications, especially for highly excited states of the parent molecule. Its usefulness gradually diminishes as the degree of vibrational excitation increases, i.e., as the initial wavefunction becomes more and more oscillatory. If both wavefunctions oscillate rapidly, they can be approximated by semiclassical WKB wavefunctions and the radial overlap integral of the bound and the continuum wavefunctions can subsequently be evaluated by the method of steepest descent. This leads to analytical expressions for the spectrum (Child 1980, 1991 ch.5 Tellinghuisen 1985, 1987). In particular, relation (13.2), which relates the coordinate R to the energy E, is replaced by... 

A relatively simple spectroscopic model of O3 absorption in the middle ultraviolet has been proposed (Adler-Golden et al., 1982). This model assumes that the internal energy of an O3 molecule adds fully to that of the absorbed ultraviolet photon and that the quantum yield of O ( Eh) varies smoothly from zero at some threshold energy (calculated as being 32900 cm ) to unity 600 cm above this threshold. The model, which is quite successful in rationalizing the observed Hartley band spectrum for vibrationally excited O3, accurately reflects the experimental temperature dependence of the ( Dz) yield at 313 nm and also predicts a dependence of oCdj) ) upon wavelength in the region above 304 nm that is quite similar to that observed in a previous experimental study... 

Figure 1. SEP spectrum of C2H2 at about 26,500 cm 1 of vibrational excitation in the ground electronic state. [Adapted from J. P. Pique, Y. Chen, R. W. Field and J. L. Kinsey, Phys. Rev. Lett. 58,475 (1987).] (a) Low-resolution ( 0.3 cm"1) spectrum (b) high-resolution ( 0.05 cm"1) spectrum Each feature in (a) is resolved into a series of lines. The overall envelope variation in intensity in (b) is the clump structure seen in (a).

Figure 17 The Raman excitation spectrum for a transition to the B electronic state of iodo-benzene with one quantum of vibrational excitation in the v, vibrational mode. (Solid line) computed in the harmonic approximation for the motion in the B state. (Dotted line) The maximal entropy fit of this spectrum obtained using Eq. (97). This fit is used to determine the cross-correlation function as shown in Fig. 18. (From Ref. (102).)...

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