Ro-vibrational level

Tennyson, J. (1983), Atomdiat—A Program for Calculating Variationally Exact Ro-Vibrational Levels of Floppy Triatomics, Comput. Phys. Comm. 29, 307. 

Figure 3-4. Schematic of size and state selection of weakly bound complexes. Weak M-HX intermolecular coupling and the corresponding long predissociation lifetimes enable ro-vibrational levels of the complex to be isolated. Ultraviolet photons at sufficiently long wavelengths act on the excited (but not the unexcited) HX moieties.

The main problem with this equation is the description of the potential energy term (V). As we shall see, insertion of a restricted form of the potential allows one to express data on the ro-vibrational levels in terms of semi-empirical constants. If the Morse potential is used, the ro-vibrational energies are given by the expression... 

The temperature dependence of the observable is obtained by assuming a Boltzmann population of the ro-vibrational levels, so that... 

In this equation we have chosen to consider a near prolate symmetric top (like anthracene). The symbols J and Ka have their usual meanings as the rotational quantum numbers of such a molecule and refer in the equation to rotational levels in the manifold of the a> zero-order vibrational level. As for the other factors in Eq. (3.36), T is the rotational temperature of the sample, W(J, Ka, T) is a weighting factor for each ro-vibrational level a,J,Ka, and Iy(J,Ka,t) is the y-type fluorescence decay which arises from the coupling of a,J, Ka) with the same rotational levels of the other zero-order vibrational states. Iy(J, Ka, t) is just given by Iy(t) of Eq. (3.12). [Note that in deriving Eq. (3.36) we have neglected the possibility of any coherence effects arising from the coherent preparation of rotational levels within the same vibrational state. This possibility is the subject of Section III D 2.]... 

Two-level vibrational coupling The first case we consider is the simple and illustrative case of two coupled vibrational levels, a> and by. The situation is represented schematically in Fig. 37. Let us consider it first in a somewhat qualitative light. If a> and h> have different rotational constants, then the zero-order energy differences between the pairs of coupled ro-vibrational levels up the two rotational manifolds (Fig. 37) will depend on J, Ka and will be of the form... 

As previously discussed, if two or more excited eigenstates can combine in absorption with a common ground-state level, then these eigenstates can be excited so as to form a coherent superposition state. The superposition state, in turn, can give rise to quantum beat-modulated fluorescence decays. All this, of course, lies at the heart of the theory of vibrational coherence effects. However, it also implies that the same experimental conditions under which vibrational coherence effects are observed should allow for the observation of rotational coherence effects. That is, since more than one rotational level in the manifold of an excited vibronic state can combine in absorption with a single ground-state ro-vibrational level, then in a picosecond-resolved fluorescence experiment rotational quantum beats should obtain. 

For a standard molecule, meaning by this a system having positive Hessian eigenvalues only, or for a transition structure, the calculations of the stationary geometries and subsequent determination of ro-vibrational levels follow normal proce-... 

Flaud, J.-M., Camy-Peyret, C., Maillard, J.P Higher ro-vibrational levels of H2O deduced from high resolution oxygen-hydrogen flame spectra between 2800-6200 cm . Mol. Phys. 1976, 32, 499-521. 

FIGURE 3 (a) Simulated spectrum of an HF laser showing several discrete laser wavelengths, (b) The transitions between ro-vibrational levels are labeled according to spectroscopic notation. 

As mentioned further above, the absorption in the U V and visible part of the spectmm is associated with electronic transitions, whereas in the IR the transitions between ro-vibrational levels are responsible for the observed absorption. 

The selection rules for CARS and CSRS are the same as for standard, spontaneous Raman spectroscopy however, it has the advantage of a vastly increased intensity. Experimentally, CARS is realized by using one fixed-wavelength laser and then mning the second one into resonance with the ro-vibrational levels of the target molecule. 

The particularly useful feature of REMPl is that the resonance wavelength for the intermediate absorption step is normally different for transitions between the various rotational and vibrational quantum states. Therefore, using REMPl, each ro-vibrational level of a molecule can be ionized individually by varying the wavelength of the excitation laser. 

The most commonly used approach to ZEKE spectroscopy is to use a two-step excitation process through a weU-defined ro-vibrational level of an intermediate state, prepared by a pump laser that is tuned to the required frequency and then locked to it (see Chapter 9, Figure 9.2). In the discussion that follows we shall concentrate our attention on the second step. 

Spectroscopic Basics. The sodium dimer s first singlet electronic state A 17+ has been studied by different cw techniques using laser-induced fluorescence, optical-optical double resonance, and Fourier transform spectroscopy [319, 320, 330-332]. Ro-vibrational levels could be numbered and... 

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