Excited vibrational levels

Osgood R M Jr, Sackett P B and Javan A 1974 Measurement of vibrational-vibrational exchange rates for excited vibrational levels (2 v 4) in hydrogen fluoride J. Chem. Phys. 60 1464-80... 

As in Section 5.2.4 on rotational spectra of asymmetric rotors, we do not treat this important group of molecules in any detail, so far as their rotational motion is concerned, because of the great complexity of their rotational energy levels. Nevertheless, however complex the stack associated with the v = 0 level, there is a very similar stack associated with each excited vibrational level. The selection mles for transitions between the rotational stacks of the vibrational levels are also complex but include... 

The ZEKE-PE process shown in Figure 9.50(c) can be modified as shown by changing the wavenumber Vj of the first laser to excite the molecule to an excited vibrational level of M. Then the Franck-Condon factors for the band system are modified. This can allow... 

Remarkably, the photoelectron spectrum provides more than just the energy of the transition state. As can be seen in Figure 5.5, the spectrum also contains peaks corresponding to the transition state in excited vibrational levels, where the activated vibrations are orthogonal to the reaction coordinate. Therefore, NIPES can even be used to carry out vibrational spectroscopy of reaction transition states. 

In contrast to classical overbarrier reactions, QMT can occur from the lowest vibrational quantum levels without thermal activation. Under these circumstances at the lowest temperatures, the degree of tunneling, and hence the reaction rate, is independent of temperature. At some point as the temperature is raised, higher vibrational levels become populated. As illustrated in Figure 10.1, the effective barrier is narrower for excited vibrational levels, and hence tunneling becomes more facile, leading to an increase in rate. Finally, as temperatures are raised further, classical reaction begins to compete, and usually dominates at room temperature (but, not always). 

Highly Excited Vibrational Levels A Prediagonalized Davidson Scheme. 

Description Coupled to a Block-Davidson Algorithm An Efficient Scheme to Calculate Highly Excited Vibrational Levels. 

Since the CO2 laser line corresponds to a transition between two excited vibrational levels, only those CO2 molecules can be excited by absorption of the laser line which are in the (OOl)-level, populated at 300 ° K with about 1 % of the total number of molecules. In spite of this low population density, the laser-excited fluorescence method is easily achieved because of the large exciting laser intensity. 

Several investigations concerned with the identification of these lines succeeded, for instance, in the case of H2O, in elucidating the rotational spectrum in excited vibrational states 356). Through comparison of wavelengths and intensities of many lines in H2O , H2 0 and DjO isotopic effects could be studied in these excited vibrational levels 357,358) Perturbations of rotational levels by Coriolis resonance which mixes different levels could be cleared up through the assignment and wavelength measurement of some DCN and HCN laser lines 359). 

Alternatively, the molecule could cross from S, into an excited vibrational level of T,. Such an event is known as intersystem crossing (ISC). After the radiationless vibrational relaxation R3, the molecule finds itself at the lowest vibrational level of T,. From here, the molecule might undergo a second intersystem crossing to S0, followed by the radiationless relaxation R4. All processes mentioned so far simply convert light into heat. 

Considering first the case where the population of excited vibrational levels is negligible, we have for the rotational frequencies... 

If the diatomic molecule has a low vibrational frequency, or if the gas is heated sufficiently, we will have substantial numbers of molecules in excited vibrational levels, and we will observe infrared absorption bands for which the initial vibrational level is not u = 0. Such bands are called hot bands. See Fig. 4.8. 

Now consider the case with appreciable population of excited vibrational levels. The set of molecules with vibrational quantum number v will have its own value of Bv and will give rise to its own pure-rotation spectrum. Thus each line in Fig. 4.5 will have a series of vibrational satellites. Bv is given by (4.75), where ae is small compared to Be, so that the vibrational satellites lie near the main line. These satellites are shown for the transition in Fig. 4.6. Note the rapid decrease in intensity... 

As previously mentioned, for most diatomic molecules at room temperature, the population of excited vibrational levels is negligible. We therefore first consider transitions for which the initial vibrational level is u = 0. The selection rules (4.108) allow the transitions v = 0- l, 0— 2,... 

Figure 3. Field-matter interactions for a pair of electronic states. The zero and first excited vibrational levels are shown for each state (A). The fields are resonant with the electronic transitions. A horizontal bar represents an eigenstate, and a solid (dashed) vertical arrow represents a single field-matter interaction on a ket (bra) state. (See Refs. 1 and 54 for more details.) A single field-matter interaction creates an electronic superposition (coherence) state (B) that decays by electronic dephasing. Two interactions with positive and negative frequencies create electronic populations (C) or vibrational coherences either in the excited (D) or in the ground ( ) electronic states. In the latter cases (D and E) the evolution of coherence is decoupled from electronic dephasing, and the coherences decay by the vibrational dephasing process.

Experimentally one can investigate resonances by various spectroscopic schemes, as indicated in Fig. 1 by direct overtone pumping [11] from the ground vibrational state, by vibrationally mediated photodissociation [12] using an excited vibrational level as an intermediate, or by stimulated emission pumping (SEP) [13-15] from an excited electronic state. In all cases it is possible to scan over a resonance and thereby determine its position j4s aHd its width hkU). A schematic illustration of an absorption or emission spectrum is depicted on the left-hand side of Fig. 1 all of the more or less sharp structures at energies above threshold are resonances. Figure 2 shows an overview SEP spectrum measured for DCO [16]. It consists of... 

Broida and Carrington58 used the 2144-A line of a cadmium discharge to excite selectively the thirteenth rotational level of the first excited vibrational level of the A2H + state. From the emission intensity and eq. (d), quenching efficiencies were computed (Table 3-3). The cadmium arc heated the reactants, the temperature sometimes reaching 550°K. For the computations, an average temperature of 400°K was used. The value found for k% is nearly three times as large as that obtained by Callear and Smith. This high value probably reflects the fact that corrections were not made for the reabsorption of emission. 

For transitions in absorption the Boltzmann distribution of molecules over the vibrational levels of the ground state implies that a majority of bands observed will emanate from the lowest, zero-point level transitions from higher levels will be weakened in proportion to the Boltzmann factor exp [ — Jiv/lcT], Hot bands arising from excited vibrational levels can be identified by studying the effect of temperature on the relative intensities. At ordinary temperatures the Boltzmann factor decreases approximately tenfold for each 500 cm-1 of vibrational... 

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