Vibrational excited states

McCoy A B and Siebert E L 1996 Canonical Van VIeck pertubation theory and its applications to studies of highly vibrationally excited states of polyatomic molecules Dynemics of Moiecuies end Chemicei Reections ed R E Wyatt and J Z H Zhang (New York Dekker) p 151... 

The vibrationally excited states of H2-OH have enough energy to decay either to H2 and OH or to cross the barrier to reaction. Time-dependent experiments have been carried out to monitor the non-reactive decay (to H2 + OH), which occurs on a timescale of microseconds for H2-OH but nanoseconds for D2-OH [52, 58]. Analogous experiments have also been carried out for complexes in which the H2 vibration is excited [59]. The reactive decay products have not yet been detected, but it is probably only a matter of time. Even if it proves impossible for H2-OH, there are plenty of other pre-reactive complexes that can be produced. There is little doubt that the spectroscopy of such species will be a rich source of infonnation on reactive potential energy surfaces in the fairly near future. 

The lifetime of an analyte in the excited state. A, is short typically 10 -10 s for electronic excited states and 10 s for vibrational excited states. Relaxation occurs through collisions between A and other species in the sample, by photochemical reactions, and by the emission of photons. In the first process, which is called vibrational deactivation, or nonradiative relaxation, the excess energy is released as heat thus... 

In addition there is the possibility of combination tones involving transitions to vibrationally excited states in which more than one normal vibration is excited. Fundamental, overtone and combination tone transitions involving two vibrations and Vj are illustrated in Figure 6.11. 

For most purposes only the Stokes-shifted Raman spectmm, which results from molecules in the ground electronic and vibrational states being excited, is measured and reported. Anti-Stokes spectra arise from molecules in vibrational excited states returning to the ground state. The relative intensities of the Stokes and anti-Stokes bands are proportional to the relative populations of the ground and excited vibrational states. These proportions are temperature-dependent and foUow a Boltzmann distribution. At room temperature, the anti-Stokes Stokes intensity ratio decreases by a factor of 10 with each 480 cm from the exciting frequency. Because of the weakness of the anti-Stokes spectmm (except at low frequency shift), the most important use of this spectmm is for optical temperature measurement (qv) using the Boltzmann distribution function. 

Color from Vibrations and Rotations. Vibrational excitation states occur in H2O molecules in water. The three fundamental frequencies occur in the infrared at more than 2500 nm, but combinations and overtones of these extend with very weak intensities just into the red end of the visible and cause the blue color of water and of ice when viewed in bulk (any green component present derives from algae, etc). This phenomenon is normally seen only in H2O, where the lightest atom H and very strong hydrogen bonding combine to move the fundamental vibrations closer to the visible than in any other material. 

Reactions of Complex Ions. For reactions of systems containing H2 or HD the failure to observe an E 1/2 dependence of reaction cross-section was probably the result of the failure to include all products of ion-molecule reaction in the calculation of the experimental cross-sections. For reactions of complex molecule ions where electron impact ionization probably produces a distribution of vibrationally excited states, kinetic energy transfer can readily open channels which yield products obscured by primary ionization processes. In such cases an E n dependence of cross-section may be determined frequently n = 1 has been found. 

Figure 4-9. Transitions occur from ground and vibrationally excited states of the ground electronic state to various vibrational components of the electronically excited state.

The superscript v indicates vibrationally excited state excited states higher than Si or T are omitted. 

The semiclassical theory introduced above can be extended to low vibrationally excited states [32]. The multidimensionality effects are more crucial in this case. As was found before [62, 70], the energy splitting may oscillate or even decrease against vibrational excitation. This cannot be explained at all by the effective ID theory. 

Next we discuss the effect of deuteratlon on low frequency modes Involving the protons> Because of the anharmonlc variation of the energy as a function of tilt angle a (Fig. 4b), the hindered rotations of H2O and D2O turn out to be qualitatively different. The first vibrational excited state of H2O Is less localized than that of D2O, because of Its larger effective mass. The oscillation frequency of the mode decreases by a factor 1.19 and the matrix elements by a factor 1.51 upon deuteratlon. Therefore, the harmonic approximation, which yields an Isotopic factor 1.4 for both the frequency and the Intensity, Is quite Inappropriate for this mode. 

The next step is to estimate how long a molecule can stay in its vibrational excited state during a single electric pulse. A conventional electronic circuit carmot generate a short pulse like 10 ps, so that the use of electric pulses longer than 100 ps is more... 

Figure 6.1 Nonlinear optical responses, (a) Second-order SF generation, the transition probability is enhanced when the IR light is resonant to the transition from the ground state g to a vibrational excited state V. CO is the angular frequency of the vibration, (b) Third-order coherent Raman scheme, the vibrational coherence is generated via impulsive stimulated...

Perhaps the first evidence for the breakdown of the Born-Oppenheimer approximation for adsorbates at metal surfaces arose from the study of infrared reflection-absorption line-widths of adsorbates on metals, a topic that has been reviewed by Hoffmann.17 In the simplest case, one considers the mechanism of vibrational relaxation operative for a diatomic molecule that has absorbed an infrared photon exciting it to its first vibrationally-excited state. Although the interpretation of spectral line-broadening experiments is always fraught with problems associated with distinguishing... 

As with solution experiments, flash photolysis in the gas phase has produced evidence for the existence of intermediates but no information about their structure. In principle gas phase IR spectra can provide much more information, although the small rotational B value of gaseous carbonyls and low lying vibrational excited states preclude the observation of rotational fine structure. As described in Section II, time-resolved IR experiments in the gas phase do not suffer from problems of solvent absorption, but they do require very fast detection systems. This requirement arises because gas-kinetic reactions in the gas phase are usually one... 

The photolysis of Cr(CO)6 also provides evidence for the formation of both CO (69) and Cr(CO) species (91,92) in vibrationally excited states. Since CO lasers operate on vibrational transitions of CO, they are particularly sensitive method for detecting vibrationally excited CO. It is still not clear in detail how these vibrationally excited molecules are formed during uv photolysis. For Cr(CO)6 (69,92), more CO appeared to be formed in the ground state than in the first vibrational excited state, and excited CO continued to be formed after the end of the uv laser pulse. Similarly, Fe(CO) and Cr(CO) fragments were initially generated with IR absorptions that were shifted to long wavelength (75,91). This shift was apparently due to rotationally-vibrationally excited molecules which relaxed at a rate dependent on the pressure of added buffer gas. 

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