Molecule vibrational relaxation

However, several items should make us continue to be wary. Most Tis for neutral small-molecule vibrational relaxations are not ultrafast events, nor, for that matter, do they involve vibrational frequencies remotely close to the few hundred cm 1 bands of typical liquids (5). More typical are the 940 ps it takes to relax the 3265 cm-1 C-H stretch in HCN (5) and the 4.4 ns required to relax the 2850 cm-1 HC1 vibration (68) when either one of these hydrides is dissolved in CCI4. Even slower relaxations are well known the 3 ms relaxation times for 02 s 1556 cm-1 vibration in liquid oxygen, for example, (69) has been the subject of much recent discussion (70-72). 

Tabor M, Levine R D, Ben-Shaul A and Steinfeld J I 1979 Microscopic and macroscopic analysis of non-linear master equations vibrational relaxation of diatomic molecules Mol. Phys. 37 141-58... 

We now discuss the lifetime of an excited electronic state of a molecule. To simplify the discussion we will consider a molecule in a high-pressure gas or in solution where vibrational relaxation occurs rapidly, we will assume that the molecule is in the lowest vibrational level of the upper electronic state, level uO, and we will fiirther assume that we need only consider the zero-order tenn of equation (BE 1.7). A number of radiative transitions are possible, ending on the various vibrational levels a of the lower state, usually the ground state. The total rate constant for radiative decay, which we will call, is the sum of the rate constants,... 

In rare gas crystals [77] and liquids [78], diatomic molecule vibrational and vibronic relaxation have been studied. In crystals, VER occurs by multiphonon emission. Everything else held constant, the VER rate should decrease exponentially with the number of emitted phonons (exponential gap law) [79, 80] The number of emitted phonons scales as, and should be close to, the ratio O/mQ, where is the Debye frequency. A possible complication is the perturbation of the local phonon density of states by the diatomic molecule guest [77]. 

Elarris C B, Smith D E and Russell D J 1990 Vibrational relaxation of diatomic molecules in liquids Chem. Rev. 90 481-8... 

Energy level diagram for a molecule showing pathways for deactivation of an excited state vr Is vibrational relaxation Ic Is Internal conversion ec Is external conversion, and Isc Is Intersystem crossing. The lowest vibrational energy level for each electronic state Is Indicated by the thicker line. 

Another form of radiationless relaxation is internal conversion, in which a molecule in the ground vibrational level of an excited electronic state passes directly into a high vibrational energy level of a lower energy electronic state of the same spin state. By a combination of internal conversions and vibrational relaxations, a molecule in an excited electronic state may return to the ground electronic state without emitting a photon. A related form of radiationless relaxation is external conversion in which excess energy is transferred to the solvent or another component in the sample matrix. 

Fast concentration and sample injection are considered with the use of a theory of vibrational relaxation. A possibility to reduce a detection limit for trinitrotoluene to 10 g/cnf in less than 1 min is shown. Such a detection limit can by obtained using selective ionization combined with ion drift spectrometry. The time of detection in this case is 1- 3 s. A detection technique based on fluorescent reinforcing polymers, when the target molecules strongly quench fluorescence, holds much promise for developing fast detectors. 

Fig. 11. (a) Diagram of energy levels for a polyatomic molecule. Optical transition occurs from the ground state Ag to the excited electronic state Ai. Aj, are the vibrational sublevels of the optically forbidden electronic state A2. Arrows indicate vibrational relaxation (VR) in the states Ai and Aj, and radiationless transition (RLT). (b) Crossing of the terms Ai and Aj. Reorganization energy E, is indicated. 

When the characteristic time of vibrational relaxation is much shorter than tr, the rate constant is independent of Zy. For molecules consisting of not too many atoms, the inequality (2.58) is not fulfilled. Moreover, Zy may even become larger than tr. This situation is beyond our present consideration. The total set of resonant sublevels partaking in RLT consists of a small number of active acceptor modes with nonzero matrix elements (2.56) and many inactive modes with Vif = 0. The latter play the role of reservoir and insure the resonance = f. 

In [162] experiments on methane provided a linear pressure dependence of the contour width. This made it possible to find the dephasing cross-section and to discriminate between contributions of rotational and vibrational relaxation to the contour width. This was done under the above-mentioned simplifying assumption that they are additive. (Let us note that processing of experimental data on linear molecules was always performed under this assumption.) The points found by this method are shown in Fig. 3.15, curves (4) and (6). 

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... 

More recently the application of sub-picosecond, time-resolved pump-probe methods revealed the timescale for vibrational relaxation of a diatomic molecule at a metal surface directly. See for example Refs. 19-21. In comparison to vibrational relaxation on NaCl salts,22 which occurs on the millisecond timescale, another relaxation mechanism is clearly at play. Theory of vibrational relaxation based on excitation of electron-hole pairs gave agreement with observed ps timescales for CO on copper.23... 

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. 

Just as above, we can derive expressions for any fluorescence lifetime for any number of pathways. In this chapter we limit our discussion to cases where the excited molecules have relaxed to their lowest excited-state vibrational level by internal conversion (ic) before pursuing any other de-excitation pathway (see the Perrin-Jablonski diagram in Fig. 1.4). This means we do not consider coherent effects whereby the molecule decays, or transfers energy, from a higher excited state, or from a non-Boltzmann distribution of vibrational levels, before coming to steady-state equilibrium in its ground electronic state (see Section 1.2.2). Internal conversion only takes a few picoseconds, or less [82-84, 106]. In the case of incoherent decay, the method of excitation does not play a role in the decay by any of the pathways from the excited state the excitation scheme is only peculiar to the method we choose to measure the fluorescence (Sections 1.7-1.11). 

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