Vibrational relaxation, energy dependence

The rate of internal conversion (IC), a radiationless transition between isoenergetic levels of different states of the same multiplicity, may be of the same order of magnitude or even faster than vibrational relaxation. It depends, however, on the energy separation AEqo between the zero-vibrational levels of the electronic states involved (energy gap law, see Section 5.2.1). Similar relations hold for intersystem crossing transitions between states of different multiplicity, which are slower by 4-8 orders of magnitude. 

Fig. 9. Incidence energy dependence of the vibrational state population distribution resulting when NO(u = 12) is scattered from LiF(OOl) at a surface temperature of (a) 480 K, and (b) 290 K. Relaxation of large amplitude vibrational motion to phonons is weak compared to what is possible on metals. Increased relaxation at the lowest incidence energies and surface temperatures are indicators of a trapping/desorption mechanism for vibrational energy transfer. Angular and rotational population distributions support this conclusion. Estimations of the residence times suggest that coupling to phonons is significant when residence times are only as long as ps. (See Ref. 58.)...

First, as the molecule on which the chromophore sits rotates, this projection will change. Second, the magnitude of the transition dipole may depend on bath coordinates, which in analogy with gas-phase spectroscopy is called a non-Condon effect For water, as we will see, this latter dependence is very important [13, 14]. In principle there are off-diagonal terms in the Hamiltonian in this truncated two-state Hilbert space, which depend on the bath coordinates and which lead to vibrational energy relaxation [4]. In practice it is usually too difficult to treat both the spectral diffusion and vibrational relaxation problems at the same time, and so one usually adds the effects of this relaxation phenomenologically, and the lifetime 7j can either be calculated separately or determined from experiment. Within this approach the line shape can be written as [92 94]... 

The loss of the B state population depends on both the dynamics of the vibrational relaxation and the strength of the coupling of the B state to the repulsive a/a states. In the simulations, the predissociation of the B state molecules is described with the help of the Landau-Zener theory. There, the coupling strength is given by the perturbation energy. Furthermore, the probability for predissociation also depends on the (classical) velocity v t) which relates this process to the vibrational relaxation dynamics of the B state. The theoretical model uses a friction coefficient a to describe the latter process. 

Nitric oxide exhibits a negative temperature coefficient for vibrational relaxation in self-collisions, below about 700° K. It has been suggested170 that this effect arises because the potential energy of the point of resonance, postulated by Nikitin, is strongly orientation dependent. (In this case the maximum depth of the potential minimum can be no greater than about 3 kcal. mole-1 which will not steepen the potential sufficiently to account for the observed relaxation rate, with l = 0.18 A.)... 

The possibility of deactivation of vibrationally excited molecules by spontaneous radiation is always present for infrared-active vibrational modes, but this is usually much slower than collisional deactivation and plays no significant role (this is obviously not the case for infrared gas lasers). CO is a particular exception in possessing an infrared-active vibration of high frequency (2144 cm-1). The probability of spontaneous emission depends on the cube of the frequency, so that the radiative life decreases as the third power of the frequency, and is, of course, independent of both pressure and temperature the collisional life, in contrast, increases exponentially with the frequency. Reference to the vibrational relaxation times given in Table 2, where CO has the highest vibrational frequency and shortest radiative lifetime of the polar molecules listed, shows that most vibrational relaxation times are much shorter than the 3 x 104 /isec radiative lifetime of CO. For CO itself radiative deactivation only becomes important at lower temperatures, where collisional deactivation is very slow indeed, and the specific heat contribution of vibrational energy is infinitesimal. Radiative processes do play an important role in reactions in the upper atmosphere, where collision rates are extremely slow. 

For the determination of product vibrational and rotational distributions, we must consider the time for vibrational or rotational relaxation by gas-phase collisions. This is not as strongly dependent on the nature of the products as it is for electronic quenching. Rotational relaxation is a much more efficient process than vibrational relaxation, requiring typically less than one hundred collisions to rotationally relax a molecule compared with several thousand collisions to bring about vibrational relaxation [76]. Thus, primary product vibrational energy distributions may be determined at pressures greater than 10-4 Torr, whilst much lower pressures are required to observe unrelaxed rotational state distributions. 

Coherent transport of vibrational energy is further limited by vibrational energy relaxation. Experiments on the amide I band of different peptides (NMA, apamin, scyllatoxin BPTI, and the cyclic pentapeptide) revealed a vibrational relaxation rate of approximately Ti = 1.2 ps, which is essentially independent of the particular peptide (30,53). A similar value has recently been reported for myoglobin at room temperature, with only a weak dependence of the relaxation rate on temperature down to cryogenic temperatures (140). In other words, vibrational relaxation of the amide I mode reflects an intrinsic property of the peptide group itself rather than a specific characteristic of the primary or secondary structural motifs of the... 

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